Nonlinear dynamical systems for theory and research in ergonomics.

PubMed

Guastello, Stephen J

2017-02-01

Nonlinear dynamical systems (NDS) theory offers new constructs, methods and explanations for phenomena that have in turn produced new paradigms of thinking within several disciplines of the behavioural sciences. This article explores the recent developments of NDS as a paradigm in ergonomics. The exposition includes its basic axioms, the primary constructs from elementary dynamics and so-called complexity theory, an overview of its methods, and growing areas of application within ergonomics. The applications considered here include: psychophysics, iconic displays, control theory, cognitive workload and fatigue, occupational accidents, resilience of systems, team coordination and synchronisation in systems. Although these applications make use of different subsets of NDS constructs, several of them share the general principles of the complex adaptive system. Practitioner Summary: Nonlinear dynamical systems theory reframes problems in ergonomics that involve complex systems as they change over time. The leading applications to date include psychophysics, control theory, cognitive workload and fatigue, biomechanics, occupational accidents, resilience of systems, team coordination and synchronisation of system components.

Fault Identification Based on Nlpca in Complex Electrical Engineering

NASA Astrophysics Data System (ADS)

Zhang, Yagang; Wang, Zengping; Zhang, Jinfang

2012-07-01

The fault is inevitable in any complex systems engineering. Electric power system is essentially a typically nonlinear system. It is also one of the most complex artificial systems in this world. In our researches, based on the real-time measurements of phasor measurement unit, under the influence of white Gaussian noise (suppose the standard deviation is 0.01, and the mean error is 0), we used mainly nonlinear principal component analysis theory (NLPCA) to resolve fault identification problem in complex electrical engineering. The simulation results show that the fault in complex electrical engineering is usually corresponding to the variable with the maximum absolute value coefficient in the first principal component. These researches will have significant theoretical value and engineering practical significance.

Using emergent order to shape a space society

NASA Technical Reports Server (NTRS)

Graps, Amara L.

1993-01-01

A fast-growing movement in the scientific community is reshaping the way that we view the world around us. The short-hand name for this movement is 'chaos'. Chaos is a science of the global, nonlinear nature of systems. The center of this set of ideas is that simple, deterministic systems can breed complexity. Systems as complex as the human body, ecology, the mind or a human society. While it is true that simple laws can breed complexity, the other side is that complex systems can breed order. It is the latter that I will focus on in this paper. In the past, nonlinear was nearly synonymous with unsolvable because no general analytic solutions exist. Mathematically, an essential difference exists between linear and nonlinear systems. For linear systems, you just break up the complicated system into many simple pieces and patch together the separated solutions for each piece to form a solution to the full problem. In contrast, solutions to a nonlinear system cannot be added to form a new solution. The system must be treated in its full complexity. While it is true that no general analytical approach exists for reducing a complex system such as a society, it can be modeled. The technical involves a mathematical construct called phase space. In this space stable structures can appear which I use as analogies for the stable structures that appear in a complex system such as an ecology, the mind or a society. The common denominator in all of these systems is that they rely on a process called feedback loops. Feedback loops link the microscopic (individual) parts to the macroscopic (global) parts. The key, then, in shaping a space society, is in effectively using feedback loops. This paper will illustrate how one can model a space society by using methods that chaoticists have developed over the last hundred years. And I will show that common threads exist in the modeling of biological, economical, philosophical, and sociological systems.

Analog nonlinear MIMO receiver for optical mode division multiplexing transmission.

PubMed

Spalvieri, Arnaldo; Boffi, Pierpaolo; Pecorino, Simone; Barletta, Luca; Magarini, Maurizio; Gatto, Alberto; Martelli, Paolo; Martinelli, Mario

2013-10-21

The complexity and the power consumption of digital signal processing are crucial issues in optical transmission systems based on mode division multiplexing and coherent multiple-input multiple-output (MIMO) processing at the receiver. In this paper the inherent characteristic of spatial separation between fiber modes is exploited, getting a MIMO system where joint demultiplexing and detection is based on spatially separated photodetectors. After photodetection, one has a MIMO system with nonlinear crosstalk between modes. The paper shows that the nonlinear crosstalk can be dealt with by a low-complexity and non-adaptive detection scheme, at least in the cases presented in the paper.

Solutions of the cylindrical nonlinear Maxwell equations.

PubMed

Xiong, Hao; Si, Liu-Gang; Ding, Chunling; Lü, Xin-You; Yang, Xiaoxue; Wu, Ying

2012-01-01

Cylindrical nonlinear optics is a burgeoning research area which describes cylindrical electromagnetic wave propagation in nonlinear media. Finding new exact solutions for different types of nonlinearity and inhomogeneity to describe cylindrical electromagnetic wave propagation is of great interest and meaningful for theory and application. This paper gives exact solutions for the cylindrical nonlinear Maxwell equations and presents an interesting connection between the exact solutions for different cylindrical nonlinear Maxwell equations. We also provide some examples and discussion to show the application of the results we obtained. Our results provide the basis for solving complex systems of nonlinearity and inhomogeneity with simple systems.

An Integrated Crustal Dynamics Simulator

NASA Astrophysics Data System (ADS)

Xing, H. L.; Mora, P.

2007-12-01

Numerical modelling offers an outstanding opportunity to gain an understanding of the crustal dynamics and complex crustal system behaviour. This presentation provides our long-term and ongoing effort on finite element based computational model and software development to simulate the interacting fault system for earthquake forecasting. A R-minimum strategy based finite-element computational model and software tool, PANDAS, for modelling 3-dimensional nonlinear frictional contact behaviour between multiple deformable bodies with the arbitrarily-shaped contact element strategy has been developed by the authors, which builds up a virtual laboratory to simulate interacting fault systems including crustal boundary conditions and various nonlinearities (e.g. from frictional contact, materials, geometry and thermal coupling). It has been successfully applied to large scale computing of the complex nonlinear phenomena in the non-continuum media involving the nonlinear frictional instability, multiple material properties and complex geometries on supercomputers, such as the South Australia (SA) interacting fault system, South California fault model and Sumatra subduction model. It has been also extended and to simulate the hot fractured rock (HFR) geothermal reservoir system in collaboration of Geodynamics Ltd which is constructing the first geothermal reservoir system in Australia and to model the tsunami generation induced by earthquakes. Both are supported by Australian Research Council.

On the dimension of complex responses in nonlinear structural vibrations

NASA Astrophysics Data System (ADS)

Wiebe, R.; Spottswood, S. M.

2016-07-01

The ability to accurately model engineering systems under extreme dynamic loads would prove a major breakthrough in many aspects of aerospace, mechanical, and civil engineering. Extreme loads frequently induce both nonlinearities and coupling which increase the complexity of the response and the computational cost of finite element models. Dimension reduction has recently gained traction and promises the ability to distill dynamic responses down to a minimal dimension without sacrificing accuracy. In this context, the dimensionality of a response is related to the number of modes needed in a reduced order model to accurately simulate the response. Thus, an important step is characterizing the dimensionality of complex nonlinear responses of structures. In this work, the dimensionality of the nonlinear response of a post-buckled beam is investigated. Significant detail is dedicated to carefully introducing the experiment, the verification of a finite element model, and the dimensionality estimation algorithm as it is hoped that this system may help serve as a benchmark test case. It is shown that with minor modifications, the method of false nearest neighbors can quantitatively distinguish between the response dimension of various snap-through, non-snap-through, random, and deterministic loads. The state-space dimension of the nonlinear system in question increased from 2-to-10 as the system response moved from simple, low-level harmonic to chaotic snap-through. Beyond the problem studied herein, the techniques developed will serve as a prescriptive guide in developing fast and accurate dimensionally reduced models of nonlinear systems, and eventually as a tool for adaptive dimension-reduction in numerical modeling. The results are especially relevant in the aerospace industry for the design of thin structures such as beams, panels, and shells, which are all capable of spatio-temporally complex dynamic responses that are difficult and computationally expensive to model.

Command Filtering-Based Fuzzy Control for Nonlinear Systems With Saturation Input.

PubMed

Yu, Jinpeng; Shi, Peng; Dong, Wenjie; Lin, Chong

2017-09-01

In this paper, command filtering-based fuzzy control is designed for uncertain multi-input multioutput (MIMO) nonlinear systems with saturation nonlinearity input. First, the command filtering method is employed to deal with the explosion of complexity caused by the derivative of virtual controllers. Then, fuzzy logic systems are utilized to approximate the nonlinear functions of MIMO systems. Furthermore, error compensation mechanism is introduced to overcome the drawback of the dynamics surface approach. The developed method will guarantee all signals of the systems are bounded. The effectiveness and advantages of the theoretic result are obtained by a simulation example.

Large Spatial and Temporal Separations of Cause and Effect in Policy Making - Dealing with Non-linear Effects

NASA Astrophysics Data System (ADS)

McCaskill, John

There can be large spatial and temporal separation of cause and effect in policy making. Determining the correct linkage between policy inputs and outcomes can be highly impractical in the complex environments faced by policy makers. In attempting to see and plan for the probable outcomes, standard linear models often overlook, ignore, or are unable to predict catastrophic events that only seem improbable due to the issue of multiple feedback loops. There are several issues with the makeup and behaviors of complex systems that explain the difficulty many mathematical models (factor analysis/structural equation modeling) have in dealing with non-linear effects in complex systems. This chapter highlights those problem issues and offers insights to the usefulness of ABM in dealing with non-linear effects in complex policy making environments.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables

NASA Astrophysics Data System (ADS)

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-01

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables.

PubMed

Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino

2013-12-07

Collective variables (CVs) are low-dimensional representations of the state of a complex system, which help us rationalize molecular conformations and sample free energy landscapes with molecular dynamics simulations. Given their importance, there is need for systematic methods that effectively identify CVs for complex systems. In recent years, nonlinear manifold learning has shown its ability to automatically characterize molecular collective behavior. Unfortunately, these methods fail to provide a differentiable function mapping high-dimensional configurations to their low-dimensional representation, as required in enhanced sampling methods. We introduce a methodology that, starting from an ensemble representative of molecular flexibility, builds smooth and nonlinear data-driven collective variables (SandCV) from the output of nonlinear manifold learning algorithms. We demonstrate the method with a standard benchmark molecule, alanine dipeptide, and show how it can be non-intrusively combined with off-the-shelf enhanced sampling methods, here the adaptive biasing force method. We illustrate how enhanced sampling simulations with SandCV can explore regions that were poorly sampled in the original molecular ensemble. We further explore the transferability of SandCV from a simpler system, alanine dipeptide in vacuum, to a more complex system, alanine dipeptide in explicit water.

Nonlinear dynamics behavior analysis of the spatial configuration of a tendril-bearing plant

NASA Astrophysics Data System (ADS)

Feng, Jingjing; Zhang, Qichang; Wang, Wei; Hao, Shuying

2017-03-01

Tendril-bearing plants appear to have a spiraling shape when tendrils climb along a support during growth. The growth characteristics of a tendril-bearer can be simplified to a model of a thin elastic rod with a cylindrical constraint. In this paper, the connection between some typical configuration characteristics of tendrils and complex nonlinear dynamic behavior are qualitatively analyzed. The space configuration problem of tendrils can be explained through the study of the nonlinear dynamic behavior of the thin elastic rod system equation. In this study, the complex non-Z2 symmetric critical orbits in the system equation under critical parameters were presented. A new function transformation method that can effectively maintain the critical orbit properties was proposed, and a new nonlinear differential equations system containing complex nonlinear terms can been obtained to describe the cross section position and direction of a rod during climbing. Numerical simulation revealed that the new system can describe the configuration of a rod with reasonable accuracy. To adequately explain the growing regulation of the rod shape, the critical orbit and configuration of rod are connected in a direct way. The high precision analytical expressions of these complex non-Z2 symmetric critical orbits are obtained by introducing a suitable analytical method, and then these expressions are used to draw the corresponding three-dimensional configuration figures of an elastic thin rod. Combined with actual tendrils on a live plant, the space configuration of the winding knots of tendril is explained by the concept of heteroclinic orbit from the perspective of nonlinear dynamics, and correctness of the theoretical analysis was verified. This theoretical analysis method could also be effectively applied to other similar slender structures.

Zero Forcing Conditions for Nonlinear channel Equalisation using a pre-coding scheme

DOE Office of Scientific and Technical Information (OSTI.GOV)

Arfa, Hichem; Belghith, Safya; El Asmi, Sadok

2009-03-05

This paper shows how we can present a zero forcing conditions for a nonlinear channel equalisation. These zero forcing conditions based on the rank of nonlinear system are issued from an algebraic approach based on the module theoretical approach, in which the rank of nonlinear channel is clearly defined. In order to improve the performance of equalisation and reduce the complexity of used nonlinear systems, we will apply a pre-coding scheme. Theoretical results are given and computer simulation is used to corroborate the theory.

Multiscale Support Vector Learning With Projection Operator Wavelet Kernel for Nonlinear Dynamical System Identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2016-02-03

A giant leap has been made in the past couple of decades with the introduction of kernel-based learning as a mainstay for designing effective nonlinear computational learning algorithms. In view of the geometric interpretation of conditional expectation and the ubiquity of multiscale characteristics in highly complex nonlinear dynamic systems [1]-[3], this paper presents a new orthogonal projection operator wavelet kernel, aiming at developing an efficient computational learning approach for nonlinear dynamical system identification. In the framework of multiresolution analysis, the proposed projection operator wavelet kernel can fulfill the multiscale, multidimensional learning to estimate complex dependencies. The special advantage of the projection operator wavelet kernel developed in this paper lies in the fact that it has a closed-form expression, which greatly facilitates its application in kernel learning. To the best of our knowledge, it is the first closed-form orthogonal projection wavelet kernel reported in the literature. It provides a link between grid-based wavelets and mesh-free kernel-based methods. Simulation studies for identifying the parallel models of two benchmark nonlinear dynamical systems confirm its superiority in model accuracy and sparsity.

On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Mahmoud, Gamal M.

Dynamical systems described by real and complex variables are currently one of the most popular areas of scientific research. These systems play an important role in several fields of physics, engineering, and computer sciences, for example, laser systems, control (or chaos suppression), secure communications, and information science. Dynamical basic properties, chaos (hyperchaos) synchronization, chaos control, and generating hyperchaotic behavior of these systems are briefly summarized. The main advantage of introducing complex variables is the reduction of phase space dimensions by a half. They are also used to describe and simulate the physics of detuned laser and thermal convection of liquid flows, where the electric field and the atomic polarization amplitudes are both complex. Clearly, if the variables of the system are complex the equations involve twice as many variables and control parameters, thus making it that much harder for a hostile agent to intercept and decipher the coded message. Chaotic and hyperchaotic complex systems are stated as examples. Finally there are many open problems in the study of chaotic and hyperchaotic complex nonlinear dynamical systems, which need further investigations. Some of these open problems are given.

Leadership within Emergent Events in Complex Systems: Micro-Enactments and the Mechanisms of Organisational Learning and Change

ERIC Educational Resources Information Center

Hazy, James K.; Silberstang, Joyce

2009-01-01

One tradition within the complexity paradigm considers organisations as complex adaptive systems in which autonomous individuals interact, often in complex ways with difficult to predict, non-linear outcomes. Building upon this tradition, and more specifically following the complex systems leadership theory approach, we describe the ways in which…

Vortex-soliton complexes in coupled nonlinear Schrödinger equations with unequal dispersion coefficients.

PubMed

Charalampidis, E G; Kevrekidis, P G; Frantzeskakis, D J; Malomed, B A

2016-08-01

We consider a two-component, two-dimensional nonlinear Schrödinger system with unequal dispersion coefficients and self-defocusing nonlinearities, chiefly with equal strengths of the self- and cross-interactions. In this setting, a natural waveform with a nonvanishing background in one component is a vortex, which induces an effective potential well in the second component, via the nonlinear coupling of the two components. We show that the potential well may support not only the fundamental bound state, but also multiring excited radial state complexes for suitable ranges of values of the dispersion coefficient of the second component. We systematically explore the existence, stability, and nonlinear dynamics of these states. The complexes involving the excited radial states are weakly unstable, with a growth rate depending on the dispersion of the second component. Their evolution leads to transformation of the multiring complexes into stable vortex-bright solitons ones with the fundamental state in the second component. The excited states may be stabilized by a harmonic-oscillator trapping potential, as well as by unequal strengths of the self- and cross-repulsive nonlinearities.

Analysis of the faster-than-Nyquist optimal linear multicarrier system

NASA Astrophysics Data System (ADS)

Marquet, Alexandre; Siclet, Cyrille; Roque, Damien

2017-02-01

Faster-than-Nyquist signalization enables a better spectral efficiency at the expense of an increased computational complexity. Regarding multicarrier communications, previous work mainly relied on the study of non-linear systems exploiting coding and/or equalization techniques, with no particular optimization of the linear part of the system. In this article, we analyze the performance of the optimal linear multicarrier system when used together with non-linear receiving structures (iterative decoding and direct feedback equalization), or in a standalone fashion. We also investigate the limits of the normality assumption of the interference, used for implementing such non-linear systems. The use of this optimal linear system leads to a closed-form expression of the bit-error probability that can be used to predict the performance and help the design of coded systems. Our work also highlights the great performance/complexity trade-off offered by decision feedback equalization in a faster-than-Nyquist context. xml:lang="fr"

Efficient nonlinear equalizer for intra-channel nonlinearity compensation for next generation agile and dynamically reconfigurable optical networks.

PubMed

Malekiha, Mahdi; Tselniker, Igor; Plant, David V

2016-02-22

In this work, we propose and experimentally demonstrate a novel low-complexity technique for fiber nonlinearity compensation. We achieved a transmission distance of 2818 km for a 32-GBaud dual-polarization 16QAM signal. For efficient implantation, and to facilitate integration with conventional digital signal processing (DSP) approaches, we independently compensate fiber nonlinearities after linear impairment equalization. Therefore this algorithm can be easily implemented in currently deployed transmission systems after using linear DSP. The proposed equalizer operates at one sample per symbol and requires only one computation step. The structure of the algorithm is based on a first-order perturbation model with quantized perturbation coefficients. Also, it does not require any prior calculation or detailed knowledge of the transmission system. We identified common symmetries between perturbation coefficients to avoid duplicate and unnecessary operations. In addition, we use only a few adaptive filter coefficients by grouping multiple nonlinear terms and dedicating only one adaptive nonlinear filter coefficient to each group. Finally, the complexity of the proposed algorithm is lower than previously studied nonlinear equalizers by more than one order of magnitude.

SU-E-J-261: Statistical Analysis and Chaotic Dynamics of Respiratory Signal of Patients in BodyFix

DOE Office of Scientific and Technical Information (OSTI.GOV)

Michalski, D; Huq, M; Bednarz, G

Purpose: To quantify respiratory signal of patients in BodyFix undergoing 4DCT scan with and without immobilization cover. Methods: 20 pairs of respiratory tracks recorded with RPM system during 4DCT scan were analyzed. Descriptive statistic was applied to selected parameters of exhale-inhale decomposition. Standardized signals were used with the delay method to build orbits in embedded space. Nonlinear behavior was tested with surrogate data. Sample entropy SE, Lempel-Ziv complexity LZC and the largest Lyapunov exponents LLE were compared. Results: Statistical tests show difference between scans for inspiration time and its variability, which is bigger for scans without cover. The same ismore » for variability of the end of exhalation and inhalation. Other parameters fail to show the difference. For both scans respiratory signals show determinism and nonlinear stationarity. Statistical test on surrogate data reveals their nonlinearity. LLEs show signals chaotic nature and its correlation with breathing period and its embedding delay time. SE, LZC and LLE measure respiratory signal complexity. Nonlinear characteristics do not differ between scans. Conclusion: Contrary to expectation cover applied to patients in BodyFix appears to have limited effect on signal parameters. Analysis based on trajectories of delay vectors shows respiratory system nonlinear character and its sensitive dependence on initial conditions. Reproducibility of respiratory signal can be evaluated with measures of signal complexity and its predictability window. Longer respiratory period is conducive for signal reproducibility as shown by these gauges. Statistical independence of the exhale and inhale times is also supported by the magnitude of LLE. The nonlinear parameters seem more appropriate to gauge respiratory signal complexity since its deterministic chaotic nature. It contrasts with measures based on harmonic analysis that are blind for nonlinear features. Dynamics of breathing, so crucial for 4D-based clinical technologies, can be better controlled if nonlinear-based methodology, which reflects respiration characteristic, is applied. Funding provided by Varian Medical Systems via Investigator Initiated Research Project.« less

Fractional analysis for nonlinear electrical transmission line and nonlinear Schroedinger equations with incomplete sub-equation

NASA Astrophysics Data System (ADS)

Fendzi-Donfack, Emmanuel; Nguenang, Jean Pierre; Nana, Laurent

2018-02-01

We use the fractional complex transform with the modified Riemann-Liouville derivative operator to establish the exact and generalized solutions of two fractional partial differential equations. We determine the solutions of fractional nonlinear electrical transmission lines (NETL) and the perturbed nonlinear Schroedinger (NLS) equation with the Kerr law nonlinearity term. The solutions are obtained for the parameters in the range (0<α≤1) of the derivative operator and we found the traditional solutions for the limiting case of α =1. We show that according to the modified Riemann-Liouville derivative, the solutions found can describe physical systems with memory effect, transient effects in electrical systems and nonlinear transmission lines, and other systems such as optical fiber.

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

NASA Astrophysics Data System (ADS)

Donges, Jonathan; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik; Marwan, Norbert; Dijkstra, Henk; Kurths, Jürgen

2016-04-01

We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology. pyunicorn is available online at https://github.com/pik-copan/pyunicorn. Reference: J.F. Donges, J. Heitzig, B. Beronov, M. Wiedermann, J. Runge, Q.-Y. Feng, L. Tupikina, V. Stolbova, R.V. Donner, N. Marwan, H.A. Dijkstra, and J. Kurths, Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package, Chaos 25, 113101 (2015), DOI: 10.1063/1.4934554, Preprint: arxiv.org:1507.01571 [physics.data-an].

Bifurcation and Hysteresis Effects in Student Performance: The Signature of Complexity and Chaos in Educational Research

ERIC Educational Resources Information Center

Stamovlasis, Dimitrios

2014-01-01

This paper addresses some methodological issues concerning traditional linear approaches and shows the need for a paradigm shift in education research towards the Complexity and Nonlinear Dynamical Systems (NDS) framework. It presents a quantitative piece of research aiming to test the nonlinear dynamical hypothesis in education. It applies…

A novel technique to solve nonlinear higher-index Hessenberg differential-algebraic equations by Adomian decomposition method.

PubMed

Benhammouda, Brahim

2016-01-01

Since 1980, the Adomian decomposition method (ADM) has been extensively used as a simple powerful tool that applies directly to solve different kinds of nonlinear equations including functional, differential, integro-differential and algebraic equations. However, for differential-algebraic equations (DAEs) the ADM is applied only in four earlier works. There, the DAEs are first pre-processed by some transformations like index reductions before applying the ADM. The drawback of such transformations is that they can involve complex algorithms, can be computationally expensive and may lead to non-physical solutions. The purpose of this paper is to propose a novel technique that applies the ADM directly to solve a class of nonlinear higher-index Hessenberg DAEs systems efficiently. The main advantage of this technique is that; firstly it avoids complex transformations like index reductions and leads to a simple general algorithm. Secondly, it reduces the computational work by solving only linear algebraic systems with a constant coefficient matrix at each iteration, except for the first iteration where the algebraic system is nonlinear (if the DAE is nonlinear with respect to the algebraic variable). To demonstrate the effectiveness of the proposed technique, we apply it to a nonlinear index-three Hessenberg DAEs system with nonlinear algebraic constraints. This technique is straightforward and can be programmed in Maple or Mathematica to simulate real application problems.

Inference of a Nonlinear Stochastic Model of the Cardiorespiratory Interaction

NASA Astrophysics Data System (ADS)

Smelyanskiy, V. N.; Luchinsky, D. G.; Stefanovska, A.; McClintock, P. V.

2005-03-01

We reconstruct a nonlinear stochastic model of the cardiorespiratory interaction in terms of a set of polynomial basis functions representing the nonlinear force governing system oscillations. The strength and direction of coupling and noise intensity are simultaneously inferred from a univariate blood pressure signal. Our new inference technique does not require extensive global optimization, and it is applicable to a wide range of complex dynamical systems subject to noise.

Photonic single nonlinear-delay dynamical node for information processing

NASA Astrophysics Data System (ADS)

Ortín, Silvia; San-Martín, Daniel; Pesquera, Luis; Gutiérrez, José Manuel

2012-06-01

An electro-optical system with a delay loop based on semiconductor lasers is investigated for information processing by performing numerical simulations. This system can replace a complex network of many nonlinear elements for the implementation of Reservoir Computing. We show that a single nonlinear-delay dynamical system has the basic properties to perform as reservoir: short-term memory and separation property. The computing performance of this system is evaluated for two prediction tasks: Lorenz chaotic time series and nonlinear auto-regressive moving average (NARMA) model. We sweep the parameters of the system to find the best performance. The results achieved for the Lorenz and the NARMA-10 tasks are comparable to those obtained by other machine learning methods.

Advanced Kalman Filter for Real-Time Responsiveness in Complex Systems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Welch, Gregory Francis; Zhang, Jinghe

2014-06-10

Complex engineering systems pose fundamental challenges in real-time operations and control because they are highly dynamic systems consisting of a large number of elements with severe nonlinearities and discontinuities. Today’s tools for real-time complex system operations are mostly based on steady state models, unable to capture the dynamic nature and too slow to prevent system failures. We developed advanced Kalman filtering techniques and the formulation of dynamic state estimation using Kalman filtering techniques to capture complex system dynamics in aiding real-time operations and control. In this work, we looked at complex system issues including severe nonlinearity of system equations, discontinuitiesmore » caused by system controls and network switches, sparse measurements in space and time, and real-time requirements of power grid operations. We sought to bridge the disciplinary boundaries between Computer Science and Power Systems Engineering, by introducing methods that leverage both existing and new techniques. While our methods were developed in the context of electrical power systems, they should generalize to other large-scale scientific and engineering applications.« less

Persistent model order reduction for complex dynamical systems using smooth orthogonal decomposition

NASA Astrophysics Data System (ADS)

Ilbeigi, Shahab; Chelidze, David

2017-11-01

Full-scale complex dynamic models are not effective for parametric studies due to the inherent constraints on available computational power and storage resources. A persistent reduced order model (ROM) that is robust, stable, and provides high-fidelity simulations for a relatively wide range of parameters and operating conditions can provide a solution to this problem. The fidelity of a new framework for persistent model order reduction of large and complex dynamical systems is investigated. The framework is validated using several numerical examples including a large linear system and two complex nonlinear systems with material and geometrical nonlinearities. While the framework is used for identifying the robust subspaces obtained from both proper and smooth orthogonal decompositions (POD and SOD, respectively), the results show that SOD outperforms POD in terms of stability, accuracy, and robustness.

Digit replacement: A generic map for nonlinear dynamical systems.

PubMed

García-Morales, Vladimir

2016-09-01

A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attractors and the hierarchical deposition of grains of different sizes on a surface.

Nonlinear Decoupling Control With ANFIS-Based Unmodeled Dynamics Compensation for a Class of Complex Industrial Processes.

PubMed

Zhang, Yajun; Chai, Tianyou; Wang, Hong; Wang, Dianhui; Chen, Xinkai

2018-06-01

Complex industrial processes are multivariable and generally exhibit strong coupling among their control loops with heavy nonlinear nature. These make it very difficult to obtain an accurate model. As a result, the conventional and data-driven control methods are difficult to apply. Using a twin-tank level control system as an example, a novel multivariable decoupling control algorithm with adaptive neural-fuzzy inference system (ANFIS)-based unmodeled dynamics (UD) compensation is proposed in this paper for a class of complex industrial processes. At first, a nonlinear multivariable decoupling controller with UD compensation is introduced. Different from the existing methods, the decomposition estimation algorithm using ANFIS is employed to estimate the UD, and the desired estimating and decoupling control effects are achieved. Second, the proposed method does not require the complicated switching mechanism which has been commonly used in the literature. This significantly simplifies the obtained decoupling algorithm and its realization. Third, based on some new lemmas and theorems, the conditions on the stability and convergence of the closed-loop system are analyzed to show the uniform boundedness of all the variables. This is then followed by the summary on experimental tests on a heavily coupled nonlinear twin-tank system that demonstrates the effectiveness and the practicability of the proposed method.

A bifurcation giving birth to order in an impulsively driven complex system

NASA Astrophysics Data System (ADS)

Seshadri, Akshay; Sujith, R. I.

2016-08-01

Nonlinear oscillations lie at the heart of numerous complex systems. Impulsive forcing arises naturally in many scenarios, and we endeavour to study nonlinear oscillators subject to such forcing. We model these kicked oscillatory systems as a piecewise smooth dynamical system, whereby their dynamics can be investigated. We investigate the problem of pattern formation in a turbulent combustion system and apply this formalism with the aim of explaining the observed dynamics. We identify that the transition of this system from low amplitude chaotic oscillations to large amplitude periodic oscillations is the result of a discontinuity induced bifurcation. Further, we provide an explanation for the occurrence of intermittent oscillations in the system.

A bifurcation giving birth to order in an impulsively driven complex system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Seshadri, Akshay, E-mail: akshayseshadri@gmail.com; Sujith, R. I., E-mail: sujith@iitm.ac.in

Nonlinear oscillations lie at the heart of numerous complex systems. Impulsive forcing arises naturally in many scenarios, and we endeavour to study nonlinear oscillators subject to such forcing. We model these kicked oscillatory systems as a piecewise smooth dynamical system, whereby their dynamics can be investigated. We investigate the problem of pattern formation in a turbulent combustion system and apply this formalism with the aim of explaining the observed dynamics. We identify that the transition of this system from low amplitude chaotic oscillations to large amplitude periodic oscillations is the result of a discontinuity induced bifurcation. Further, we provide anmore » explanation for the occurrence of intermittent oscillations in the system.« less

Efficient Lookup Table-Based Adaptive Baseband Predistortion Architecture for Memoryless Nonlinearity

NASA Astrophysics Data System (ADS)

Ba, Seydou N.; Waheed, Khurram; Zhou, G. Tong

2010-12-01

Digital predistortion is an effective means to compensate for the nonlinear effects of a memoryless system. In case of a cellular transmitter, a digital baseband predistorter can mitigate the undesirable nonlinear effects along the signal chain, particularly the nonlinear impairments in the radiofrequency (RF) amplifiers. To be practically feasible, the implementation complexity of the predistorter must be minimized so that it becomes a cost-effective solution for the resource-limited wireless handset. This paper proposes optimizations that facilitate the design of a low-cost high-performance adaptive digital baseband predistorter for memoryless systems. A comparative performance analysis of the amplitude and power lookup table (LUT) indexing schemes is presented. An optimized low-complexity amplitude approximation and its hardware synthesis results are also studied. An efficient LUT predistorter training algorithm that combines the fast convergence speed of the normalized least mean squares (NLMSs) with a small hardware footprint is proposed. Results of fixed-point simulations based on the measured nonlinear characteristics of an RF amplifier are presented.

Modelling the influence of sensory dynamics on linear and nonlinear driver steering control

NASA Astrophysics Data System (ADS)

Nash, C. J.; Cole, D. J.

2018-05-01

A recent review of the literature has indicated that sensory dynamics play an important role in the driver-vehicle steering task, motivating the design of a new driver model incorporating human sensory systems. This paper presents a full derivation of the linear driver model developed in previous work, and extends the model to control a vehicle with nonlinear tyres. Various nonlinear controllers and state estimators are compared with different approximations of the true system dynamics. The model simulation time is found to increase significantly with the complexity of the controller and state estimator. In general the more complex controllers perform best, although with certain vehicle and tyre models linearised controllers perform as well as a full nonlinear optimisation. Various extended Kalman filters give similar results, although the driver's sensory dynamics reduce control performance compared with full state feedback. The new model could be used to design vehicle systems which interact more naturally and safely with a human driver.

Unified functional network and nonlinear time series analysis for complex systems science: The pyunicorn package

NASA Astrophysics Data System (ADS)

Donges, Jonathan F.; Heitzig, Jobst; Beronov, Boyan; Wiedermann, Marc; Runge, Jakob; Feng, Qing Yi; Tupikina, Liubov; Stolbova, Veronika; Donner, Reik V.; Marwan, Norbert; Dijkstra, Henk A.; Kurths, Jürgen

2015-11-01

We introduce the pyunicorn (Pythonic unified complex network and recurrence analysis toolbox) open source software package for applying and combining modern methods of data analysis and modeling from complex network theory and nonlinear time series analysis. pyunicorn is a fully object-oriented and easily parallelizable package written in the language Python. It allows for the construction of functional networks such as climate networks in climatology or functional brain networks in neuroscience representing the structure of statistical interrelationships in large data sets of time series and, subsequently, investigating this structure using advanced methods of complex network theory such as measures and models for spatial networks, networks of interacting networks, node-weighted statistics, or network surrogates. Additionally, pyunicorn provides insights into the nonlinear dynamics of complex systems as recorded in uni- and multivariate time series from a non-traditional perspective by means of recurrence quantification analysis, recurrence networks, visibility graphs, and construction of surrogate time series. The range of possible applications of the library is outlined, drawing on several examples mainly from the field of climatology.

Relations between nonlinear Riccati equations and other equations in fundamental physics

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2014-10-01

Many phenomena in the observable macroscopic world obey nonlinear evolution equations while the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. Linearizing nonlinear dynamics would destroy the fundamental property of this theory, however, it can be shown that quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown that the information about the dynamics of quantum systems with analytical solutions can not only be obtainable from the time-dependent Schrödinger equation but equally-well from a complex Riccati equation. Comparison with supersymmetric quantum mechanics shows that even additional information can be obtained from the nonlinear formulation. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation for any potential. Extension of the Riccati formulation to include irreversible dissipative effects is straightforward. Via (real and complex) Riccati equations, other fields of physics can also be treated within the same formalism, e.g., statistical thermodynamics, nonlinear dynamical systems like those obeying a logistic equation as well as wave equations in classical optics, Bose- Einstein condensates and cosmological models. Finally, the link to abstract "quantizations" such as the Pythagorean triples and Riccati equations connected with trigonometric and hyperbolic functions will be shown.

Nonlinear optical oscillation dynamics in high-Q lithium niobate microresonators.

PubMed

Sun, Xuan; Liang, Hanxiao; Luo, Rui; Jiang, Wei C; Zhang, Xi-Cheng; Lin, Qiang

2017-06-12

Recent advance of lithium niobate microphotonic devices enables the exploration of intriguing nonlinear optical effects. We show complex nonlinear oscillation dynamics in high-Q lithium niobate microresonators that results from unique competition between the thermo-optic nonlinearity and the photorefractive effect, distinctive to other device systems and mechanisms ever reported. The observed phenomena are well described by our theory. This exploration helps understand the nonlinear optical behavior of high-Q lithium niobate microphotonic devices which would be crucial for future application of on-chip nonlinear lithium niobate photonics.

Order reduction, identification and localization studies of dynamical systems

NASA Astrophysics Data System (ADS)

Ma, Xianghong

In this thesis methods are developed for performing order reduction, system identification and induction of nonlinear localization in complex mechanical dynamic systems. General techniques are proposed for constructing low-order models of linear and nonlinear mechanical systems; in addition, novel mechanical designs are considered for inducing nonlinear localization phenomena for the purpose of enhancing their dynamical performance. The thesis is in three major parts. In the first part, the transient dynamics of an impulsively loaded multi-bay truss is numerically computed by employing the Direct Global Matrix (DGM) approach. The approach is applicable to large-scale flexible structures with periodicity. Karhunen-Loeve (K-L) decomposition is used to discretize the dynamics of the truss and to create the low-order models of the truss. The leading order K-L modes are recovered by an experiment, which shows the feasibility of K-L based order reduction technique. In the second part of the thesis, nonlinear localization in dynamical systems is studied through two applications. In the seismic base isolation study, it is shown that the dynamics are sensitive to the presence of nonlinear elements and that passive motion confinement can be induced under proper design. In the coupled rod system, numerical simulation of the transient dynamics shows that a nonlinear backlash spring can induce either nonlinear localization or delocalization in the form of beat phenomena. K-L decomposition and poincare maps are utilized to study the nonlinear effects. The study shows that nonlinear localization can be induced in complex structures through backlash. In the third and final part of the thesis, a new technique based on Green!s function method is proposed to identify the dynamics of practical bolted joints. By modeling the difference between the dynamics of the bolted structure and the corresponding unbolted one, one constructs a nonparametric model for the joint dynamics. Two applications are given with a bolted beam and a truss joint in order to show the applicability of the technique.

Research Methodology on Language Development from a Complex Systems Perspective

ERIC Educational Resources Information Center

Larsen-Freeman, Diane; Cameron, Lynne

2008-01-01

Changes to research methodology motivated by the adoption of a complexity theory perspective on language development are considered. The dynamic, nonlinear, and open nature of complex systems, together with their tendency toward self-organization and interaction across levels and timescales, requires changes in traditional views of the functions…

Revisiting the Quantum Brain Hypothesis: Toward Quantum (Neuro)biology?

PubMed

Jedlicka, Peter

2017-01-01

The nervous system is a non-linear dynamical complex system with many feedback loops. A conventional wisdom is that in the brain the quantum fluctuations are self-averaging and thus functionally negligible. However, this intuition might be misleading in the case of non-linear complex systems. Because of an extreme sensitivity to initial conditions, in complex systems the microscopic fluctuations may be amplified and thereby affect the system's behavior. In this way quantum dynamics might influence neuronal computations. Accumulating evidence in non-neuronal systems indicates that biological evolution is able to exploit quantum stochasticity. The recent rise of quantum biology as an emerging field at the border between quantum physics and the life sciences suggests that quantum events could play a non-trivial role also in neuronal cells. Direct experimental evidence for this is still missing but future research should address the possibility that quantum events contribute to an extremely high complexity, variability and computational power of neuronal dynamics.

Multiuser receiver for DS-CDMA signals in multipath channels: an enhanced multisurface method.

PubMed

Mahendra, Chetan; Puthusserypady, Sadasivan

2006-11-01

This paper deals with the problem of multiuser detection in direct-sequence code-division multiple-access (DS-CDMA) systems in multipath environments. The existing multiuser detectors can be divided into two categories: (1) low-complexity poor-performance linear detectors and (2) high-complexity good-performance nonlinear detectors. In particular, in channels where the orthogonality of the code sequences is destroyed by multipath, detectors with linear complexity perform much worse than the nonlinear detectors. In this paper, we propose an enhanced multisurface method (EMSM) for multiuser detection in multipath channels. EMSM is an intermediate piecewise linear detection scheme with a run-time complexity linear in the number of users. Its bit error rate performance is compared with existing linear detectors, a nonlinear radial basis function detector trained by the new support vector learning algorithm, and Verdu's optimal detector. Simulations in multipath channels, for both synchronous and asynchronous cases, indicate that it always outperforms all other linear detectors, performing nearly as well as nonlinear detectors.

Atomic switch networks—nanoarchitectonic design of a complex system for natural computing

NASA Astrophysics Data System (ADS)

Demis, E. C.; Aguilera, R.; Sillin, H. O.; Scharnhorst, K.; Sandouk, E. J.; Aono, M.; Stieg, A. Z.; Gimzewski, J. K.

2015-05-01

Self-organized complex systems are ubiquitous in nature, and the structural complexity of these natural systems can be used as a model to design new classes of functional nanotechnology based on highly interconnected networks of interacting units. Conventional fabrication methods for electronic computing devices are subject to known scaling limits, confining the diversity of possible architectures. This work explores methods of fabricating a self-organized complex device known as an atomic switch network and discusses its potential utility in computing. Through a merger of top-down and bottom-up techniques guided by mathematical and nanoarchitectonic design principles, we have produced functional devices comprising nanoscale elements whose intrinsic nonlinear dynamics and memorization capabilities produce robust patterns of distributed activity and a capacity for nonlinear transformation of input signals when configured in the appropriate network architecture. Their operational characteristics represent a unique potential for hardware implementation of natural computation, specifically in the area of reservoir computing—a burgeoning field that investigates the computational aptitude of complex biologically inspired systems.

Atomic switch networks-nanoarchitectonic design of a complex system for natural computing.

PubMed

Demis, E C; Aguilera, R; Sillin, H O; Scharnhorst, K; Sandouk, E J; Aono, M; Stieg, A Z; Gimzewski, J K

2015-05-22

Self-organized complex systems are ubiquitous in nature, and the structural complexity of these natural systems can be used as a model to design new classes of functional nanotechnology based on highly interconnected networks of interacting units. Conventional fabrication methods for electronic computing devices are subject to known scaling limits, confining the diversity of possible architectures. This work explores methods of fabricating a self-organized complex device known as an atomic switch network and discusses its potential utility in computing. Through a merger of top-down and bottom-up techniques guided by mathematical and nanoarchitectonic design principles, we have produced functional devices comprising nanoscale elements whose intrinsic nonlinear dynamics and memorization capabilities produce robust patterns of distributed activity and a capacity for nonlinear transformation of input signals when configured in the appropriate network architecture. Their operational characteristics represent a unique potential for hardware implementation of natural computation, specifically in the area of reservoir computing-a burgeoning field that investigates the computational aptitude of complex biologically inspired systems.

Nonlinear Systems.

ERIC Educational Resources Information Center

Seider, Warren D.; Ungar, Lyle H.

1987-01-01

Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…

Entropy production and nonlinear Fokker-Planck equations.

PubMed

Casas, G A; Nobre, F D; Curado, E M F

2012-12-01

The entropy time rate of systems described by nonlinear Fokker-Planck equations--which are directly related to generalized entropic forms--is analyzed. Both entropy production, associated with irreversible processes, and entropy flux from the system to its surroundings are studied. Some examples of known generalized entropic forms are considered, and particularly, the flux and production of the Boltzmann-Gibbs entropy, obtained from the linear Fokker-Planck equation, are recovered as particular cases. Since nonlinear Fokker-Planck equations are appropriate for the dynamical behavior of several physical phenomena in nature, like many within the realm of complex systems, the present analysis should be applicable to irreversible processes in a large class of nonlinear systems, such as those described by Tsallis and Kaniadakis entropies.

Localization of intense electromagnetic waves in a relativistically hot plasma.

PubMed

Shukla, P K; Eliasson, B

2005-02-18

We consider nonlinear interactions between intense short electromagnetic waves (EMWs) and a relativistically hot electron plasma that supports relativistic electron holes (REHs). It is shown that such EMW-REH interactions are governed by a coupled nonlinear system of equations composed of a nonlinear Schro dinger equation describing the dynamics of the EMWs and the Poisson-relativistic Vlasov system describing the dynamics of driven REHs. The present nonlinear system of equations admits both a linearly trapped discrete number of eigenmodes of the EMWs in a quasistationary REH and a modification of the REH by large-amplitude trapped EMWs. Computer simulations of the relativistic Vlasov and Maxwell-Poisson system of equations show complex interactions between REHs loaded with localized EMWs.

Study of Piezoelectric Vibration Energy Harvester with non-linear conditioning circuit using an integrated model

NASA Astrophysics Data System (ADS)

Manzoor, Ali; Rafique, Sajid; Usman Iftikhar, Muhammad; Mahmood Ul Hassan, Khalid; Nasir, Ali

2017-08-01

Piezoelectric vibration energy harvester (PVEH) consists of a cantilever bimorph with piezoelectric layers pasted on its top and bottom, which can harvest power from vibrations and feed to low power wireless sensor nodes through some power conditioning circuit. In this paper, a non-linear conditioning circuit, consisting of a full-bridge rectifier followed by a buck-boost converter, is employed to investigate the issues of electrical side of the energy harvesting system. An integrated mathematical model of complete electromechanical system has been developed. Previously, researchers have studied PVEH with sophisticated piezo-beam models but employed simplistic linear circuits, such as resistor, as electrical load. In contrast, other researchers have worked on more complex non-linear circuits but with over-simplified piezo-beam models. Such models neglect different aspects of the system which result from complex interactions of its electrical and mechanical subsystems. In this work, authors have integrated the distributed parameter-based model of piezo-beam presented in literature with a real world non-linear electrical load. Then, the developed integrated model is employed to analyse the stability of complete energy harvesting system. This work provides a more realistic and useful electromechanical model having realistic non-linear electrical load unlike the simplistic linear circuit elements employed by many researchers.

Dark solitons, modulation instability and breathers in a chain of weakly nonlinear oscillators with cyclic symmetry

NASA Astrophysics Data System (ADS)

Fontanela, F.; Grolet, A.; Salles, L.; Chabchoub, A.; Hoffmann, N.

2018-01-01

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex nonlinear phenomena can be expected. We consider a cyclically symmetric system of coupled weakly nonlinear undamped oscillators that could be considered a minimal model for different cyclic and symmetric aerospace structures experiencing large deformations. The focus is on localised vibrations that arise from wave envelope modulation of travelling waves. For the defocussing parameter range of the approximative nonlinear evolution equation, we show the possible existence of dark solitons and discuss their characteristics. For the focussing parameter range, we characterise modulation instability and illustrate corresponding nonlinear breather dynamics. Furthermore, we show that for stronger nonlinearity or randomness in initial conditions, transient breather-type dynamics and decay into bright solitons appear. The findings suggest that significant vibration localisation may arise due to mechanisms of nonlinear modulation dynamics.

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

This paper presents an unconventional theory and method for solving general nonlinear dynamical systems. Instead of the direct iterative methods, the discretized nonlinear system is first formulated as a global optimization problem via the least squares method. A newly developed canonical duality theory shows that this nonconvex minimization problem can be solved deterministically in polynomial time if a global optimality condition is satisfied. The so-called pseudo-chaos produced by linear iterative methods are mainly due to the intrinsic numerical error accumulations. Otherwise, the global optimization problem could be NP-hard and the nonlinear system can be really chaotic. A conjecture is proposed, which reveals the connection between chaos in nonlinear dynamics and NP-hardness in computer science. The methodology and the conjecture are verified by applications to the well-known logistic equation, a forced memristive circuit and the Lorenz system. Computational results show that the canonical duality theory can be used to identify chaotic systems and to obtain realistic global optimal solutions in nonlinear dynamical systems. The method and results presented in this paper should bring some new insights into nonlinear dynamical systems and NP-hardness in computational complexity theory.

A review on prognostic techniques for non-stationary and non-linear rotating systems

NASA Astrophysics Data System (ADS)

Kan, Man Shan; Tan, Andy C. C.; Mathew, Joseph

2015-10-01

The field of prognostics has attracted significant interest from the research community in recent times. Prognostics enables the prediction of failures in machines resulting in benefits to plant operators such as shorter downtimes, higher operation reliability, reduced operations and maintenance cost, and more effective maintenance and logistics planning. Prognostic systems have been successfully deployed for the monitoring of relatively simple rotating machines. However, machines and associated systems today are increasingly complex. As such, there is an urgent need to develop prognostic techniques for such complex systems operating in the real world. This review paper focuses on prognostic techniques that can be applied to rotating machinery operating under non-linear and non-stationary conditions. The general concept of these techniques, the pros and cons of applying these methods, as well as their applications in the research field are discussed. Finally, the opportunities and challenges in implementing prognostic systems and developing effective techniques for monitoring machines operating under non-stationary and non-linear conditions are also discussed.

Revisiting the Quantum Brain Hypothesis: Toward Quantum (Neuro)biology?

PubMed Central

Jedlicka, Peter

2017-01-01

The nervous system is a non-linear dynamical complex system with many feedback loops. A conventional wisdom is that in the brain the quantum fluctuations are self-averaging and thus functionally negligible. However, this intuition might be misleading in the case of non-linear complex systems. Because of an extreme sensitivity to initial conditions, in complex systems the microscopic fluctuations may be amplified and thereby affect the system’s behavior. In this way quantum dynamics might influence neuronal computations. Accumulating evidence in non-neuronal systems indicates that biological evolution is able to exploit quantum stochasticity. The recent rise of quantum biology as an emerging field at the border between quantum physics and the life sciences suggests that quantum events could play a non-trivial role also in neuronal cells. Direct experimental evidence for this is still missing but future research should address the possibility that quantum events contribute to an extremely high complexity, variability and computational power of neuronal dynamics. PMID:29163041

Modeling Stochastic Complexity in Complex Adaptive Systems: Non-Kolmogorov Probability and the Process Algebra Approach.

PubMed

Sulis, William H

2017-10-01

Walter Freeman III pioneered the application of nonlinear dynamical systems theories and methodologies in his work on mesoscopic brain dynamics.Sadly, mainstream psychology and psychiatry still cling to linear correlation based data analysis techniques, which threaten to subvert the process of experimentation and theory building. In order to progress, it is necessary to develop tools capable of managing the stochastic complexity of complex biopsychosocial systems, which includes multilevel feedback relationships, nonlinear interactions, chaotic dynamics and adaptability. In addition, however, these systems exhibit intrinsic randomness, non-Gaussian probability distributions, non-stationarity, contextuality, and non-Kolmogorov probabilities, as well as the absence of mean and/or variance and conditional probabilities. These properties and their implications for statistical analysis are discussed. An alternative approach, the Process Algebra approach, is described. It is a generative model, capable of generating non-Kolmogorov probabilities. It has proven useful in addressing fundamental problems in quantum mechanics and in the modeling of developing psychosocial systems.

Human systems dynamics: Toward a computational model

NASA Astrophysics Data System (ADS)

Eoyang, Glenda H.

2012-09-01

A robust and reliable computational model of complex human systems dynamics could support advancements in theory and practice for social systems at all levels, from intrapersonal experience to global politics and economics. Models of human interactions have evolved from traditional, Newtonian systems assumptions, which served a variety of practical and theoretical needs of the past. Another class of models has been inspired and informed by models and methods from nonlinear dynamics, chaos, and complexity science. None of the existing models, however, is able to represent the open, high dimension, and nonlinear self-organizing dynamics of social systems. An effective model will represent interactions at multiple levels to generate emergent patterns of social and political life of individuals and groups. Existing models and modeling methods are considered and assessed against characteristic pattern-forming processes in observed and experienced phenomena of human systems. A conceptual model, CDE Model, based on the conditions for self-organizing in human systems, is explored as an alternative to existing models and methods. While the new model overcomes the limitations of previous models, it also provides an explanatory base and foundation for prospective analysis to inform real-time meaning making and action taking in response to complex conditions in the real world. An invitation is extended to readers to engage in developing a computational model that incorporates the assumptions, meta-variables, and relationships of this open, high dimension, and nonlinear conceptual model of the complex dynamics of human systems.

Complexity and Health Coaching: Synergies in Nursing

PubMed Central

Mitchell, Gail J.; Wong, Winnie; Rush, Danica

2013-01-01

Health care professionals are increasingly aware that persons are complex and live in relation with other complex human communities and broader systems. Complex beings and systems are living and evolving in nonlinear ways through a process of mutual influence. Traditional standardized approaches in chronic disease management do not address these non-linear linkages and the meaning and changes that impact day-to-day life and caring for self and family. The RN health coach role described in this paper addresses the complexities and ambiguities for persons living with chronic illness in order to provide person-centered care and support that are unique and responsive to the context of persons' lives. Informed by complexity thinking and relational inquiry, the RN health coach is an emergent innovation of creative action with community and groups that support persons as they shape their health and patterns of living. PMID:24102025

Non-Linear Approach in Kinesiology Should Be Preferred to the Linear--A Case of Basketball.

PubMed

Trninić, Marko; Jeličić, Mario; Papić, Vladan

2015-07-01

In kinesiology, medicine, biology and psychology, in which research focus is on dynamical self-organized systems, complex connections exist between variables. Non-linear nature of complex systems has been discussed and explained by the example of non-linear anthropometric predictors of performance in basketball. Previous studies interpreted relations between anthropometric features and measures of effectiveness in basketball by (a) using linear correlation models, and by (b) including all basketball athletes in the same sample of participants regardless of their playing position. In this paper the significance and character of linear and non-linear relations between simple anthropometric predictors (AP) and performance criteria consisting of situation-related measures of effectiveness (SE) in basketball were determined and evaluated. The sample of participants consisted of top-level junior basketball players divided in three groups according to their playing time (8 minutes and more per game) and playing position: guards (N = 42), forwards (N = 26) and centers (N = 40). Linear (general model) and non-linear (general model) regression models were calculated simultaneously and separately for each group. The conclusion is viable: non-linear regressions are frequently superior to linear correlations when interpreting actual association logic among research variables.

1991 Annual report on scientific programs: A broad research program on the sciences of complexity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1991-01-01

1991 was continued rapid growth for the Santa Fe Institute (SFI) as it broadened its interdisciplinary research into the organization, evolution and operation of complex systems and sought deeply the principles underlying their dynamic behavior. Research on complex systems--the focus of work at SFI--involves an extraordinary range of topics normally studied in seemingly disparate fields. Natural systems displaying complex behavior range upwards from proteins and DNA through cells and evolutionary systems to human societies. Research models exhibiting complexity include nonlinear equations, spin glasses, cellular automata, genetic algorithms, classifier systems, and an array of other computational models. Some of the majormore » questions facing complex systems researchers are: (1) explaining how complexity arises from the nonlinear interaction of simples components, (2) describing the mechanisms underlying high-level aggregate behavior of complex systems (such as the overt behavior of an organism, the flow of energy in an ecology, the GNP of an economy), and (3) creating a theoretical framework to enable predictions about the likely behavior of such systems in various conditions. The importance of understanding such systems in enormous: many of the most serious challenges facing humanity--e.g., environmental sustainability, economic stability, the control of disease--as well as many of the hardest scientific questions--e.g., protein folding, the distinction between self and non-self in the immune system, the nature of intelligence, the origin of life--require deep understanding of complex systems.« less

1991 Annual report on scientific programs: A broad research program on the sciences of complexity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1991-12-31

1991 was continued rapid growth for the Santa Fe Institute (SFI) as it broadened its interdisciplinary research into the organization, evolution and operation of complex systems and sought deeply the principles underlying their dynamic behavior. Research on complex systems--the focus of work at SFI--involves an extraordinary range of topics normally studied in seemingly disparate fields. Natural systems displaying complex behavior range upwards from proteins and DNA through cells and evolutionary systems to human societies. Research models exhibiting complexity include nonlinear equations, spin glasses, cellular automata, genetic algorithms, classifier systems, and an array of other computational models. Some of the majormore » questions facing complex systems researchers are: (1) explaining how complexity arises from the nonlinear interaction of simples components, (2) describing the mechanisms underlying high-level aggregate behavior of complex systems (such as the overt behavior of an organism, the flow of energy in an ecology, the GNP of an economy), and (3) creating a theoretical framework to enable predictions about the likely behavior of such systems in various conditions. The importance of understanding such systems in enormous: many of the most serious challenges facing humanity--e.g., environmental sustainability, economic stability, the control of disease--as well as many of the hardest scientific questions--e.g., protein folding, the distinction between self and non-self in the immune system, the nature of intelligence, the origin of life--require deep understanding of complex systems.« less

Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays

NASA Astrophysics Data System (ADS)

Zhang, Chuan; Wang, Xingyuan; Luo, Chao; Li, Junqiu; Wang, Chunpeng

2018-03-01

In this paper, we focus on the robust outer synchronization problem between two nonlinear complex networks with parametric disturbances and mixed time-varying delays. Firstly, a general complex network model is proposed. Besides the nonlinear couplings, the network model in this paper can possess parametric disturbances, internal time-varying delay, discrete time-varying delay and distributed time-varying delay. Then, according to the robust control strategy, linear matrix inequality and Lyapunov stability theory, several outer synchronization protocols are strictly derived. Simple linear matrix controllers are designed to driver the response network synchronize to the drive network. Additionally, our results can be applied on the complex networks without parametric disturbances. Finally, by utilizing the delayed Lorenz chaotic system as the dynamics of all nodes, simulation examples are given to demonstrate the effectiveness of our theoretical results.

Reservoir Computing Beyond Memory-Nonlinearity Trade-off.

PubMed

Inubushi, Masanobu; Yoshimura, Kazuyuki

2017-08-31

Reservoir computing is a brain-inspired machine learning framework that employs a signal-driven dynamical system, in particular harnessing common-signal-induced synchronization which is a widely observed nonlinear phenomenon. Basic understanding of a working principle in reservoir computing can be expected to shed light on how information is stored and processed in nonlinear dynamical systems, potentially leading to progress in a broad range of nonlinear sciences. As a first step toward this goal, from the viewpoint of nonlinear physics and information theory, we study the memory-nonlinearity trade-off uncovered by Dambre et al. (2012). Focusing on a variational equation, we clarify a dynamical mechanism behind the trade-off, which illustrates why nonlinear dynamics degrades memory stored in dynamical system in general. Moreover, based on the trade-off, we propose a mixture reservoir endowed with both linear and nonlinear dynamics and show that it improves the performance of information processing. Interestingly, for some tasks, significant improvements are observed by adding a few linear dynamics to the nonlinear dynamical system. By employing the echo state network model, the effect of the mixture reservoir is numerically verified for a simple function approximation task and for more complex tasks.

Coupling nonlinear optical waves to photoreactive and phase-separating soft matter: Current status and perspectives

NASA Astrophysics Data System (ADS)

Biria, Saeid; Morim, Derek R.; An Tsao, Fu; Saravanamuttu, Kalaichelvi; Hosein, Ian D.

2017-10-01

Nonlinear optics and polymer systems are distinct fields that have been studied for decades. These two fields intersect with the observation of nonlinear wave propagation in photoreactive polymer systems. This has led to studies on the nonlinear dynamics of transmitted light in polymer media, particularly for optical self-trapping and optical modulation instability. The irreversibility of polymerization leads to permanent capture of nonlinear optical patterns in the polymer structure, which is a new synthetic route to complex structured soft materials. Over time more intricate polymer systems are employed, whereby nonlinear optical dynamics can couple to nonlinear chemical dynamics, opening opportunities for self-organization. This paper discusses the work to date on nonlinear optical pattern formation processes in polymers. A brief overview of nonlinear optical phenomenon is provided to set the stage for understanding their effects. We review the accomplishments of the field on studying nonlinear waveform propagation in photopolymerizable systems, then discuss our most recent progress in coupling nonlinear optical pattern formation to polymer blends and phase separation. To this end, perspectives on future directions and areas of sustained inquiry are provided. This review highlights the significant opportunity in exploiting nonlinear optical pattern formation in soft matter for the discovery of new light-directed and light-stimulated materials phenomenon, and in turn, soft matter provides a platform by which new nonlinear optical phenomenon may be discovered.

Complexity and health professions education: a basic glossary.

PubMed

Mennin, Stewart

2010-08-01

The study of health professions education in the context of complexity science and complex adaptive systems involves different concepts and terminology that are likely to be unfamiliar to many health professions educators. A list of selected key terms and definitions from the literature of complexity science is provided to assist readers to navigate familiar territory from a different perspective. include agent, attractor, bifurcation, chaos, co-evolution, collective variable, complex adaptive systems, complexity science, deterministic systems, dynamical system, edge of chaos, emergence, equilibrium, far from equilibrium, fuzzy boundaries, linear system, non-linear system, random, self-organization and self-similarity.

Investigation of complexity dynamics in a DC glow discharge magnetized plasma using recurrence quantification analysis

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mitra, Vramori; Sarma, Bornali; Sarma, Arun

Recurrence is an ubiquitous feature which provides deep insights into the dynamics of real dynamical systems. A suitable tool for investigating recurrences is recurrence quantification analysis (RQA). It allows, e.g., the detection of regime transitions with respect to varying control parameters. We investigate the complexity of different coexisting nonlinear dynamical regimes of the plasma floating potential fluctuations at different magnetic fields and discharge voltages by using recurrence quantification variables, in particular, DET, L{sub max}, and Entropy. The recurrence analysis reveals that the predictability of the system strongly depends on discharge voltage. Furthermore, the persistent behaviour of the plasma time seriesmore » is characterized by the Detrended fluctuation analysis technique to explore the complexity in terms of long range correlation. The enhancement of the discharge voltage at constant magnetic field increases the nonlinear correlations; hence, the complexity of the system decreases, which corroborates the RQA analysis.« less

Complex Nonlinear Dynamic System of Oligopolies Price Game with Heterogeneous Players Under Noise

NASA Astrophysics Data System (ADS)

Liu, Feng; Li, Yaguang

A nonlinear four oligopolies price game with heterogeneous players, that are boundedly rational and adaptive, is built using two different special demand costs. Based on the theory of complex discrete dynamical system, the stability and the existing equilibrium point are investigated. The complex dynamic behavior is presented via bifurcation diagrams, the Lyapunov exponents to show equilibrium state, bifurcation and chaos with the variation in parameters. As disturbance is ubiquitous in economic systems, this paper focuses on the analysis of delay feedback control method under noise circumstances. Stable dynamics is confirmed to depend mainly on the low price adjustment speed, and if all four players have limited opportunities to stabilize the market, the new adaptive player facing profits of scale are found to be higher than the incumbents of bounded rational.

Optical solitons, nonlinear self-adjointness and conservation laws for the cubic nonlinear Shrödinger's equation with repulsive delta potential

NASA Astrophysics Data System (ADS)

Baleanu, Dumitru; Inc, Mustafa; Aliyu, Aliyu Isa; Yusuf, Abdullahi

2017-11-01

In this paper, the complex envelope function ansatz method is used to acquire the optical solitons to the cubic nonlinear Shrödinger's equation with repulsive delta potential (δ-NLSE). The method reveals dark and bright optical solitons. The necessary constraint conditions which guarantee the existence of the solitons are also presented. We studied the δ-NLSE by analyzing a system of partial differential equations (PDEs) obtained by decomposing the equation into real and imaginary components. We derive the Lie point symmetry generators of the system and prove that the system is nonlinearly self-adjoint with an explicit form of a differential substitution satisfying the nonlinear self-adjoint condition. Then we use these facts to establish a set of conserved vectors for the system using the general Cls theorem presented by Ibragimov. Some interesting figures for the acquired solutions are also presented.

A linear framework for time-scale separation in nonlinear biochemical systems.

PubMed

Gunawardena, Jeremy

2012-01-01

Cellular physiology is implemented by formidably complex biochemical systems with highly nonlinear dynamics, presenting a challenge for both experiment and theory. Time-scale separation has been one of the few theoretical methods for distilling general principles from such complexity. It has provided essential insights in areas such as enzyme kinetics, allosteric enzymes, G-protein coupled receptors, ion channels, gene regulation and post-translational modification. In each case, internal molecular complexity has been eliminated, leading to rational algebraic expressions among the remaining components. This has yielded familiar formulas such as those of Michaelis-Menten in enzyme kinetics, Monod-Wyman-Changeux in allostery and Ackers-Johnson-Shea in gene regulation. Here we show that these calculations are all instances of a single graph-theoretic framework. Despite the biochemical nonlinearity to which it is applied, this framework is entirely linear, yet requires no approximation. We show that elimination of internal complexity is feasible when the relevant graph is strongly connected. The framework provides a new methodology with the potential to subdue combinatorial explosion at the molecular level.

Two Studies of Complex Nonlinear Systems: Engineered Granular Crystals and Coarse-Graining Optimization Problems

NASA Astrophysics Data System (ADS)

Pozharskiy, Dmitry

In recent years a nonlinear, acoustic metamaterial, named granular crystals, has gained prominence due to its high accessibility, both experimentally and computationally. The observation of a wide range of dynamical phenomena in the system, due to its inherent nonlinearities, has suggested its importance in many engineering applications related to wave propagation. In the first part of this dissertation, we explore the nonlinear dynamics of damped-driven granular crystals. In one case, we consider a highly nonlinear setting, also known as a sonic vacuum, and derive a nonlinear analogue of a linear spectrum, corresponding to resonant periodic propagation and antiresonances. Experimental studies confirm the computational findings and the assimilation of experimental data into a numerical model is demonstrated. In the second case, global bifurcations in a precompressed granular crystal are examined, and their involvement in the appearance of chaotic dynamics is demonstrated. Both results highlight the importance of exploring the nonlinear dynamics, to gain insight into how a granular crystal responds to different external excitations. In the second part, we borrow established ideas from coarse-graining of dynamical systems, and extend them to optimization problems. We combine manifold learning algorithms, such as Diffusion Maps, with stochastic optimization methods, such as Simulated Annealing, and show that we can retrieve an ensemble, of few, important parameters that should be explored in detail. This framework can lead to acceleration of convergence when dealing with complex, high-dimensional optimization, and could potentially be applied to design engineered granular crystals.

From embodied mind to embodied robotics: humanities and system theoretical aspects.

PubMed

Mainzer, Klaus

2009-01-01

After an introduction (1) the article analyzes the evolution of the embodied mind (2), the innovation of embodied robotics (3), and finally discusses conclusions of embodied robotics for human responsibility (4). Considering the evolution of the embodied mind (2), we start with an introduction of complex systems and nonlinear dynamics (2.1), apply this approach to neural self-organization (2.2), distinguish degrees of complexity of the brain (2.3), explain the emergence of cognitive states by complex systems dynamics (2.4), and discuss criteria for modeling the brain as complex nonlinear system (2.5). The innovation of embodied robotics (3) is a challenge of future technology. We start with the distinction of symbolic and embodied AI (3.1) and explain embodied robots as dynamical systems (3.2). Self-organization needs self-control of technical systems (3.3). Cellular neural networks (CNN) are an example of self-organizing technical systems offering new avenues for neurobionics (3.4). In general, technical neural networks support different kinds of learning robots (3.5). Finally, embodied robotics aim at the development of cognitive and conscious robots (3.6).

A SPATIALLY EXPLICIT HIERARCHICAL APPROACH TO MODELING COMPLEX ECOLOGICAL SYSTEMS: THEORY AND APPLICATIONS. (R827676)

EPA Science Inventory

Ecological systems are generally considered among the most complex because they are characterized by a large number of diverse components, nonlinear interactions, scale multiplicity, and spatial heterogeneity. Hierarchy theory, as well as empirical evidence, suggests that comp...

Application of Nonlinear Systems Inverses to Automatic Flight Control Design: System Concepts and Flight Evaluations

NASA Technical Reports Server (NTRS)

Meyer, G.; Cicolani, L.

1981-01-01

A practical method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented. The method is effective for a large class of dynamic systems requiring multi-axis control which have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. It exploits the concept of inverse dynamic systems, and an algorithm for the construction of inverse is given. A hierarchic structure for the total control logic with inverses is presented. The method is illustrated with an application to the Augmentor Wing Jet STOL Research Aircraft equipped with a digital flight control system. Results of flight evaluation of the control concept on this aircraft are presented.

Dynamic control and information processing in chemical reaction systems by tuning self-organization behavior

NASA Astrophysics Data System (ADS)

Lebiedz, Dirk; Brandt-Pollmann, Ulrich

2004-09-01

Specific external control of chemical reaction systems and both dynamic control and signal processing as central functions in biochemical reaction systems are important issues of modern nonlinear science. For example nonlinear input-output behavior and its regulation are crucial for the maintainance of the life process that requires extensive communication between cells and their environment. An important question is how the dynamical behavior of biochemical systems is controlled and how they process information transmitted by incoming signals. But also from a general point of view external forcing of complex chemical reaction processes is important in many application areas ranging from chemical engineering to biomedicine. In order to study such control issues numerically, here, we choose a well characterized chemical system, the CO oxidation on Pt(110), which is interesting per se as an externally forced chemical oscillator model. We show numerically that tuning of temporal self-organization by input signals in this simple nonlinear chemical reaction exhibiting oscillatory behavior can in principle be exploited for both specific external control of dynamical system behavior and processing of complex information.

Sequential state estimation of nonlinear/non-Gaussian systems with stochastic input for turbine degradation estimation

NASA Astrophysics Data System (ADS)

Hanachi, Houman; Liu, Jie; Banerjee, Avisekh; Chen, Ying

2016-05-01

Health state estimation of inaccessible components in complex systems necessitates effective state estimation techniques using the observable variables of the system. The task becomes much complicated when the system is nonlinear/non-Gaussian and it receives stochastic input. In this work, a novel sequential state estimation framework is developed based on particle filtering (PF) scheme for state estimation of general class of nonlinear dynamical systems with stochastic input. Performance of the developed framework is then validated with simulation on a Bivariate Non-stationary Growth Model (BNGM) as a benchmark. In the next step, three-year operating data of an industrial gas turbine engine (GTE) are utilized to verify the effectiveness of the developed framework. A comprehensive thermodynamic model for the GTE is therefore developed to formulate the relation of the observable parameters and the dominant degradation symptoms of the turbine, namely, loss of isentropic efficiency and increase of the mass flow. The results confirm the effectiveness of the developed framework for simultaneous estimation of multiple degradation symptoms in complex systems with noisy measured inputs.

Nonlinear channel equalization for QAM signal constellation using artificial neural networks.

PubMed

Patra, J C; Pal, R N; Baliarsingh, R; Panda, G

1999-01-01

Application of artificial neural networks (ANN's) to adaptive channel equalization in a digital communication system with 4-QAM signal constellation is reported in this paper. A novel computationally efficient single layer functional link ANN (FLANN) is proposed for this purpose. This network has a simple structure in which the nonlinearity is introduced by functional expansion of the input pattern by trigonometric polynomials. Because of input pattern enhancement, the FLANN is capable of forming arbitrarily nonlinear decision boundaries and can perform complex pattern classification tasks. Considering channel equalization as a nonlinear classification problem, the FLANN has been utilized for nonlinear channel equalization. The performance of the FLANN is compared with two other ANN structures [a multilayer perceptron (MLP) and a polynomial perceptron network (PPN)] along with a conventional linear LMS-based equalizer for different linear and nonlinear channel models. The effect of eigenvalue ratio (EVR) of input correlation matrix on the equalizer performance has been studied. The comparison of computational complexity involved for the three ANN structures is also provided.

Structural Evolutions of STOCK Markets Controlled by Generalized Entropy Principles of Complex Systems

NASA Astrophysics Data System (ADS)

Wang, Yi Jiao; Feng, Qing Yi; Chai, Li He

As one of the most important financial markets and one of the main parts of economic system, the stock market has become the research focus in economics. The stock market is a typical complex open system far from equilibrium. Many available models that make huge contribution to researches on market are strong in describing the market however, ignoring strong nonlinear interactions among active agents and weak in reveal underlying dynamic mechanisms of structural evolutions of market. From econophysical perspectives, this paper analyzes the complex interactions among agents and defines the generalized entropy in stock markets. Nonlinear evolutionary dynamic equation for the stock markets is then derived from Maximum Generalized Entropy Principle. Simulations are accordingly conducted for a typical case with the given data, by which the structural evolution of the stock market system is demonstrated. Some discussions and implications are finally provided.

Data-based virtual unmodeled dynamics driven multivariable nonlinear adaptive switching control.

PubMed

Chai, Tianyou; Zhang, Yajun; Wang, Hong; Su, Chun-Yi; Sun, Jing

2011-12-01

For a complex industrial system, its multivariable and nonlinear nature generally make it very difficult, if not impossible, to obtain an accurate model, especially when the model structure is unknown. The control of this class of complex systems is difficult to handle by the traditional controller designs around their operating points. This paper, however, explores the concepts of controller-driven model and virtual unmodeled dynamics to propose a new design framework. The design consists of two controllers with distinct functions. First, using input and output data, a self-tuning controller is constructed based on a linear controller-driven model. Then the output signals of the controller-driven model are compared with the true outputs of the system to produce so-called virtual unmodeled dynamics. Based on the compensator of the virtual unmodeled dynamics, the second controller based on a nonlinear controller-driven model is proposed. Those two controllers are integrated by an adaptive switching control algorithm to take advantage of their complementary features: one offers stabilization function and another provides improved performance. The conditions on the stability and convergence of the closed-loop system are analyzed. Both simulation and experimental tests on a heavily coupled nonlinear twin-tank system are carried out to confirm the effectiveness of the proposed method.

Resonant tunneling via a Ru-dye complex using a nanoparticle bridge junction.

PubMed

Nishijima, Satoshi; Otsuka, Yoichi; Ohoyama, Hiroshi; Kajimoto, Kentaro; Araki, Kento; Matsumoto, Takuya

2018-06-15

Nonlinear current-voltage (I-V) characteristics is an important property for the realization of information processing in molecular electronics. We studied the electrical conduction through a Ru-dye complex (N-719) on a 2-aminoethanethiol (2-AET) monolayer in a nanoparticle bridge junction system. The nonlinear I-V characteristics exhibited a threshold voltage at around 1.2 V and little temperature dependence. From the calculation of the molecular states using density functional theory and the energy alignment between the electrodes and molecules, the conduction mechanism in this system was considered to be resonant tunneling via the HOMO level of N-719. Our results indicate that the weak electronic coupling of electrodes and molecules is essential for obtaining nonlinear I-V characteristics with a clear threshold voltage that reflect the intrinsic molecular state.

Resonant tunneling via a Ru–dye complex using a nanoparticle bridge junction

NASA Astrophysics Data System (ADS)

Nishijima, Satoshi; Otsuka, Yoichi; Ohoyama, Hiroshi; Kajimoto, Kentaro; Araki, Kento; Matsumoto, Takuya

2018-06-01

Nonlinear current–voltage (I–V) characteristics is an important property for the realization of information processing in molecular electronics. We studied the electrical conduction through a Ru–dye complex (N-719) on a 2-aminoethanethiol (2-AET) monolayer in a nanoparticle bridge junction system. The nonlinear I–V characteristics exhibited a threshold voltage at around 1.2 V and little temperature dependence. From the calculation of the molecular states using density functional theory and the energy alignment between the electrodes and molecules, the conduction mechanism in this system was considered to be resonant tunneling via the HOMO level of N-719. Our results indicate that the weak electronic coupling of electrodes and molecules is essential for obtaining nonlinear I–V characteristics with a clear threshold voltage that reflect the intrinsic molecular state.

Complex Riccati equations as a link between different approaches for the description of dissipative and irreversible systems

NASA Astrophysics Data System (ADS)

Schuch, Dieter

2012-08-01

Quantum mechanics is essentially described in terms of complex quantities like wave functions. The interesting point is that phase and amplitude of the complex wave function are not independent of each other, but coupled by some kind of conservation law. This coupling exists in time-independent quantum mechanics and has a counterpart in its time-dependent form. It can be traced back to a reformulation of quantum mechanics in terms of nonlinear real Ermakov equations or equivalent complex nonlinear Riccati equations, where the quadratic term in the latter equation explains the origin of the phase-amplitude coupling. Since realistic physical systems are always in contact with some kind of environment this aspect is also taken into account. In this context, different approaches for describing open quantum systems, particularly effective ones, are discussed and compared. Certain kinds of nonlinear modifications of the Schrödinger equation are discussed as well as their interrelations and their relations to linear approaches via non-unitary transformations. The modifications of the aforementioned Ermakov and Riccati equations when environmental effects are included can be determined in the time-dependent case. From formal similarities conclusions can be drawn how the equations of time-independent quantum mechanics can be modified to also incluce the enviromental aspects.

Weighted fractional permutation entropy and fractional sample entropy for nonlinear Potts financial dynamics

NASA Astrophysics Data System (ADS)

Xu, Kaixuan; Wang, Jun

2017-02-01

In this paper, recently introduced permutation entropy and sample entropy are further developed to the fractional cases, weighted fractional permutation entropy (WFPE) and fractional sample entropy (FSE). The fractional order generalization of information entropy is utilized in the above two complexity approaches, to detect the statistical characteristics of fractional order information in complex systems. The effectiveness analysis of proposed methods on the synthetic data and the real-world data reveals that tuning the fractional order allows a high sensitivity and more accurate characterization to the signal evolution, which is useful in describing the dynamics of complex systems. Moreover, the numerical research on nonlinear complexity behaviors is compared between the returns series of Potts financial model and the actual stock markets. And the empirical results confirm the feasibility of the proposed model.

Social complexity, modernity and suicide: an assessment of Durkheim's suicide from the perspective of a non-linear analysis of complex social systems.

PubMed

Condorelli, Rosalia

2016-01-01

Can we share even today the same vision of modernity which Durkheim left us by its suicide analysis? or can society 'surprise us'? The answer to these questions can be inspired by several studies which found that beginning the second half of the twentieth century suicides in western countries more industrialized and modernized do not increase in a constant, linear way as modernization and social fragmentation process increases, as well as Durkheim's theory seems to lead us to predict. Despite continued modernizing process, they found stabilizing or falling overall suicide rate trends. Therefore, a gradual process of adaptation to the stress of modernization associated to low social integration levels seems to be activated in modern society. Assuming this perspective, the paper highlights as this tendency may be understood in the light of the new concept of social systems as complex adaptive systems, systems which are able to adapt to environmental perturbations and generate as a whole surprising, emergent effects due to nonlinear interactions among their components. So, in the frame of Nonlinear Dynamical System Modeling, we formalize the logic of suicide decision-making process responsible for changes at aggregate level in suicide growth rates by a nonlinear differential equation structured in a logistic way, and in so doing we attempt to capture the mechanism underlying the change process in suicide growth rate and to test the hypothesis that system's dynamics exhibits a restrained increase process as expression of an adaptation process to the liquidity of social ties in modern society. In particular, a Nonlinear Logistic Map is applied to suicide data in a modern society such as the Italian one from 1875 to 2010. The analytic results, seeming to confirm the idea of the activation of an adaptation process to the liquidity of social ties, constitutes an opportunity for a more general reflection on the current configuration of modern society, by relating the Durkheimian Theory with the Halbwachs' Theory and most current visions of modernity such as the Baumanian one. Complexity completes the interpretative framework by rooting the generating mechanism of adaptation process in the precondition of a new General Theory of Systems making the non linearity property of social system's interactions and surprise the functioning and evolution rule of social systems.

Coping with the Bounds: Speculations on Nonlinearity in Military Affairs

DTIC Science & Technology

2003-08-01

organizing criticality, cellular automata, solitons, and so on–because they all globally share this property . Nonlinearity reflects the science of the...Why does it matter? One rea- son for emphasizing nonlinearity is that it constitutes the well-established mathematical property underlying and making...have some hints as to what those principles might be.3 Complex adaptive systems, or cas, contain seven basic attributes. These consist of four properties

Asymmetric Rogue Waves, Breather-to-Soliton Conversion, and Nonlinear Wave Interactions in the Hirota-Maxwell-Bloch System

NASA Astrophysics Data System (ADS)

Wang, Lei; Zhu, Yu-Jie; Wang, Zi-Qi; Xu, Tao; Qi, Feng-Hua; Xue, Yu-Shan

2016-02-01

We study the nonlinear localized waves on constant backgrounds of the Hirota-Maxwell-Bloch (HMB) system arising from the erbium doped fibers. We derive the asymmetric breather, rogue wave (RW) and semirational solutions of the HMB system. We show that the breather and RW solutions can be converted into various soliton solutions. Under different conditions of parameters, we calculate the locus of the eigenvalues on the complex plane which converts the breathers or RWs into solitons. Based on the second-order solutions, we investigate the interactions among different types of nonlinear waves including the breathers, RWs and solitons.

Nonlinear dynamics in ecosystem response to climatic change: Case studies and policy implications

USGS Publications Warehouse

Burkett, Virginia R.; Wilcox, Douglas A.; Stottlemyer, Robert; Barrow, Wylie; Fagre, Dan; Baron, Jill S.; Price, Jeff; Nielsen, Jennifer L.; Allen, Craig D.; Peterson, David L.; Ruggerone, Greg; Doyle, Thomas

2005-01-01

Many biological, hydrological, and geological processes are interactively linked in ecosystems. These ecological phenomena normally vary within bounded ranges, but rapid, nonlinear changes to markedly different conditions can be triggered by even small differences if threshold values are exceeded. Intrinsic and extrinsic ecological thresholds can lead to effects that cascade among systems, precluding accurate modeling and prediction of system response to climate change. Ten case studies from North America illustrate how changes in climate can lead to rapid, threshold-type responses within ecological communities; the case studies also highlight the role of human activities that alter the rate or direction of system response to climate change. Understanding and anticipating nonlinear dynamics are important aspects of adaptation planning since responses of biological resources to changes in the physical climate system are not necessarily proportional and sometimes, as in the case of complex ecological systems, inherently nonlinear.

Complex and unexpected dynamics in simple genetic regulatory networks

NASA Astrophysics Data System (ADS)

Borg, Yanika; Ullner, Ekkehard; Alagha, Afnan; Alsaedi, Ahmed; Nesbeth, Darren; Zaikin, Alexey

2014-03-01

One aim of synthetic biology is to construct increasingly complex genetic networks from interconnected simpler ones to address challenges in medicine and biotechnology. However, as systems increase in size and complexity, emergent properties lead to unexpected and complex dynamics due to nonlinear and nonequilibrium properties from component interactions. We focus on four different studies of biological systems which exhibit complex and unexpected dynamics. Using simple synthetic genetic networks, small and large populations of phase-coupled quorum sensing repressilators, Goodwin oscillators, and bistable switches, we review how coupled and stochastic components can result in clustering, chaos, noise-induced coherence and speed-dependent decision making. A system of repressilators exhibits oscillations, limit cycles, steady states or chaos depending on the nature and strength of the coupling mechanism. In large repressilator networks, rich dynamics can also be exhibited, such as clustering and chaos. In populations of Goodwin oscillators, noise can induce coherent oscillations. In bistable systems, the speed with which incoming external signals reach steady state can bias the network towards particular attractors. These studies showcase the range of dynamical behavior that simple synthetic genetic networks can exhibit. In addition, they demonstrate the ability of mathematical modeling to analyze nonlinearity and inhomogeneity within these systems.

A Tribute to J. C. Sprott

NASA Astrophysics Data System (ADS)

Nazarimehr, Fahimeh; Jafari, Sajad; Chen, Guanrong; Kapitaniak, Tomasz; Kuznetsov, Nikolay V.; Leonov, Gennady A.; Li, Chunbiao; Wei, Zhouchao

2017-12-01

In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems, nonautonomous systems, partial differential equations, fractional-order systems, delay differential systems, spatiotemporal systems, artificial neural networks, and chaotic electrical circuits. He has also studied dynamical properties of complex systems such as bifurcations and basins of attraction. He has done work on generating fractal art. He has examined models of real-world systems that exhibit chaos. The second group of his works comprise control and synchronization of chaos. Finally, the third group is extracting dynamical properties of systems using time-series analysis. This paper highlights the impact of Sprott’s work on the promotion of nonlinear dynamics.

Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

PubMed Central

Li, YuHui; Jin, FeiTeng

2017-01-01

The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller. PMID:29410680

Multistage Spectral Relaxation Method for Solving the Hyperchaotic Complex Systems

PubMed Central

Saberi Nik, Hassan; Rebelo, Paulo

2014-01-01

We present a pseudospectral method application for solving the hyperchaotic complex systems. The proposed method, called the multistage spectral relaxation method (MSRM) is based on a technique of extending Gauss-Seidel type relaxation ideas to systems of nonlinear differential equations and using the Chebyshev pseudospectral methods to solve the resulting system on a sequence of multiple intervals. In this new application, the MSRM is used to solve famous hyperchaotic complex systems such as hyperchaotic complex Lorenz system and the complex permanent magnet synchronous motor. We compare this approach to the Runge-Kutta based ode45 solver to show that the MSRM gives accurate results. PMID:25386624

Modeling the pressure-strain correlation of turbulence: An invariant dynamical systems approach

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu; Gatski, Thomas B.

1990-01-01

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Modelling the pressure-strain correlation of turbulence - An invariant dynamical systems approach

NASA Technical Reports Server (NTRS)

Speziale, Charles G.; Sarkar, Sutanu; Gatski, Thomas B.

1991-01-01

The modeling of the pressure-strain correlation of turbulence is examined from a basic theoretical standpoint with a view toward developing improved second-order closure models. Invariance considerations along with elementary dynamical systems theory are used in the analysis of the standard hierarchy of closure models. In these commonly used models, the pressure-strain correlation is assumed to be a linear function of the mean velocity gradients with coefficients that depend algebraically on the anisotropy tensor. It is proven that for plane homogeneous turbulent flows the equilibrium structure of this hierarchy of models is encapsulated by a relatively simple model which is only quadratically nonlinear in the anisotropy tensor. This new quadratic model - the SSG model - is shown to outperform the Launder, Reece, and Rodi model (as well as more recent models that have a considerably more complex nonlinear structure) in a variety of homogeneous turbulent flows. Some deficiencies still remain for the description of rotating turbulent shear flows that are intrinsic to this general hierarchy of models and, hence, cannot be overcome by the mere introduction of more complex nonlinearities. It is thus argued that the recent trend of adding substantially more complex nonlinear terms containing the anisotropy tensor may be of questionable value in the modeling of the pressure-strain correlation. Possible alternative approaches are discussed briefly.

Complex behavior in chains of nonlinear oscillators.

PubMed

Alonso, Leandro M

2017-06-01

This article outlines sufficient conditions under which a one-dimensional chain of identical nonlinear oscillators can display complex spatio-temporal behavior. The units are described by phase equations and consist of excitable oscillators. The interactions are local and the network is poised to a critical state by balancing excitation and inhibition locally. The results presented here suggest that in networks composed of many oscillatory units with local interactions, excitability together with balanced interactions is sufficient to give rise to complex emergent features. For values of the parameters where complex behavior occurs, the system also displays a high-dimensional bifurcation where an exponentially large number of equilibria are borne in pairs out of multiple saddle-node bifurcations.

Memetic computing through bio-inspired heuristics integration with sequential quadratic programming for nonlinear systems arising in different physical models.

PubMed

Raja, Muhammad Asif Zahoor; Kiani, Adiqa Kausar; Shehzad, Azam; Zameer, Aneela

2016-01-01

In this study, bio-inspired computing is exploited for solving system of nonlinear equations using variants of genetic algorithms (GAs) as a tool for global search method hybrid with sequential quadratic programming (SQP) for efficient local search. The fitness function is constructed by defining the error function for systems of nonlinear equations in mean square sense. The design parameters of mathematical models are trained by exploiting the competency of GAs and refinement are carried out by viable SQP algorithm. Twelve versions of the memetic approach GA-SQP are designed by taking a different set of reproduction routines in the optimization process. Performance of proposed variants is evaluated on six numerical problems comprising of system of nonlinear equations arising in the interval arithmetic benchmark model, kinematics, neurophysiology, combustion and chemical equilibrium. Comparative studies of the proposed results in terms of accuracy, convergence and complexity are performed with the help of statistical performance indices to establish the worth of the schemes. Accuracy and convergence of the memetic computing GA-SQP is found better in each case of the simulation study and effectiveness of the scheme is further established through results of statistics based on different performance indices for accuracy and complexity.

Multiscale asymmetric orthogonal wavelet kernel for linear programming support vector learning and nonlinear dynamic systems identification.

PubMed

Lu, Zhao; Sun, Jing; Butts, Kenneth

2014-05-01

Support vector regression for approximating nonlinear dynamic systems is more delicate than the approximation of indicator functions in support vector classification, particularly for systems that involve multitudes of time scales in their sampled data. The kernel used for support vector learning determines the class of functions from which a support vector machine can draw its solution, and the choice of kernel significantly influences the performance of a support vector machine. In this paper, to bridge the gap between wavelet multiresolution analysis and kernel learning, the closed-form orthogonal wavelet is exploited to construct new multiscale asymmetric orthogonal wavelet kernels for linear programming support vector learning. The closed-form multiscale orthogonal wavelet kernel provides a systematic framework to implement multiscale kernel learning via dyadic dilations and also enables us to represent complex nonlinear dynamics effectively. To demonstrate the superiority of the proposed multiscale wavelet kernel in identifying complex nonlinear dynamic systems, two case studies are presented that aim at building parallel models on benchmark datasets. The development of parallel models that address the long-term/mid-term prediction issue is more intricate and challenging than the identification of series-parallel models where only one-step ahead prediction is required. Simulation results illustrate the effectiveness of the proposed multiscale kernel learning.

Investigation of a mathematical model of the system of electro-optical sensors for monitoring nonlinear surfaces

NASA Astrophysics Data System (ADS)

Petrochenko, Andrew V.; Konyakhin, Igor A.

2015-06-01

Actually during construction of the high building actively are used objects of various nonlinear surface, for example, sinuous (parabolic or hyperbolic) roofs of the sport complexes that require automatic deformation control [1,2,3,4]. This type of deformation has character of deflection that is impossible to monitor objectively with just one optoelectronic sensor (which is fixed on this surface). In this article is described structure of remote optoelectronic sensor, which is part of the optoelectronic monitoring system of nonlinear surface, and mathematical transformation of exterior orientation sensor elements in the coordinates of control points.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wang, Shi-bing, E-mail: wang-shibing@dlut.edu.cn, E-mail: wangxy@dlut.edu.cn; Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024; Wang, Xing-yuan, E-mail: wang-shibing@dlut.edu.cn, E-mail: wangxy@dlut.edu.cn

With comprehensive consideration of generalized synchronization, combination synchronization and adaptive control, this paper investigates a novel adaptive generalized combination complex synchronization (AGCCS) scheme for different real and complex nonlinear systems with unknown parameters. On the basis of Lyapunov stability theory and adaptive control, an AGCCS controller and parameter update laws are derived to achieve synchronization and parameter identification of two real drive systems and a complex response system, as well as two complex drive systems and a real response system. Two simulation examples, namely, ACGCS for chaotic real Lorenz and Chen systems driving a hyperchaotic complex Lü system, and hyperchaoticmore » complex Lorenz and Chen systems driving a real chaotic Lü system, are presented to verify the feasibility and effectiveness of the proposed scheme.« less

Nonlinear channelizer.

PubMed

In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D; Leung, Daniel; Liu, Norman; Meadows, Brian K; Gordon, Frank; Bulsara, Adi R; Palacios, Antonio

2012-12-01

The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.

TEMPERATURE SENSITIVITY OF SOIL RESPIRATION AND ITS EFFECTS ON ECOSYSTEM CARBON BUDGET: NONLINEARITY BEGETS SURPRISES. (R827676)

EPA Science Inventory

Nonlinearity is a salient feature in all complex systems, and it certainly characterizes biogeochemical cycles in ecosystems across a wide range of scales. Soil carbon emission is a major source of uncertainty in estimating the terrestrial carbon budget at the ecosystem level ...

Computational Nonlinear Morphology with Emphasis on Semitic Languages. Studies in Natural Language Processing.

ERIC Educational Resources Information Center

Kiraz, George Anton

This book presents a tractable computational model that can cope with complex morphological operations, especially in Semitic languages, and less complex morphological systems present in Western languages. It outlines a new generalized regular rewrite rule system that uses multiple finite-state automata to cater to root-and-pattern morphology,…

Retrieving hydrological connectivity from empirical causality in karst systems

NASA Astrophysics Data System (ADS)

Delforge, Damien; Vanclooster, Marnik; Van Camp, Michel; Poulain, Amaël; Watlet, Arnaud; Hallet, Vincent; Kaufmann, Olivier; Francis, Olivier

2017-04-01

Because of their complexity, karst systems exhibit nonlinear dynamics. Moreover, if one attempts to model a karst, the hidden behavior complicates the choice of the most suitable model. Therefore, both intense investigation methods and nonlinear data analysis are needed to reveal the underlying hydrological connectivity as a prior for a consistent physically based modelling approach. Convergent Cross Mapping (CCM), a recent method, promises to identify causal relationships between time series belonging to the same dynamical systems. The method is based on phase space reconstruction and is suitable for nonlinear dynamics. As an empirical causation detection method, it could be used to highlight the hidden complexity of a karst system by revealing its inner hydrological and dynamical connectivity. Hence, if one can link causal relationships to physical processes, the method should show great potential to support physically based model structure selection. We present the results of numerical experiments using karst model blocks combined in different structures to generate time series from actual rainfall series. CCM is applied between the time series to investigate if the empirical causation detection is consistent with the hydrological connectivity suggested by the karst model.

Comparing and improving proper orthogonal decomposition (POD) to reduce the complexity of groundwater models

NASA Astrophysics Data System (ADS)

Gosses, Moritz; Nowak, Wolfgang; Wöhling, Thomas

2017-04-01

Physically-based modeling is a wide-spread tool in understanding and management of natural systems. With the high complexity of many such models and the huge amount of model runs necessary for parameter estimation and uncertainty analysis, overall run times can be prohibitively long even on modern computer systems. An encouraging strategy to tackle this problem are model reduction methods. In this contribution, we compare different proper orthogonal decomposition (POD, Siade et al. (2010)) methods and their potential applications to groundwater models. The POD method performs a singular value decomposition on system states as simulated by the complex (e.g., PDE-based) groundwater model taken at several time-steps, so-called snapshots. The singular vectors with the highest information content resulting from this decomposition are then used as a basis for projection of the system of model equations onto a subspace of much lower dimensionality than the original complex model, thereby greatly reducing complexity and accelerating run times. In its original form, this method is only applicable to linear problems. Many real-world groundwater models are non-linear, tough. These non-linearities are introduced either through model structure (unconfined aquifers) or boundary conditions (certain Cauchy boundaries, like rivers with variable connection to the groundwater table). To date, applications of POD focused on groundwater models simulating pumping tests in confined aquifers with constant head boundaries. In contrast, POD model reduction either greatly looses accuracy or does not significantly reduce model run time if the above-mentioned non-linearities are introduced. We have also found that variable Dirichlet boundaries are problematic for POD model reduction. An extension to the POD method, called POD-DEIM, has been developed for non-linear groundwater models by Stanko et al. (2016). This method uses spatial interpolation points to build the equation system in the reduced model space, thereby allowing the recalculation of system matrices at every time-step necessary for non-linear models while retaining the speed of the reduced model. This makes POD-DEIM applicable for groundwater models simulating unconfined aquifers. However, in our analysis, the method struggled to reproduce variable river boundaries accurately and gave no advantage for variable Dirichlet boundaries compared to the original POD method. We have developed another extension for POD that targets to address these remaining problems by performing a second POD operation on the model matrix on the left-hand side of the equation. The method aims to at least reproduce the accuracy of the other methods where they are applicable while outperforming them for setups with changing river boundaries or variable Dirichlet boundaries. We compared the new extension with original POD and POD-DEIM for different combinations of model structures and boundary conditions. The new method shows the potential of POD extensions for applications to non-linear groundwater systems and complex boundary conditions that go beyond the current, relatively limited range of applications. References: Siade, A. J., Putti, M., and Yeh, W. W.-G. (2010). Snapshot selection for groundwater model reduction using proper orthogonal decomposition. Water Resour. Res., 46(8):W08539. Stanko, Z. P., Boyce, S. E., and Yeh, W. W.-G. (2016). Nonlinear model reduction of unconfined groundwater flow using pod and deim. Advances in Water Resources, 97:130 - 143.

Analysis of friction and instability by the centre manifold theory for a non-linear sprag-slip model

NASA Astrophysics Data System (ADS)

Sinou, J.-J.; Thouverez, F.; Jezequel, L.

2003-08-01

This paper presents the research devoted to the study of instability phenomena in non-linear model with a constant brake friction coefficient. Indeed, the impact of unstable oscillations can be catastrophic. It can cause vehicle control problems and component degradation. Accordingly, complex stability analysis is required. This paper outlines stability analysis and centre manifold approach for studying instability problems. To put it more precisely, one considers brake vibrations and more specifically heavy trucks judder where the dynamic characteristics of the whole front axle assembly is concerned, even if the source of judder is located in the brake system. The modelling introduces the sprag-slip mechanism based on dynamic coupling due to buttressing. The non-linearity is expressed as a polynomial with quadratic and cubic terms. This model does not require the use of brake negative coefficient, in order to predict the instability phenomena. Finally, the centre manifold approach is used to obtain equations for the limit cycle amplitudes. The centre manifold theory allows the reduction of the number of equations of the original system in order to obtain a simplified system, without loosing the dynamics of the original system as well as the contributions of non-linear terms. The goal is the study of the stability analysis and the validation of the centre manifold approach for a complex non-linear model by comparing results obtained by solving the full system and by using the centre manifold approach. The brake friction coefficient is used as an unfolding parameter of the fundamental Hopf bifurcation point.

Ecological resilience

USGS Publications Warehouse

Allen, Craig R.; Garmestiani, Ahjond S.; Sundstrom, Shana; Angeler, David G.

2016-01-01

Resilience is the capacity of complex systems of people and nature to withstand disturbance without shifting into an alternate regime, or a different type of system organized around different processes and structures (Holling, 1973). Resilience theory was developed to explain the non-linear dynamics of complex adaptive systems, like social-ecological systems (SES) (Walker & Salt, 2006). It is often apparent when the resilience of a SES has been exceeded as the system discernibly changes, such as when a thriving city shifts into a poverty trap, but it is difficult to predict when that shift might occur because of the non-linear dynamics of complex systems. Ecological resilience should not be confused with engineering resilience (Angeler & Allen, 2016), which emphasizes the ability of a SES to perform a specific task consistently and predictably, and to re-establish performance quickly should a disturbance occur. Engineering resilience assumes that complex systems are characterized by a single equilibrium state, and this assumption is not appropriate for complex adaptive systems such as SES. In the risk governance context this means that compounded perturbations derived from hazards or global change can have unexpected and highly uncertain effects on natural resources, humans and societies. These effects can manifest in regime shifts, potentially spurring environmental degradation that might lock SES in an undesirable system state that can be difficult to reverse, and as a consequence economic crises, conflict, human health problems.

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Applications

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1998-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

Structure Detection of Nonlinear Aeroelastic Systems with Application to Aeroelastic Flight Test Data. Part 2

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Brenner, martin J.

2006-01-01

This viewgraph presentation reviews the 1. Motivation for the study 2. Nonlinear Model Form 3. Structure Detection 4. Least Absolute Shrinkage and Selection Operator (LASSO) 5. Objectives 6. Results 7. Assess LASSO as a Structure Detection Tool: Simulated Nonlinear Models 8. Applicability to Complex Systems: F/A-18 Active Aeroelastic Wing Flight Test Data. The authors conclude that 1. this is a novel approach for detecting the structure of highly over-parameterised nonlinear models in situations where other methods may be inadequate 2. that it is a practical significance in the analysis of aircraft dynamics during envelope expansion and could lead to more efficient control strategies and 3. this could allow greater insight into the functionality of various systems dynamics, by providing a quantitative model which is easily interpretable

A Multi-Resolution Nonlinear Mapping Technique for Design and Analysis Application

NASA Technical Reports Server (NTRS)

Phan, Minh Q.

1997-01-01

This report describes a nonlinear mapping technique where the unknown static or dynamic system is approximated by a sum of dimensionally increasing functions (one-dimensional curves, two-dimensional surfaces, etc.). These lower dimensional functions are synthesized from a set of multi-resolution basis functions, where the resolutions specify the level of details at which the nonlinear system is approximated. The basis functions also cause the parameter estimation step to become linear. This feature is taken advantage of to derive a systematic procedure to determine and eliminate basis functions that are less significant for the particular system under identification. The number of unknown parameters that must be estimated is thus reduced and compact models obtained. The lower dimensional functions (identified curves and surfaces) permit a kind of "visualization" into the complexity of the nonlinearity itself.

Cluster Synchronization of Diffusively Coupled Nonlinear Systems: A Contraction-Based Approach

NASA Astrophysics Data System (ADS)

Aminzare, Zahra; Dey, Biswadip; Davison, Elizabeth N.; Leonard, Naomi Ehrich

2018-04-01

Finding the conditions that foster synchronization in networked nonlinear systems is critical to understanding a wide range of biological and mechanical systems. However, the conditions proved in the literature for synchronization in nonlinear systems with linear coupling, such as has been used to model neuronal networks, are in general not strict enough to accurately determine the system behavior. We leverage contraction theory to derive new sufficient conditions for cluster synchronization in terms of the network structure, for a network where the intrinsic nonlinear dynamics of each node may differ. Our result requires that network connections satisfy a cluster-input-equivalence condition, and we explore the influence of this requirement on network dynamics. For application to networks of nodes with FitzHugh-Nagumo dynamics, we show that our new sufficient condition is tighter than those found in previous analyses that used smooth or nonsmooth Lyapunov functions. Improving the analytical conditions for when cluster synchronization will occur based on network configuration is a significant step toward facilitating understanding and control of complex networked systems.

Nonlinear dispersion effects in elastic plates: numerical modelling and validation

NASA Astrophysics Data System (ADS)

Kijanka, Piotr; Radecki, Rafal; Packo, Pawel; Staszewski, Wieslaw J.; Uhl, Tadeusz; Leamy, Michael J.

2017-04-01

Nonlinear features of elastic wave propagation have attracted significant attention recently. The particular interest herein relates to complex wave-structure interactions, which provide potential new opportunities for feature discovery and identification in a variety of applications. Due to significant complexity associated with wave propagation in nonlinear media, numerical modeling and simulations are employed to facilitate design and development of new measurement, monitoring and characterization systems. However, since very high spatio- temporal accuracy of numerical models is required, it is critical to evaluate their spectral properties and tune discretization parameters for compromise between accuracy and calculation time. Moreover, nonlinearities in structures give rise to various effects that are not present in linear systems, e.g. wave-wave interactions, higher harmonics generation, synchronism and | recently reported | shifts to dispersion characteristics. This paper discusses local computational model based on a new HYBRID approach for wave propagation in nonlinear media. The proposed approach combines advantages of the Local Interaction Simulation Approach (LISA) and Cellular Automata for Elastodynamics (CAFE). The methods are investigated in the context of their accuracy for predicting nonlinear wavefields, in particular shifts to dispersion characteristics for finite amplitude waves and secondary wavefields. The results are validated against Finite Element (FE) calculations for guided waves in copper plate. Critical modes i.e., modes determining accuracy of a model at given excitation frequency - are identified and guidelines for numerical model parameters are proposed.

Linear and Non-Linear Visual Feature Learning in Rat and Humans

PubMed Central

Bossens, Christophe; Op de Beeck, Hans P.

2016-01-01

The visual system processes visual input in a hierarchical manner in order to extract relevant features that can be used in tasks such as invariant object recognition. Although typically investigated in primates, recent work has shown that rats can be trained in a variety of visual object and shape recognition tasks. These studies did not pinpoint the complexity of the features used by these animals. Many tasks might be solved by using a combination of relatively simple features which tend to be correlated. Alternatively, rats might extract complex features or feature combinations which are nonlinear with respect to those simple features. In the present study, we address this question by starting from a small stimulus set for which one stimulus-response mapping involves a simple linear feature to solve the task while another mapping needs a well-defined nonlinear combination of simpler features related to shape symmetry. We verified computationally that the nonlinear task cannot be trivially solved by a simple V1-model. We show how rats are able to solve the linear feature task but are unable to acquire the nonlinear feature. In contrast, humans are able to use the nonlinear feature and are even faster in uncovering this solution as compared to the linear feature. The implications for the computational capabilities of the rat visual system are discussed. PMID:28066201

Market Orientation within University Schools of Business: Can a Dynamical Systems Viewpoint Applied to a Non-Temporal Data Set Yield Valuable Insights for University Managers?

ERIC Educational Resources Information Center

Cox, John C.; Webster, Robert L.; Hammond, Kevin L.

2009-01-01

This study investigates the use of using complexity theory--the study of nonlinear dynamical systems of which chaos and catastrophe theory are subsets--in the analysis of a non temporal data set to derive valuable insights into the functioning of university schools of business. The approach is unusual in that studies of nonlinearity in complex…

On the integration of a class of nonlinear systems of ordinary differential equations

NASA Astrophysics Data System (ADS)

Talyshev, Aleksandr A.

2017-11-01

For each associative, commutative, and unitary algebra over the field of real or complex numbers and an integrable nonlinear ordinary differential equation we can to construct integrable systems of ordinary differential equations and integrable systems of partial differential equations. In this paper we consider in some sense the inverse problem. Determine the conditions under which a given system of ordinary differential equations can be represented as a differential equation in some associative, commutative and unitary algebra. It is also shown that associativity is not a necessary condition.

Systems and complexity thinking in the general practice literature: an integrative, historical narrative review.

PubMed

Sturmberg, Joachim P; Martin, Carmel M; Katerndahl, David A

2014-01-01

Over the past 7 decades, theories in the systems and complexity sciences have had a major influence on academic thinking and research. We assessed the impact of complexity science on general practice/family medicine. We performed a historical integrative review using the following systematic search strategy: medical subject heading [humans] combined in turn with the terms complex adaptive systems, nonlinear dynamics, systems biology, and systems theory, limited to general practice/family medicine and published before December 2010. A total of 16,242 articles were retrieved, of which 49 were published in general practice/family medicine journals. Hand searches and snowballing retrieved another 35. After a full-text review, we included 56 articles dealing specifically with systems sciences and general/family practice. General practice/family medicine engaged with the emerging systems and complexity theories in 4 stages. Before 1995, articles tended to explore common phenomenologic general practice/family medicine experiences. Between 1995 and 2000, articles described the complex adaptive nature of this discipline. Those published between 2000 and 2005 focused on describing the system dynamics of medical practice. After 2005, articles increasingly applied the breadth of complex science theories to health care, health care reform, and the future of medicine. This historical review describes the development of general practice/family medicine in relation to complex adaptive systems theories, and shows how systems sciences more accurately reflect the discipline's philosophy and identity. Analysis suggests that general practice/family medicine first embraced systems theories through conscious reorganization of its boundaries and scope, before applying empirical tools. Future research should concentrate on applying nonlinear dynamics and empirical modeling to patient care, and to organizing and developing local practices, engaging in community development, and influencing health care reform.

Systems and Complexity Thinking in the General Practice Literature: An Integrative, Historical Narrative Review

PubMed Central

Sturmberg, Joachim P.; Martin, Carmel M.; Katerndahl, David A.

2014-01-01

PURPOSE Over the past 7 decades, theories in the systems and complexity sciences have had a major influence on academic thinking and research. We assessed the impact of complexity science on general practice/family medicine. METHODS We performed a historical integrative review using the following systematic search strategy: medical subject heading [humans] combined in turn with the terms complex adaptive systems, nonlinear dynamics, systems biology, and systems theory, limited to general practice/family medicine and published before December 2010. A total of 16,242 articles were retrieved, of which 49 were published in general practice/family medicine journals. Hand searches and snowballing retrieved another 35. After a full-text review, we included 56 articles dealing specifically with systems sciences and general/family practice. RESULTS General practice/family medicine engaged with the emerging systems and complexity theories in 4 stages. Before 1995, articles tended to explore common phenomenologic general practice/family medicine experiences. Between 1995 and 2000, articles described the complex adaptive nature of this discipline. Those published between 2000 and 2005 focused on describing the system dynamics of medical practice. After 2005, articles increasingly applied the breadth of complex science theories to health care, health care reform, and the future of medicine. CONCLUSIONS This historical review describes the development of general practice/family medicine in relation to complex adaptive systems theories, and shows how systems sciences more accurately reflect the discipline’s philosophy and identity. Analysis suggests that general practice/family medicine first embraced systems theories through conscious reorganization of its boundaries and scope, before applying empirical tools. Future research should concentrate on applying nonlinear dynamics and empirical modeling to patient care, and to organizing and developing local practices, engaging in community development, and influencing health care reform. PMID:24445105

Complexity of EEG-signal in Time Domain - Possible Biomedical Application

NASA Astrophysics Data System (ADS)

Klonowski, Wlodzimierz; Olejarczyk, Elzbieta; Stepien, Robert

2002-07-01

Human brain is a highly complex nonlinear system. So it is not surprising that in analysis of EEG-signal, which represents overall activity of the brain, the methods of Nonlinear Dynamics (or Chaos Theory as it is commonly called) can be used. Even if the signal is not chaotic these methods are a motivating tool to explore changes in brain activity due to different functional activation states, e.g. different sleep stages, or to applied therapy, e.g. exposure to chemical agents (drugs) and physical factors (light, magnetic field). The methods supplied by Nonlinear Dynamics reveal signal characteristics that are not revealed by linear methods like FFT. Better understanding of principles that govern dynamics and complexity of EEG-signal can help to find `the signatures' of different physiological and pathological states of human brain, quantitative characteristics that may find applications in medical diagnostics.

A study on axial and torsional resonant mode matching for a mechanical system with complex nonlinear geometries

NASA Astrophysics Data System (ADS)

Watson, Brett; Yeo, Leslie; Friend, James

2010-06-01

Making use of mechanical resonance has many benefits for the design of microscale devices. A key to successfully incorporating this phenomenon in the design of a device is to understand how the resonant frequencies of interest are affected by changes to the geometric parameters of the design. For simple geometric shapes, this is quite easy, but for complex nonlinear designs, it becomes significantly more complex. In this paper, two novel modeling techniques are demonstrated to extract the axial and torsional resonant frequencies of a complex nonlinear geometry. The first decomposes the complex geometry into easy to model components, while the second uses scaling techniques combined with the finite element method. Both models overcome problems associated with using current analytical methods as design tools, and enable a full investigation of how changes in the geometric parameters affect the resonant frequencies of interest. The benefit of such models is then demonstrated through their use in the design of a prototype piezoelectric ultrasonic resonant micromotor which has improved performance characteristics over previous prototypes.

Hierarchical cluster-based partial least squares regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models.

PubMed

Tøndel, Kristin; Indahl, Ulf G; Gjuvsland, Arne B; Vik, Jon Olav; Hunter, Peter; Omholt, Stig W; Martens, Harald

2011-06-01

Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems.

Hierarchical Cluster-based Partial Least Squares Regression (HC-PLSR) is an efficient tool for metamodelling of nonlinear dynamic models

PubMed Central

2011-01-01

Background Deterministic dynamic models of complex biological systems contain a large number of parameters and state variables, related through nonlinear differential equations with various types of feedback. A metamodel of such a dynamic model is a statistical approximation model that maps variation in parameters and initial conditions (inputs) to variation in features of the trajectories of the state variables (outputs) throughout the entire biologically relevant input space. A sufficiently accurate mapping can be exploited both instrumentally and epistemically. Multivariate regression methodology is a commonly used approach for emulating dynamic models. However, when the input-output relations are highly nonlinear or non-monotone, a standard linear regression approach is prone to give suboptimal results. We therefore hypothesised that a more accurate mapping can be obtained by locally linear or locally polynomial regression. We present here a new method for local regression modelling, Hierarchical Cluster-based PLS regression (HC-PLSR), where fuzzy C-means clustering is used to separate the data set into parts according to the structure of the response surface. We compare the metamodelling performance of HC-PLSR with polynomial partial least squares regression (PLSR) and ordinary least squares (OLS) regression on various systems: six different gene regulatory network models with various types of feedback, a deterministic mathematical model of the mammalian circadian clock and a model of the mouse ventricular myocyte function. Results Our results indicate that multivariate regression is well suited for emulating dynamic models in systems biology. The hierarchical approach turned out to be superior to both polynomial PLSR and OLS regression in all three test cases. The advantage, in terms of explained variance and prediction accuracy, was largest in systems with highly nonlinear functional relationships and in systems with positive feedback loops. Conclusions HC-PLSR is a promising approach for metamodelling in systems biology, especially for highly nonlinear or non-monotone parameter to phenotype maps. The algorithm can be flexibly adjusted to suit the complexity of the dynamic model behaviour, inviting automation in the metamodelling of complex systems. PMID:21627852

A comparative analysis of alternative approaches for quantifying nonlinear dynamics in cardiovascular system.

PubMed

Chen, Yun; Yang, Hui

2013-01-01

Heart rate variability (HRV) analysis has emerged as an important research topic to evaluate autonomic cardiac function. However, traditional time and frequency-domain analysis characterizes and quantify only linear and stationary phenomena. In the present investigation, we made a comparative analysis of three alternative approaches (i.e., wavelet multifractal analysis, Lyapunov exponents and multiscale entropy analysis) for quantifying nonlinear dynamics in heart rate time series. Note that these extracted nonlinear features provide information about nonlinear scaling behaviors and the complexity of cardiac systems. To evaluate the performance, we used 24-hour HRV recordings from 54 healthy subjects and 29 heart failure patients, available in PhysioNet. Three nonlinear methods are evaluated not only individually but also in combination using three classification algorithms, i.e., linear discriminate analysis, quadratic discriminate analysis and k-nearest neighbors. Experimental results show that three nonlinear methods capture nonlinear dynamics from different perspectives and the combined feature set achieves the best performance, i.e., sensitivity 97.7% and specificity 91.5%. Collectively, nonlinear HRV features are shown to have the promise to identify the disorders in autonomic cardiovascular function.

Nonlinear Fourier transform—towards the construction of nonlinear Fourier modes

NASA Astrophysics Data System (ADS)

Saksida, Pavle

2018-01-01

We study a version of the nonlinear Fourier transform associated with ZS-AKNS systems. This version is suitable for the construction of nonlinear analogues of Fourier modes, and for the perturbation-theoretic study of their superposition. We provide an iterative scheme for computing the inverse of our transform. The relevant formulae are expressed in terms of Bell polynomials and functions related to them. In order to prove the validity of our iterative scheme, we show that our transform has the necessary analytic properties. We show that up to order three of the perturbation parameter, the nonlinear Fourier mode is a complex sinusoid modulated by the second Bernoulli polynomial. We describe an application of the nonlinear superposition of two modes to a problem of transmission through a nonlinear medium.

Bound vector solitons and soliton complexes for the coupled nonlinear Schrödinger equations.

PubMed

Sun, Zhi-Yuan; Gao, Yi-Tian; Yu, Xin; Liu, Wen-Jun; Liu, Ying

2009-12-01

Dynamic features describing the collisions of the bound vector solitons and soliton complexes are investigated for the coupled nonlinear Schrödinger (CNLS) equations, which model the propagation of the multimode soliton pulses under some physical situations in nonlinear fiber optics. Equations of such type have also been seen in water waves and plasmas. By the appropriate choices of the arbitrary parameters for the multisoliton solutions derived through the Hirota bilinear method, the periodic structures along the propagation are classified according to the relative relations of the real wave numbers. Furthermore, parameters are shown to control the intensity distributions and interaction patterns for the bound vector solitons and soliton complexes. Transformations of the soliton types (shape changing with intensity redistribution) during the collisions of those stationary structures with the regular one soliton are discussed, in which a class of inelastic properties is involved. Discussions could be expected to be helpful in interpreting such structures in the multimode nonlinear fiber optics and equally applied to other systems governed by the CNLS equations, e.g., the plasma physics and Bose-Einstein condensates.

Low-complexity nonlinear adaptive filter based on a pipelined bilinear recurrent neural network.

PubMed

Zhao, Haiquan; Zeng, Xiangping; He, Zhengyou

2011-09-01

To reduce the computational complexity of the bilinear recurrent neural network (BLRNN), a novel low-complexity nonlinear adaptive filter with a pipelined bilinear recurrent neural network (PBLRNN) is presented in this paper. The PBLRNN, inheriting the modular architectures of the pipelined RNN proposed by Haykin and Li, comprises a number of BLRNN modules that are cascaded in a chained form. Each module is implemented by a small-scale BLRNN with internal dynamics. Since those modules of the PBLRNN can be performed simultaneously in a pipelined parallelism fashion, it would result in a significant improvement of computational efficiency. Moreover, due to nesting module, the performance of the PBLRNN can be further improved. To suit for the modular architectures, a modified adaptive amplitude real-time recurrent learning algorithm is derived on the gradient descent approach. Extensive simulations are carried out to evaluate the performance of the PBLRNN on nonlinear system identification, nonlinear channel equalization, and chaotic time series prediction. Experimental results show that the PBLRNN provides considerably better performance compared to the single BLRNN and RNN models.

Real-Time linux dynamic clamp: a fast and flexible way to construct virtual ion channels in living cells.

PubMed

Dorval, A D; Christini, D J; White, J A

2001-10-01

We describe a system for real-time control of biological and other experiments. This device, based around the Real-Time Linux operating system, was tested specifically in the context of dynamic clamping, a demanding real-time task in which a computational system mimics the effects of nonlinear membrane conductances in living cells. The system is fast enough to represent dozens of nonlinear conductances in real time at clock rates well above 10 kHz. Conductances can be represented in deterministic form, or more accurately as discrete collections of stochastically gating ion channels. Tests were performed using a variety of complex models of nonlinear membrane mechanisms in excitable cells, including simulations of spatially extended excitable structures, and multiple interacting cells. Only in extreme cases does the computational load interfere with high-speed "hard" real-time processing (i.e., real-time processing that never falters). Freely available on the worldwide web, this experimental control system combines good performance. immense flexibility, low cost, and reasonable ease of use. It is easily adapted to any task involving real-time control, and excels in particular for applications requiring complex control algorithms that must operate at speeds over 1 kHz.

A multiphase non-linear mixed effects model: An application to spirometry after lung transplantation.

PubMed

Rajeswaran, Jeevanantham; Blackstone, Eugene H

2017-02-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time-varying coefficients.

Technology of Synergy Manifestation in the Research of Solution's Stability of Differential Equations System

ERIC Educational Resources Information Center

Dvoryatkina, Svetlana N.; Melnikov, Roman A. M.; Smirnov, Eugeny I.

2017-01-01

Effectiveness of mathematical education as non-linear, composite and open system, formation and development of cognitive abilities of the trainee are wholly defined in the solution of complex tasks by means of modern achievements in science to high school practice adaptation. The possibility of complex tasks solution arises at identification of…

Wave processes in the human cardiovascular system: The measuring complex, computing models, and diagnostic analysis

NASA Astrophysics Data System (ADS)

Ganiev, R. F.; Reviznikov, D. L.; Rogoza, A. N.; Slastushenskiy, Yu. V.; Ukrainskiy, L. E.

2017-03-01

A description of a complex approach to investigation of nonlinear wave processes in the human cardiovascular system based on a combination of high-precision methods of measuring a pulse wave, mathematical methods of processing the empirical data, and methods of direct numerical modeling of hemodynamic processes in an arterial tree is given.

A novel auto-tuning PID control mechanism for nonlinear systems.

PubMed

Cetin, Meric; Iplikci, Serdar

2015-09-01

In this paper, a novel Runge-Kutta (RK) discretization-based model-predictive auto-tuning proportional-integral-derivative controller (RK-PID) is introduced for the control of continuous-time nonlinear systems. The parameters of the PID controller are tuned using RK model of the system through prediction error-square minimization where the predicted information of tracking error provides an enhanced tuning of the parameters. Based on the model-predictive control (MPC) approach, the proposed mechanism provides necessary PID parameter adaptations while generating additive correction terms to assist the initially inadequate PID controller. Efficiency of the proposed mechanism has been tested on two experimental real-time systems: an unstable single-input single-output (SISO) nonlinear magnetic-levitation system and a nonlinear multi-input multi-output (MIMO) liquid-level system. RK-PID has been compared to standard PID, standard nonlinear MPC (NMPC), RK-MPC and conventional sliding-mode control (SMC) methods in terms of control performance, robustness, computational complexity and design issue. The proposed mechanism exhibits acceptable tuning and control performance with very small steady-state tracking errors, and provides very short settling time for parameter convergence. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Volterra series truncation and kernel estimation of nonlinear systems in the frequency domain

NASA Astrophysics Data System (ADS)

Zhang, B.; Billings, S. A.

2017-02-01

The Volterra series model is a direct generalisation of the linear convolution integral and is capable of displaying the intrinsic features of a nonlinear system in a simple and easy to apply way. Nonlinear system analysis using Volterra series is normally based on the analysis of its frequency-domain kernels and a truncated description. But the estimation of Volterra kernels and the truncation of Volterra series are coupled with each other. In this paper, a novel complex-valued orthogonal least squares algorithm is developed. The new algorithm provides a powerful tool to determine which terms should be included in the Volterra series expansion and to estimate the kernels and thus solves the two problems all together. The estimated results are compared with those determined using the analytical expressions of the kernels to validate the method. To further evaluate the effectiveness of the method, the physical parameters of the system are also extracted from the measured kernels. Simulation studies demonstrates that the new approach not only can truncate the Volterra series expansion and estimate the kernels of a weakly nonlinear system, but also can indicate the applicability of the Volterra series analysis in a severely nonlinear system case.

Nonlinear dynamics as an engine of computation.

PubMed

Kia, Behnam; Lindner, John F; Ditto, William L

2017-03-06

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics-cybernetical physics-opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Nonlinear dynamics as an engine of computation

PubMed Central

Lindner, John F.; Ditto, William L.

2017-01-01

Control of chaos teaches that control theory can tame the complex, random-like behaviour of chaotic systems. This alliance between control methods and physics—cybernetical physics—opens the door to many applications, including dynamics-based computing. In this article, we introduce nonlinear dynamics and its rich, sometimes chaotic behaviour as an engine of computation. We review our work that has demonstrated how to compute using nonlinear dynamics. Furthermore, we investigate the interrelationship between invariant measures of a dynamical system and its computing power to strengthen the bridge between physics and computation. This article is part of the themed issue ‘Horizons of cybernetical physics’. PMID:28115619

A Numerical Scheme for Ordinary Differential Equations Having Time Varying and Nonlinear Coefficients Based on the State Transition Matrix

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2002-01-01

A variable order method of integrating initial value ordinary differential equations that is based on the state transition matrix has been developed. The method has been evaluated for linear time variant and nonlinear systems of equations. While it is more complex than most other methods, it produces exact solutions at arbitrary time step size when the time variation of the system can be modeled exactly by a polynomial. Solutions to several nonlinear problems exhibiting chaotic behavior have been computed. Accuracy of the method has been demonstrated by comparison with an exact solution and with solutions obtained by established methods.

Adaptive learning in complex reproducing kernel Hilbert spaces employing Wirtinger's subgradients.

PubMed

Bouboulis, Pantelis; Slavakis, Konstantinos; Theodoridis, Sergios

2012-03-01

This paper presents a wide framework for non-linear online supervised learning tasks in the context of complex valued signal processing. The (complex) input data are mapped into a complex reproducing kernel Hilbert space (RKHS), where the learning phase is taking place. Both pure complex kernels and real kernels (via the complexification trick) can be employed. Moreover, any convex, continuous and not necessarily differentiable function can be used to measure the loss between the output of the specific system and the desired response. The only requirement is the subgradient of the adopted loss function to be available in an analytic form. In order to derive analytically the subgradients, the principles of the (recently developed) Wirtinger's calculus in complex RKHS are exploited. Furthermore, both linear and widely linear (in RKHS) estimation filters are considered. To cope with the problem of increasing memory requirements, which is present in almost all online schemes in RKHS, the sparsification scheme, based on projection onto closed balls, has been adopted. We demonstrate the effectiveness of the proposed framework in a non-linear channel identification task, a non-linear channel equalization problem and a quadrature phase shift keying equalization scheme, using both circular and non circular synthetic signal sources.

Hypothesis: the chaos and complexity theory may help our understanding of fibromyalgia and similar maladies.

PubMed

Martinez-Lavin, Manuel; Infante, Oscar; Lerma, Claudia

2008-02-01

Modern clinicians are often frustrated by their inability to understand fibromyalgia and similar maladies since these illnesses cannot be explained by the prevailing linear-reductionist medical paradigm. This article proposes that new concepts derived from the Complexity Theory may help understand the pathogenesis of fibromyalgia, chronic fatigue syndrome, and Gulf War syndrome. This hypothesis is based on the recent recognition of chaos fractals and complex systems in human physiology. These nonlinear dynamics concepts offer a different perspective to the notion of homeostasis and disease. They propose that the essence of disease is dysfunction and not structural damage. Studies using novel nonlinear instruments have shown that fibromyalgia and similar maladies may be caused by the degraded performance of our main complex adaptive system. This dysfunction explains the multifaceted manifestations of these entities. To understand and alleviate the suffering associated with these complex illnesses, a paradigm shift from reductionism to holism based on the Complexity Theory is suggested. This shift perceives health as resilient adaptation and some chronic illnesses as rigid dysfunction.

Acoustic signatures of sound source-tract coupling.

PubMed

Arneodo, Ezequiel M; Perl, Yonatan Sanz; Mindlin, Gabriel B

2011-04-01

Birdsong is a complex behavior, which results from the interaction between a nervous system and a biomechanical peripheral device. While much has been learned about how complex sounds are generated in the vocal organ, little has been learned about the signature on the vocalizations of the nonlinear effects introduced by the acoustic interactions between a sound source and the vocal tract. The variety of morphologies among bird species makes birdsong a most suitable model to study phenomena associated to the production of complex vocalizations. Inspired by the sound production mechanisms of songbirds, in this work we study a mathematical model of a vocal organ, in which a simple sound source interacts with a tract, leading to a delay differential equation. We explore the system numerically, and by taking it to the weakly nonlinear limit, we are able to examine its periodic solutions analytically. By these means we are able to explore the dynamics of oscillatory solutions of a sound source-tract coupled system, which are qualitatively different from those of a sound source-filter model of a vocal organ. Nonlinear features of the solutions are proposed as the underlying mechanisms of observed phenomena in birdsong, such as unilaterally produced "frequency jumps," enhancement of resonances, and the shift of the fundamental frequency observed in heliox experiments. ©2011 American Physical Society

Acoustic signatures of sound source-tract coupling

PubMed Central

Arneodo, Ezequiel M.; Perl, Yonatan Sanz; Mindlin, Gabriel B.

2014-01-01

Birdsong is a complex behavior, which results from the interaction between a nervous system and a biomechanical peripheral device. While much has been learned about how complex sounds are generated in the vocal organ, little has been learned about the signature on the vocalizations of the nonlinear effects introduced by the acoustic interactions between a sound source and the vocal tract. The variety of morphologies among bird species makes birdsong a most suitable model to study phenomena associated to the production of complex vocalizations. Inspired by the sound production mechanisms of songbirds, in this work we study a mathematical model of a vocal organ, in which a simple sound source interacts with a tract, leading to a delay differential equation. We explore the system numerically, and by taking it to the weakly nonlinear limit, we are able to examine its periodic solutions analytically. By these means we are able to explore the dynamics of oscillatory solutions of a sound source-tract coupled system, which are qualitatively different from those of a sound source-filter model of a vocal organ. Nonlinear features of the solutions are proposed as the underlying mechanisms of observed phenomena in birdsong, such as unilaterally produced “frequency jumps,” enhancement of resonances, and the shift of the fundamental frequency observed in heliox experiments. PMID:21599213

Simultaneous gains tuning in boiler/turbine PID-based controller clusters using iterative feedback tuning methodology.

PubMed

Zhang, Shu; Taft, Cyrus W; Bentsman, Joseph; Hussey, Aaron; Petrus, Bryan

2012-09-01

Tuning a complex multi-loop PID based control system requires considerable experience. In today's power industry the number of available qualified tuners is dwindling and there is a great need for better tuning tools to maintain and improve the performance of complex multivariable processes. Multi-loop PID tuning is the procedure for the online tuning of a cluster of PID controllers operating in a closed loop with a multivariable process. This paper presents the first application of the simultaneous tuning technique to the multi-input-multi-output (MIMO) PID based nonlinear controller in the power plant control context, with the closed-loop system consisting of a MIMO nonlinear boiler/turbine model and a nonlinear cluster of six PID-type controllers. Although simplified, the dynamics and cross-coupling of the process and the PID cluster are similar to those used in a real power plant. The particular technique selected, iterative feedback tuning (IFT), utilizes the linearized version of the PID cluster for signal conditioning, but the data collection and tuning is carried out on the full nonlinear closed-loop system. Based on the figure of merit for the control system performance, the IFT is shown to deliver performance favorably comparable to that attained through the empirical tuning carried out by an experienced control engineer. Copyright © 2012 ISA. Published by Elsevier Ltd. All rights reserved.

Sparsity enabled cluster reduced-order models for control

NASA Astrophysics Data System (ADS)

Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.

2018-01-01

Characterizing and controlling nonlinear, multi-scale phenomena are central goals in science and engineering. Cluster-based reduced-order modeling (CROM) was introduced to exploit the underlying low-dimensional dynamics of complex systems. CROM builds a data-driven discretization of the Perron-Frobenius operator, resulting in a probabilistic model for ensembles of trajectories. A key advantage of CROM is that it embeds nonlinear dynamics in a linear framework, which enables the application of standard linear techniques to the nonlinear system. CROM is typically computed on high-dimensional data; however, access to and computations on this full-state data limit the online implementation of CROM for prediction and control. Here, we address this key challenge by identifying a small subset of critical measurements to learn an efficient CROM, referred to as sparsity-enabled CROM. In particular, we leverage compressive measurements to faithfully embed the cluster geometry and preserve the probabilistic dynamics. Further, we show how to identify fewer optimized sensor locations tailored to a specific problem that outperform random measurements. Both of these sparsity-enabled sensing strategies significantly reduce the burden of data acquisition and processing for low-latency in-time estimation and control. We illustrate this unsupervised learning approach on three different high-dimensional nonlinear dynamical systems from fluids with increasing complexity, with one application in flow control. Sparsity-enabled CROM is a critical facilitator for real-time implementation on high-dimensional systems where full-state information may be inaccessible.

Information and material flows in complex networks

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Armbruster, Dieter; Mikhailov, Alexander S.; Lefeber, Erjen

2006-04-01

In this special issue, an overview of the Thematic Institute (TI) on Information and Material Flows in Complex Systems is given. The TI was carried out within EXYSTENCE, the first EU Network of Excellence in the area of complex systems. Its motivation, research approach and subjects are presented here. Among the various methods used are many-particle and statistical physics, nonlinear dynamics, as well as complex systems, network and control theory. The contributions are relevant for complex systems as diverse as vehicle and data traffic in networks, logistics, production, and material flows in biological systems. The key disciplines involved are socio-, econo-, traffic- and bio-physics, and a new research area that could be called “biologistics”.

Living on the edge of chaos: minimally nonlinear models of genetic regulatory dynamics.

PubMed

Hanel, Rudolf; Pöchacker, Manfred; Thurner, Stefan

2010-12-28

Linearized catalytic reaction equations (modelling, for example, the dynamics of genetic regulatory networks), under the constraint that expression levels, i.e. molecular concentrations of nucleic material, are positive, exhibit non-trivial dynamical properties, which depend on the average connectivity of the reaction network. In these systems, an inflation of the edge of chaos and multi-stability have been demonstrated to exist. The positivity constraint introduces a nonlinearity, which makes chaotic dynamics possible. Despite the simplicity of such minimally nonlinear systems, their basic properties allow us to understand the fundamental dynamical properties of complex biological reaction networks. We analyse the Lyapunov spectrum, determine the probability of finding stationary oscillating solutions, demonstrate the effect of the nonlinearity on the effective in- and out-degree of the active interaction network, and study how the frequency distributions of oscillatory modes of such a system depend on the average connectivity.

Theoretical and software considerations for nonlinear dynamic analysis

NASA Technical Reports Server (NTRS)

Schmidt, R. J.; Dodds, R. H., Jr.

1983-01-01

In the finite element method for structural analysis, it is generally necessary to discretize the structural model into a very large number of elements to accurately evaluate displacements, strains, and stresses. As the complexity of the model increases, the number of degrees of freedom can easily exceed the capacity of present-day software system. Improvements of structural analysis software including more efficient use of existing hardware and improved structural modeling techniques are discussed. One modeling technique that is used successfully in static linear and nonlinear analysis is multilevel substructuring. This research extends the use of multilevel substructure modeling to include dynamic analysis and defines the requirements for a general purpose software system capable of efficient nonlinear dynamic analysis. The multilevel substructuring technique is presented, the analytical formulations and computational procedures for dynamic analysis and nonlinear mechanics are reviewed, and an approach to the design and implementation of a general purpose structural software system is presented.

Nonlinear force feedback control of piezoelectric-hydraulic pump actuator for automotive transmission shift control

NASA Astrophysics Data System (ADS)

Kim, Gi-Woo; Wang, K. W.

2008-03-01

In recent years, researchers have investigated the feasibility of utilizing piezoelectric-hydraulic pump based actuation systems for automotive transmission controls. This new concept could eventually reduce the complexity, weight, and fuel consumption of the current transmissions. In this research, we focus on how to utilize this new approach on the shift control of automatic transmissions (AT), which generally requires pressure profiling for friction elements during the operation. To illustrate the concept, we will consider the 1--> 2 up shift control using band brake friction elements. In order to perform the actuation force tracking for AT shift control, nonlinear force feedback control laws are designed based on the sliding mode theory for the given nonlinear system. This paper will describe the modeling of the band brake actuation system, the design of the nonlinear force feedback controller, and simulation and experimental results for demonstration of the new concept.

Decentralized robust nonlinear model predictive controller for unmanned aerial systems

NASA Astrophysics Data System (ADS)

Garcia Garreton, Gonzalo A.

The nonlinear and unsteady nature of aircraft aerodynamics together with limited practical range of controls and state variables make the use of the linear control theory inadequate especially in the presence of external disturbances, such as wind. In the classical approach, aircraft are controlled by multiple inner and outer loops, designed separately and sequentially. For unmanned aerial systems in particular, control technology must evolve to a point where autonomy is extended to the entire mission flight envelope. This requires advanced controllers that have sufficient robustness, track complex trajectories, and use all the vehicles control capabilities at higher levels of accuracy. In this work, a robust nonlinear model predictive controller is designed to command and control an unmanned aerial system to track complex tight trajectories in the presence of internal and external perturbance. The Flight System developed in this work achieves the above performance by using: 1. A nonlinear guidance algorithm that enables the vehicle to follow an arbitrary trajectory shaped by moving points; 2. A formulation that embeds the guidance logic and trajectory information in the aircraft model, avoiding cross coupling and control degradation; 3. An artificial neural network, designed to adaptively estimate and provide aerodynamic and propulsive forces in real-time; and 4. A mixed sensitivity approach that enhances the robustness for a nonlinear model predictive controller overcoming the effect of un-modeled dynamics, external disturbances such as wind, and measurement additive perturbations, such as noise and biases. These elements have been integrated and tested in simulation and with previously stored flight test data and shown to be feasible.

Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

PubMed

Sigalov, G; Gendelman, O V; AL-Shudeifat, M A; Manevitch, L I; Vakakis, A F; Bergman, L A

2012-03-01

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Nonlinear digital signal processing in mental health: characterization of major depression using instantaneous entropy measures of heartbeat dynamics.

PubMed

Valenza, Gaetano; Garcia, Ronald G; Citi, Luca; Scilingo, Enzo P; Tomaz, Carlos A; Barbieri, Riccardo

2015-01-01

Nonlinear digital signal processing methods that address system complexity have provided useful computational tools for helping in the diagnosis and treatment of a wide range of pathologies. More specifically, nonlinear measures have been successful in characterizing patients with mental disorders such as Major Depression (MD). In this study, we propose the use of instantaneous measures of entropy, namely the inhomogeneous point-process approximate entropy (ipApEn) and the inhomogeneous point-process sample entropy (ipSampEn), to describe a novel characterization of MD patients undergoing affective elicitation. Because these measures are built within a nonlinear point-process model, they allow for the assessment of complexity in cardiovascular dynamics at each moment in time. Heartbeat dynamics were characterized from 48 healthy controls and 48 patients with MD while emotionally elicited through either neutral or arousing audiovisual stimuli. Experimental results coming from the arousing tasks show that ipApEn measures are able to instantaneously track heartbeat complexity as well as discern between healthy subjects and MD patients. Conversely, standard heart rate variability (HRV) analysis performed in both time and frequency domains did not show any statistical significance. We conclude that measures of entropy based on nonlinear point-process models might contribute to devising useful computational tools for care in mental health.

Robust scalable stabilisability conditions for large-scale heterogeneous multi-agent systems with uncertain nonlinear interactions: towards a distributed computing architecture

NASA Astrophysics Data System (ADS)

Manfredi, Sabato

2016-06-01

Large-scale dynamic systems are becoming highly pervasive in their occurrence with applications ranging from system biology, environment monitoring, sensor networks, and power systems. They are characterised by high dimensionality, complexity, and uncertainty in the node dynamic/interactions that require more and more computational demanding methods for their analysis and control design, as well as the network size and node system/interaction complexity increase. Therefore, it is a challenging problem to find scalable computational method for distributed control design of large-scale networks. In this paper, we investigate the robust distributed stabilisation problem of large-scale nonlinear multi-agent systems (briefly MASs) composed of non-identical (heterogeneous) linear dynamical systems coupled by uncertain nonlinear time-varying interconnections. By employing Lyapunov stability theory and linear matrix inequality (LMI) technique, new conditions are given for the distributed control design of large-scale MASs that can be easily solved by the toolbox of MATLAB. The stabilisability of each node dynamic is a sufficient assumption to design a global stabilising distributed control. The proposed approach improves some of the existing LMI-based results on MAS by both overcoming their computational limits and extending the applicative scenario to large-scale nonlinear heterogeneous MASs. Additionally, the proposed LMI conditions are further reduced in terms of computational requirement in the case of weakly heterogeneous MASs, which is a common scenario in real application where the network nodes and links are affected by parameter uncertainties. One of the main advantages of the proposed approach is to allow to move from a centralised towards a distributed computing architecture so that the expensive computation workload spent to solve LMIs may be shared among processors located at the networked nodes, thus increasing the scalability of the approach than the network size. Finally, a numerical example shows the applicability of the proposed method and its advantage in terms of computational complexity when compared with the existing approaches.

Bayesian dynamical systems modelling in the social sciences.

PubMed

Ranganathan, Shyam; Spaiser, Viktoria; Mann, Richard P; Sumpter, David J T

2014-01-01

Data arising from social systems is often highly complex, involving non-linear relationships between the macro-level variables that characterize these systems. We present a method for analyzing this type of longitudinal or panel data using differential equations. We identify the best non-linear functions that capture interactions between variables, employing Bayes factor to decide how many interaction terms should be included in the model. This method punishes overly complicated models and identifies models with the most explanatory power. We illustrate our approach on the classic example of relating democracy and economic growth, identifying non-linear relationships between these two variables. We show how multiple variables and variable lags can be accounted for and provide a toolbox in R to implement our approach.

Nonlinear absorption dynamics using field-induced surface hopping: zinc porphyrin in water.

PubMed

Röhr, Merle I S; Petersen, Jens; Wohlgemuth, Matthias; Bonačić-Koutecký, Vlasta; Mitrić, Roland

2013-05-10

We wish to present the application of our field-induced surface-hopping (FISH) method to simulate nonlinear absorption dynamics induced by strong nonresonant laser fields. We provide a systematic comparison of the FISH approach with exact quantum dynamics simulations on a multistate model system and demonstrate that FISH allows for accurate simulations of nonlinear excitation processes including multiphoton electronic transitions. In particular, two different approaches for simulating two-photon transitions are compared. The first approach is essentially exact and involves the solution of the time-dependent Schrödinger equation in an extended manifold of excited states, while in the second one only transiently populated nonessential states are replaced by an effective quadratic coupling term, and dynamics is performed in a considerably smaller manifold of states. We illustrate the applicability of our method to complex molecular systems by simulating the linear and nonlinear laser-driven dynamics in zinc (Zn) porphyrin in the gas phase and in water. For this purpose, the FISH approach is connected with the quantum mechanical-molecular mechanical approach (QM/MM) which is generally applicable to large classes of complex systems. Our findings that multiphoton absorption and dynamics increase the population of higher excited states of Zn porphyrin in the nonlinear regime, in particular in solution, provides a means for manipulating excited-state properties, such as transient absorption dynamics and electronic relaxation. Copyright © 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Theorems and application of local activity of CNN with five state variables and one port.

PubMed

Xiong, Gang; Dong, Xisong; Xie, Li; Yang, Thomas

2012-01-01

Coupled nonlinear dynamical systems have been widely studied recently. However, the dynamical properties of these systems are difficult to deal with. The local activity of cellular neural network (CNN) has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice, which is composed of coupled cells. In this paper, the analytical criteria for the local activity in reaction-diffusion CNN with five state variables and one port are presented, which consists of four theorems, including a serial of inequalities involving CNN parameters. These theorems can be used for calculating the bifurcation diagram to determine or analyze the emergence of complex dynamic patterns, such as chaos. As a case study, a reaction-diffusion CNN of hepatitis B Virus (HBV) mutation-selection model is analyzed and simulated, the bifurcation diagram is calculated. Using the diagram, numerical simulations of this CNN model provide reasonable explanations of complex mutant phenomena during therapy. Therefore, it is demonstrated that the local activity of CNN provides a practical tool for the complex dynamics study of some coupled nonlinear systems.

A LEAST ABSOLUTE SHRINKAGE AND SELECTION OPERATOR (LASSO) FOR NONLINEAR SYSTEM IDENTIFICATION

NASA Technical Reports Server (NTRS)

Kukreja, Sunil L.; Lofberg, Johan; Brenner, Martin J.

2006-01-01

Identification of parametric nonlinear models involves estimating unknown parameters and detecting its underlying structure. Structure computation is concerned with selecting a subset of parameters to give a parsimonious description of the system which may afford greater insight into the functionality of the system or a simpler controller design. In this study, a least absolute shrinkage and selection operator (LASSO) technique is investigated for computing efficient model descriptions of nonlinear systems. The LASSO minimises the residual sum of squares by the addition of a 1 penalty term on the parameter vector of the traditional 2 minimisation problem. Its use for structure detection is a natural extension of this constrained minimisation approach to pseudolinear regression problems which produces some model parameters that are exactly zero and, therefore, yields a parsimonious system description. The performance of this LASSO structure detection method was evaluated by using it to estimate the structure of a nonlinear polynomial model. Applicability of the method to more complex systems such as those encountered in aerospace applications was shown by identifying a parsimonious system description of the F/A-18 Active Aeroelastic Wing using flight test data.

Numerical simulation and comparison of nonlinear self-focusing based on iteration and ray tracing

NASA Astrophysics Data System (ADS)

Li, Xiaotong; Chen, Hao; Wang, Weiwei; Ruan, Wangchao; Zhang, Luwei; Cen, Zhaofeng

2017-05-01

Self-focusing is observed in nonlinear materials owing to the interaction between laser and matter when laser beam propagates. Some of numerical simulation strategies such as the beam propagation method (BPM) based on nonlinear Schrödinger equation and ray tracing method based on Fermat's principle have applied to simulate the self-focusing process. In this paper we present an iteration nonlinear ray tracing method in that the nonlinear material is also cut into massive slices just like the existing approaches, but instead of paraxial approximation and split-step Fourier transform, a large quantity of sampled real rays are traced step by step through the system with changing refractive index and laser intensity by iteration. In this process a smooth treatment is employed to generate a laser density distribution at each slice to decrease the error caused by the under-sampling. The characteristics of this method is that the nonlinear refractive indices of the points on current slice are calculated by iteration so as to solve the problem of unknown parameters in the material caused by the causal relationship between laser intensity and nonlinear refractive index. Compared with the beam propagation method, this algorithm is more suitable for engineering application with lower time complexity, and has the calculation capacity for numerical simulation of self-focusing process in the systems including both of linear and nonlinear optical media. If the sampled rays are traced with their complex amplitudes and light paths or phases, it will be possible to simulate the superposition effects of different beam. At the end of the paper, the advantages and disadvantages of this algorithm are discussed.

Vibrational dynamics of vocal folds using nonlinear normal modes.

PubMed

Pinheiro, Alan P; Kerschen, Gaëtan

2013-08-01

Many previous works involving physical models, excised and in vivo larynges have pointed out nonlinear vibration in vocal folds during voice production. Moreover, theoretical studies involving mechanical modeling of these folds have tried to gain a profound understanding of the observed nonlinear phenomena. In this context, the present work uses the nonlinear normal mode theory to investigate the nonlinear modal behavior of 16 subjects using a two-mass mechanical modeling of the vocal folds. The free response of the conservative system at different energy levels is considered to assess the impact of the structural nonlinearity of the vocal fold tissues. The results show very interesting and complex nonlinear phenomena including frequency-energy dependence, subharmonic regimes and, in some cases, modal interactions, entrainment and bifurcations. Copyright © 2012 IPEM. Published by Elsevier Ltd. All rights reserved.

Application of Conjugate Gradient methods to tidal simulation

USGS Publications Warehouse

Barragy, E.; Carey, G.F.; Walters, R.A.

1993-01-01

A harmonic decomposition technique is applied to the shallow water equations to yield a complex, nonsymmetric, nonlinear, Helmholtz type problem for the sea surface and an accompanying complex, nonlinear diagonal problem for the velocities. The equation for the sea surface is linearized using successive approximation and then discretized with linear, triangular finite elements. The study focuses on applying iterative methods to solve the resulting complex linear systems. The comparative evaluation includes both standard iterative methods for the real subsystems and complex versions of the well known Bi-Conjugate Gradient and Bi-Conjugate Gradient Squared methods. Several Incomplete LU type preconditioners are discussed, and the effects of node ordering, rejection strategy, domain geometry and Coriolis parameter (affecting asymmetry) are investigated. Implementation details for the complex case are discussed. Performance studies are presented and comparisons made with a frontal solver. ?? 1993.

The Importance of Why: An Intelligence Approach for a Multi-Polar World

DTIC Science & Technology

2016-04-04

December 27, 2015). 12. 2 Jupiter Scientific, “Definitions of Important Terms in Chaos Theory ,” Jupiter Scientific website, http...Important Terms in Chaos Theory .” Linearizing a system is approximating a nonlinear system through the application of linear system model. 25...Complexity Theory to Anticipate Strategic Surprise,” 24. 16 M. Mitchell Waldrop, Complexity: The Emerging Science at the Edge of Order and Chaos (New

Weighted multiscale Rényi permutation entropy of nonlinear time series

NASA Astrophysics Data System (ADS)

Chen, Shijian; Shang, Pengjian; Wu, Yue

2018-04-01

In this paper, based on Rényi permutation entropy (RPE), which has been recently suggested as a relative measure of complexity in nonlinear systems, we propose multiscale Rényi permutation entropy (MRPE) and weighted multiscale Rényi permutation entropy (WMRPE) to quantify the complexity of nonlinear time series over multiple time scales. First, we apply MPRE and WMPRE to the synthetic data and make a comparison of modified methods and RPE. Meanwhile, the influence of the change of parameters is discussed. Besides, we interpret the necessity of considering not only multiscale but also weight by taking the amplitude into account. Then MRPE and WMRPE methods are employed to the closing prices of financial stock markets from different areas. By observing the curves of WMRPE and analyzing the common statistics, stock markets are divided into 4 groups: (1) DJI, S&P500, and HSI, (2) NASDAQ and FTSE100, (3) DAX40 and CAC40, and (4) ShangZheng and ShenCheng. Results show that the standard deviations of weighted methods are smaller, showing WMRPE is able to ensure the results more robust. Besides, WMPRE can provide abundant dynamical properties of complex systems, and demonstrate the intrinsic mechanism.

Nonlinear Focal Modulation Microscopy.

PubMed

Zhao, Guangyuan; Zheng, Cheng; Kuang, Cuifang; Zhou, Renjie; Kabir, Mohammad M; Toussaint, Kimani C; Wang, Wensheng; Xu, Liang; Li, Haifeng; Xiu, Peng; Liu, Xu

2018-05-11

We demonstrate nonlinear focal modulation microscopy (NFOMM) to achieve superresolution imaging. Traditional approaches to superresolution that utilize point scanning often rely on spatially reducing the size of the emission pattern by directly narrowing (e.g., through minimizing the detection pinhole in Airyscan, Zeiss) or indirectly peeling its outer profiles [e.g., through depleting the outer emission region in stimulated emission depletion (STED) microscopy]. We show that an alternative conceptualization that focuses on maximizing the optical system's frequency shifting ability offers advantages in further improving resolution while reducing system complexity. In NFOMM, a spatial light modulator and a suitably intense laser illumination are used to implement nonlinear focal-field modulation to achieve a transverse spatial resolution of ∼60  nm (∼λ/10). We show that NFOMM is comparable with STED microscopy and suitable for fundamental biology studies, as evidenced in imaging nuclear pore complexes, tubulin and vimentin in Vero cells. Since NFOMM is readily implemented as an add-on module to a laser-scanning microscope, we anticipate wide utility of this new imaging technique.

Nonlinear Focal Modulation Microscopy

NASA Astrophysics Data System (ADS)

Zhao, Guangyuan; Zheng, Cheng; Kuang, Cuifang; Zhou, Renjie; Kabir, Mohammad M.; Toussaint, Kimani C.; Wang, Wensheng; Xu, Liang; Li, Haifeng; Xiu, Peng; Liu, Xu

2018-05-01

We demonstrate nonlinear focal modulation microscopy (NFOMM) to achieve superresolution imaging. Traditional approaches to superresolution that utilize point scanning often rely on spatially reducing the size of the emission pattern by directly narrowing (e.g., through minimizing the detection pinhole in Airyscan, Zeiss) or indirectly peeling its outer profiles [e.g., through depleting the outer emission region in stimulated emission depletion (STED) microscopy]. We show that an alternative conceptualization that focuses on maximizing the optical system's frequency shifting ability offers advantages in further improving resolution while reducing system complexity. In NFOMM, a spatial light modulator and a suitably intense laser illumination are used to implement nonlinear focal-field modulation to achieve a transverse spatial resolution of ˜60 nm (˜λ /10 ). We show that NFOMM is comparable with STED microscopy and suitable for fundamental biology studies, as evidenced in imaging nuclear pore complexes, tubulin and vimentin in Vero cells. Since NFOMM is readily implemented as an add-on module to a laser-scanning microscope, we anticipate wide utility of this new imaging technique.

Nonlinear Dynamics and Chaos in Astrophysics: A Festschrift in Honor of George Contopoulos

NASA Astrophysics Data System (ADS)

Buchler, J. Robert; Gottesman, Stephen T.; Kandrup, Henry E.

1998-12-01

The annals of the New York Academy of Sciences is a compilation of work in the area of nonlinear dynamics and chaos in Astrophysics. Sections included are: From Quasars to Extraordinary N-body Problems; Dynamical Spectra and the Onset of Chaos; Orbital Complexity, Short-Time Lyapunov Exponents, and Phase Space Transport in Time-Independent Hamiltonian Systems; Bifurcations of Periodic Orbits in Axisymmetric Scalefree Potentials; Irregular Period-Tripling Bifurcations in Axisymmetric Scalefree Potentials; Negative Energy Modes and Gravitational Instability of Interpenetrating Fluids; Invariants and Labels in Lie-Poisson Systems; From Jupiter's Great Red Spot to the Structure of Galaxies: Statistical Mechanics of Two-Dimensional Vortices and Stellar Systems; N-Body Simulations of Galaxies and Groups of Galaxies with the Marseille GRAPE Systems; On Nonlinear Dynamics of Three-Dimensional Astrophysical Disks; Satellites as Probes of the Masses of Spiral Galaxies; Chaos in the Centers of Galaxies; Counterrotating Galaxies and Accretion Disks; Global Spiral Patterns in Galaxies: Complexity and Simplicity; Candidates for Abundance Gradients at Intermediate Red-Shift Clusters; Scaling Regimes in the Distribution of Galaxies; Recent Progress in the Study of One-Dimensional Gravitating Systems; Modeling the Time Variability of Black Hole Candidates; Stellar Oscillons; Chaos in Cosmological Hamiltonians; and Phase Space Transport in Noisy Hamiltonian Systems.

Fractal dynamics in physiology: Alterations with disease and aging

PubMed Central

Goldberger, Ary L.; Amaral, Luis A. N.; Hausdorff, Jeffrey M.; Ivanov, Plamen Ch.; Peng, C.-K.; Stanley, H. Eugene

2002-01-01

According to classical concepts of physiologic control, healthy systems are self-regulated to reduce variability and maintain physiologic constancy. Contrary to the predictions of homeostasis, however, the output of a wide variety of systems, such as the normal human heartbeat, fluctuates in a complex manner, even under resting conditions. Scaling techniques adapted from statistical physics reveal the presence of long-range, power-law correlations, as part of multifractal cascades operating over a wide range of time scales. These scaling properties suggest that the nonlinear regulatory systems are operating far from equilibrium, and that maintaining constancy is not the goal of physiologic control. In contrast, for subjects at high risk of sudden death (including those with heart failure), fractal organization, along with certain nonlinear interactions, breaks down. Application of fractal analysis may provide new approaches to assessing cardiac risk and forecasting sudden cardiac death, as well as to monitoring the aging process. Similar approaches show promise in assessing other regulatory systems, such as human gait control in health and disease. Elucidating the fractal and nonlinear mechanisms involved in physiologic control and complex signaling networks is emerging as a major challenge in the postgenomic era. PMID:11875196

Nonlinear Complexity Analysis of Brain fMRI Signals in Schizophrenia

PubMed Central

Sokunbi, Moses O.; Gradin, Victoria B.; Waiter, Gordon D.; Cameron, George G.; Ahearn, Trevor S.; Murray, Alison D.; Steele, Douglas J.; Staff, Roger T.

2014-01-01

We investigated the differences in brain fMRI signal complexity in patients with schizophrenia while performing the Cyberball social exclusion task, using measures of Sample entropy and Hurst exponent (H). 13 patients meeting diagnostic and Statistical Manual of Mental Disorders, 4th Edition (DSM IV) criteria for schizophrenia and 16 healthy controls underwent fMRI scanning at 1.5 T. The fMRI data of both groups of participants were pre-processed, the entropy characterized and the Hurst exponent extracted. Whole brain entropy and H maps of the groups were generated and analysed. The results after adjusting for age and sex differences together show that patients with schizophrenia exhibited higher complexity than healthy controls, at mean whole brain and regional levels. Also, both Sample entropy and Hurst exponent agree that patients with schizophrenia have more complex fMRI signals than healthy controls. These results suggest that schizophrenia is associated with more complex signal patterns when compared to healthy controls, supporting the increase in complexity hypothesis, where system complexity increases with age or disease, and also consistent with the notion that schizophrenia is characterised by a dysregulation of the nonlinear dynamics of underlying neuronal systems. PMID:24824731

Stability of chirped bright and dark soliton-like solutions of the cubic complex Ginzburg Landau equation with variable coefficients

NASA Astrophysics Data System (ADS)

Fang, Fang; Xiao, Yan

2006-12-01

We consider an inhomogeneous optical fiber system described by the generalized cubic complex Ginzburg-Landau (CGL) equation with varying dispersion, nonlinearity, gain (loss), nonlinear gain (absorption) and the effect of spectral limitation. Exact chirped bright and dark soliton-like solutions of the CGL equation were found by using a suitable ansatz. Furthermore, we analyze the features of the solitons and consider the problem of stability of these soliton-like solutions under finite initial perturbations. It is shown by extensive numerical simulations that both bright and dark soliton-like solutions are stable in an inhomogeneous fiber system. Finally, the interaction between two chirped bright and dark soliton-like pulses is investigated numerically.

Nonlinear system identification of smart structures under high impact loads

NASA Astrophysics Data System (ADS)

Sarp Arsava, Kemal; Kim, Yeesock; El-Korchi, Tahar; Park, Hyo Seon

2013-05-01

The main purpose of this paper is to develop numerical models for the prediction and analysis of the highly nonlinear behavior of integrated structure control systems subjected to high impact loading. A time-delayed adaptive neuro-fuzzy inference system (TANFIS) is proposed for modeling of the complex nonlinear behavior of smart structures equipped with magnetorheological (MR) dampers under high impact forces. Experimental studies are performed to generate sets of input and output data for training and validation of the TANFIS models. The high impact load and current signals are used as the input disturbance and control signals while the displacement and acceleration responses from the structure-MR damper system are used as the output signals. The benchmark adaptive neuro-fuzzy inference system (ANFIS) is used as a baseline. Comparisons of the trained TANFIS models with experimental results demonstrate that the TANFIS modeling framework is an effective way to capture nonlinear behavior of integrated structure-MR damper systems under high impact loading. In addition, the performance of the TANFIS model is much better than that of ANFIS in both the training and the validation processes.

Controllability of complex networks for sustainable system dynamics

EPA Science Inventory

Successful implementation of sustainability ideas in ecosystem management requires a basic understanding of the often non-linear and non-intuitive relationships among different dimensions of sustainability, particularly the system-wide implications of human actions. This basic un...

Nonlinear Dynamics of a Multistage Gear Transmission System with Multi-Clearance

NASA Astrophysics Data System (ADS)

Xiang, Ling; Zhang, Yue; Gao, Nan; Hu, Aijun; Xing, Jingtang

The nonlinear torsional model of a multistage gear transmission system which consists of a planetary gear and two parallel gear stages is established with time-varying meshing stiffness, comprehensive gear error and multi-clearance. The nonlinear dynamic responses are analyzed by applying the reference of backlash bifurcation parameters. The motions of the system on the change of backlash are identified through global bifurcation diagram, largest Lyapunov exponent (LLE), FFT spectra, Poincaré maps, the phase diagrams and time series. The numerical results demonstrate that the system exhibits rich features of nonlinear dynamics such as the periodic motion, nonperiodic states and chaotic states. It is found that the sun-planet backlash has more complex effect on the system than the ring-planet backlash. The motions of the system with backlash of parallel gear are diverse including some different multi-periodic motions. Furthermore, the state of the system can change from chaos into quasi-periodic behavior, which means that the dynamic behavior of the system is composed of more stable components with the increase of the backlash. Correspondingly, the parameters of the system should be designed properly and controlled timely for better operation and enhancing the life of the system.

A Multiphase Non-Linear Mixed Effects Model: An Application to Spirometry after Lung Transplantation

PubMed Central

Rajeswaran, Jeevanantham; Blackstone, Eugene H.

2014-01-01

In medical sciences, we often encounter longitudinal temporal relationships that are non-linear in nature. The influence of risk factors may also change across longitudinal follow-up. A system of multiphase non-linear mixed effects model is presented to model temporal patterns of longitudinal continuous measurements, with temporal decomposition to identify the phases and risk factors within each phase. Application of this model is illustrated using spirometry data after lung transplantation using readily available statistical software. This application illustrates the usefulness of our flexible model when dealing with complex non-linear patterns and time varying coefficients. PMID:24919830

A new analytical method for characterizing nonlinear visual processes with stimuli of arbitrary distribution: Theory and applications.

PubMed

Hayashi, Ryusuke; Watanabe, Osamu; Yokoyama, Hiroki; Nishida, Shin'ya

2017-06-01

Characterization of the functional relationship between sensory inputs and neuronal or observers' perceptual responses is one of the fundamental goals of systems neuroscience and psychophysics. Conventional methods, such as reverse correlation and spike-triggered data analyses are limited in their ability to resolve complex and inherently nonlinear neuronal/perceptual processes because these methods require input stimuli to be Gaussian with a zero mean. Recent studies have shown that analyses based on a generalized linear model (GLM) do not require such specific input characteristics and have advantages over conventional methods. GLM, however, relies on iterative optimization algorithms and its calculation costs become very expensive when estimating the nonlinear parameters of a large-scale system using large volumes of data. In this paper, we introduce a new analytical method for identifying a nonlinear system without relying on iterative calculations and yet also not requiring any specific stimulus distribution. We demonstrate the results of numerical simulations, showing that our noniterative method is as accurate as GLM in estimating nonlinear parameters in many cases and outperforms conventional, spike-triggered data analyses. As an example of the application of our method to actual psychophysical data, we investigated how different spatiotemporal frequency channels interact in assessments of motion direction. The nonlinear interaction estimated by our method was consistent with findings from previous vision studies and supports the validity of our method for nonlinear system identification.

The Life-Changing Magic of Nonlinearity in Network Control

NASA Astrophysics Data System (ADS)

Cornelius, Sean

The proper functioning and reliability of many man-made and natural systems is fundamentally tied to our ability to control them. Indeed, applications as diverse as ecosystem management, emergency response and cell reprogramming all, at their heart, require us to drive a system to--or keep it in--a desired state. This process is complicated by the nonlinear dynamics inherent to most real systems, which has traditionally been viewed as the principle obstacle to their control. In this talk, I will discuss two ways in which nonlinearity turns this view on its head, in fact representing an asset to the control of complex systems. First, I will show how nonlinearity in the form of multistability allows one to systematically design control interventions that can deliberately induce ``reverse cascading failures'', in which a network spontaneously evolves to a desirable (rather than a failed) state. Second, I will show that nonlinearity in the form of time-varying dynamics unexpectedly makes temporal networks easier to control than their static counterparts, with the former enjoying dramatic and simultaneous reductions in all costs of control. This is true despite the fact that temporality tends to fragment a network's structure, disrupting the paths that allow the directly-controlled or ``driver'' nodes to communicate with the rest of the network. Taken together, these studies shed new light on the crucial role of nonlinearity in network control, and provide support to the idea we can control nonlinearity, rather than letting nonlinearity control us.

Discontinuous Galerkin method with Gaussian artificial viscosity on graphical processing units for nonlinear acoustics

NASA Astrophysics Data System (ADS)

Tripathi, Bharat B.; Marchiano, Régis; Baskar, Sambandam; Coulouvrat, François

2015-10-01

Propagation of acoustical shock waves in complex geometry is a topic of interest in the field of nonlinear acoustics. For instance, simulation of Buzz Saw Noice requires the treatment of shock waves generated by the turbofan through the engines of aeroplanes with complex geometries and wall liners. Nevertheless, from a numerical point of view it remains a challenge. The two main hurdles are to take into account the complex geometry of the domain and to deal with the spurious oscillations (Gibbs phenomenon) near the discontinuities. In this work, first we derive the conservative hyperbolic system of nonlinear acoustics (up to quadratic nonlinear terms) using the fundamental equations of fluid dynamics. Then, we propose to adapt the classical nodal discontinuous Galerkin method to develop a high fidelity solver for nonlinear acoustics. The discontinuous Galerkin method is a hybrid of finite element and finite volume method and is very versatile to handle complex geometry. In order to obtain better performance, the method is parallelized on Graphical Processing Units. Like other numerical methods, discontinuous Galerkin method suffers with the problem of Gibbs phenomenon near the shock, which is a numerical artifact. Among the various ways to manage these spurious oscillations, we choose the method of parabolic regularization. Although, the introduction of artificial viscosity into the system is a popular way of managing shocks, we propose a new approach of introducing smooth artificial viscosity locally in each element, wherever needed. Firstly, a shock sensor using the linear coefficients of the spectral solution is used to locate the position of the discontinuities. Then, a viscosity coefficient depending on the shock sensor is introduced into the hyperbolic system of equations, only in the elements near the shock. The viscosity is applied as a two-dimensional Gaussian patch with its shape parameters depending on the element dimensions, referred here as Element Centered Smooth Artificial Viscosity. Using this numerical solver, various numerical experiments are presented for one and two-dimensional test cases in homogeneous and quiescent medium. This work is funded by CEFIPRA (Indo-French Centre for the Promotion of Advance Research) and partially aided by EGIDE (Campus France).

Hilbert complexes of nonlinear elasticity

NASA Astrophysics Data System (ADS)

Angoshtari, Arzhang; Yavari, Arash

2016-12-01

We introduce some Hilbert complexes involving second-order tensors on flat compact manifolds with boundary that describe the kinematics and the kinetics of motion in nonlinear elasticity. We then use the general framework of Hilbert complexes to write Hodge-type and Helmholtz-type orthogonal decompositions for second-order tensors. As some applications of these decompositions in nonlinear elasticity, we study the strain compatibility equations of linear and nonlinear elasticity in the presence of Dirichlet boundary conditions and the existence of stress functions on non-contractible bodies. As an application of these Hilbert complexes in computational mechanics, we briefly discuss the derivation of a new class of mixed finite element methods for nonlinear elasticity.

Residual mode correction in calibrating nonlinear damper for vibration control of flexible structures

NASA Astrophysics Data System (ADS)

Sun, Limin; Chen, Lin

2017-10-01

Residual mode correction is found crucial in calibrating linear resonant absorbers for flexible structures. The classic modal representation augmented with stiffness and inertia correction terms accounting for non-resonant modes improves the calibration accuracy and meanwhile avoids complex modal analysis of the full system. This paper explores the augmented modal representation in calibrating control devices with nonlinearity, by studying a taut cable attached with a general viscous damper and its Equivalent Dynamic Systems (EDSs), i.e. the augmented modal representations connected to the same damper. As nonlinearity is concerned, Frequency Response Functions (FRFs) of the EDSs are investigated in detail for parameter calibration, using the harmonic balance method in combination with numerical continuation. The FRFs of the EDSs and corresponding calibration results are then compared with those of the full system documented in the literature for varied structural modes, damper locations and nonlinearity. General agreement is found and in particular the EDS with both stiffness and inertia corrections (quasi-dynamic correction) performs best among available approximate methods. This indicates that the augmented modal representation although derived from linear cases is applicable to a relatively wide range of damper nonlinearity. Calibration of nonlinear devices by this means still requires numerical analysis while the efficiency is largely improved owing to the system order reduction.

Nonlinear dynamic macromodeling techniques for audio systems

NASA Astrophysics Data System (ADS)

Ogrodzki, Jan; Bieńkowski, Piotr

2015-09-01

This paper develops a modelling method and a models identification technique for the nonlinear dynamic audio systems. Identification is performed by means of a behavioral approach based on a polynomial approximation. This approach makes use of Discrete Fourier Transform and Harmonic Balance Method. A model of an audio system is first created and identified and then it is simulated in real time using an algorithm of low computational complexity. The algorithm consists in real time emulation of the system response rather than in simulation of the system itself. The proposed software is written in Python language using object oriented programming techniques. The code is optimized for a multithreads environment.

Maximized gust loads for a nonlinear airplane using matched filter theory and constrained optimization

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Pototzky, Anthony S.; Perry, Boyd, III

1991-01-01

Two matched filter theory based schemes are described and illustrated for obtaining maximized and time correlated gust loads for a nonlinear aircraft. The first scheme is computationally fast because it uses a simple 1-D search procedure to obtain its answers. The second scheme is computationally slow because it uses a more complex multi-dimensional search procedure to obtain its answers, but it consistently provides slightly higher maximum loads than the first scheme. Both schemes are illustrated with numerical examples involving a nonlinear control system.

Maximized gust loads for a nonlinear airplane using matched filter theory and constrained optimization

NASA Technical Reports Server (NTRS)

Scott, Robert C.; Perry, Boyd, III; Pototzky, Anthony S.

1991-01-01

This paper describes and illustrates two matched-filter-theory based schemes for obtaining maximized and time-correlated gust-loads for a nonlinear airplane. The first scheme is computationally fast because it uses a simple one-dimensional search procedure to obtain its answers. The second scheme is computationally slow because it uses a more complex multidimensional search procedure to obtain its answers, but it consistently provides slightly higher maximum loads than the first scheme. Both schemes are illustrated with numerical examples involving a nonlinear control system.

The design of nonlinear observers for wind turbine dynamic state and parameter estimation

NASA Astrophysics Data System (ADS)

Ritter, B.; Schild, A.; Feldt, M.; Konigorski, U.

2016-09-01

This contribution addresses the dynamic state and parameter estimation problem which arises with more advanced wind turbine controllers. These control devices need precise information about the system's current state to outperform conventional industrial controllers effectively. First, the necessity of a profound scientific treatment on nonlinear observers for wind turbine application is highlighted. Secondly, the full estimation problem is introduced and the variety of nonlinear filters is discussed. Finally, a tailored observer architecture is proposed and estimation results of an illustrative application example from a complex simulation set-up are presented.

Remote optoelectronic sensors for monitoring of nonlinear surfaces

NASA Astrophysics Data System (ADS)

Petrochenko, Andrew V.; Konyakhin, Igor A.

2015-05-01

Actually during construction of the high building actively are used objects of various nonlinear surface, for example, sinuous (parabolic or hyperbolic) roofs of the sport complexes that require automatic deformation control [1]. This type of deformation has character of deflection that is impossible to monitor objectively with just one optoelectronic sensor (which is fixed on this surface). In this article is described structure of remote optoelectronic sensor, which is part of the optoelectronic monitoring system of nonlinear surface, and mathematical transformation of exterior orientation sensor elements in the coordinates of control points.

1998 Complex Systems Summer School

DOE Office of Scientific and Technical Information (OSTI.GOV)

NONE

1998-12-15

For the past eleven years a group of institutes, centers, and universities throughout the country have sponsored a summer school in Santa Fe, New Mexico as part of an interdisciplinary effort to promote the understanding of complex systems. The goal of these summer schools is to provide graduate students, postdoctoral fellows and active research scientists with an introduction to the study of complex behavior in mathematical, physical, and living systems. The Center for Nonlinear Studies supported the eleventh in this series of highly successful schools in Santa Fe in June, 1998.

Neural Network Control of a Magnetically Suspended Rotor System

NASA Technical Reports Server (NTRS)

Choi, Benjamin B.

1998-01-01

Magnetic bearings offer significant advantages because they do not come into contact with other parts during operation, which can reduce maintenance. Higher speeds, no friction, no lubrication, weight reduction, precise position control, and active damping make them far superior to conventional contact bearings. However, there are technical barriers that limit the application of this technology in industry. One of them is the need for a nonlinear controller that can overcome the system nonlinearity and uncertainty inherent in magnetic bearings. At the NASA Lewis Research Center, a neural network was selected as a nonlinear controller because it generates a neural model without any detailed information regarding the internal working of the magnetic bearing system. It can be used even for systems that are too complex for an accurate system model to be derived. A feed-forward architecture with a back-propagation learning algorithm was selected because of its proven performance, accuracy, and relatively easy implementation.

Nonlinear forecasting analysis of inflation-deflation patterns of an active caldera (Campi Flegrei, Italy)

USGS Publications Warehouse

Cortini, M.; Barton, C.C.

1993-01-01

The ground level in Pozzuoli, Italy, at the center of the Campi Flegrei caldera, has been monitored by tide gauges. Previous work suggests that the dynamics of the Campi Flegrei system, as reconstructed from the tide gauge record, is chaotic and low dimensional. According to this suggestion, in spite of the complexity of the system, at a time scale of days the ground motion is driven by a deterministic mechanism with few degrees of freedom; however, the interactions of the system may never be describable in full detail. New analysis of the tide gauge record using Nonlinear Forecasting, confirms low-dimensional chaos in the ground elevation record at Campi Flegrei and suggests that Nonlinear Forecasting could be a useful tool in volcanic surveillance. -from Authors

HyFIS: adaptive neuro-fuzzy inference systems and their application to nonlinear dynamical systems.

PubMed

Kim, J; Kasabov, N

1999-11-01

This paper proposes an adaptive neuro-fuzzy system, HyFIS (Hybrid neural Fuzzy Inference System), for building and optimising fuzzy models. The proposed model introduces the learning power of neural networks to fuzzy logic systems and provides linguistic meaning to the connectionist architectures. Heuristic fuzzy logic rules and input-output fuzzy membership functions can be optimally tuned from training examples by a hybrid learning scheme comprised of two phases: rule generation phase from data; and rule tuning phase using error backpropagation learning scheme for a neural fuzzy system. To illustrate the performance and applicability of the proposed neuro-fuzzy hybrid model, extensive simulation studies of nonlinear complex dynamic systems are carried out. The proposed method can be applied to an on-line incremental adaptive learning for the prediction and control of nonlinear dynamical systems. Two benchmark case studies are used to demonstrate that the proposed HyFIS system is a superior neuro-fuzzy modelling technique.

Quantitative evaluation method for nonlinear characteristics of piezoelectric transducers under high stress with complex nonlinear elastic constant

NASA Astrophysics Data System (ADS)

Miyake, Susumu; Kasashima, Takashi; Yamazaki, Masato; Okimura, Yasuyuki; Nagata, Hajime; Hosaka, Hiroshi; Morita, Takeshi

2018-07-01

The high power properties of piezoelectric transducers were evaluated considering a complex nonlinear elastic constant. The piezoelectric LCR equivalent circuit with nonlinear circuit parameters was utilized to measure them. The deformed admittance curve of piezoelectric transducers was measured under a high stress and the complex nonlinear elastic constant was calculated by curve fitting. Transducers with various piezoelectric materials, Pb(Zr,Ti)O3, (K,Na)NbO3, and Ba(Zr,Ti)O3–(Ba,Ca)TiO3, were investigated by the proposed method. The measured complex nonlinear elastic constant strongly depends on the linear elastic and piezoelectric constants. This relationship indicates that piezoelectric high power properties can be controlled by modifying the linear elastic and piezoelectric constants.

Conveying the Complex: Updating U.S. Joint Systems Analysis Doctrine with Complexity Theory

DTIC Science & Technology

2013-12-10

screech during a public address, or sustain and amplify it during a guitar solo. Since the systems are nonlinear, understanding cause and effect... Classics , 2007), 12. 34 those frames.58 A technique to cope with the potentially confusing...Reynolds, Paul Davidson. A Primer in Theory Construction. Boston: Allyn and Bacon Classics , 2007. Riolo, Rick L. “The Effects and Evolution of Tag

Multifractality Signatures in Quasars Time Series. I. 3C 273

NASA Astrophysics Data System (ADS)

Belete, A. Bewketu; Bravo, J. P.; Canto Martins, B. L.; Leão, I. C.; De Araujo, J. M.; De Medeiros, J. R.

2018-05-01

The presence of multifractality in a time series shows different correlations for different time scales as well as intermittent behaviour that cannot be captured by a single scaling exponent. The identification of a multifractal nature allows for a characterization of the dynamics and of the intermittency of the fluctuations in non-linear and complex systems. In this study, we search for a possible multifractal structure (multifractality signature) of the flux variability in the quasar 3C 273 time series for all electromagnetic wavebands at different observation points, and the origins for the observed multifractality. This study is intended to highlight how the scaling behaves across the different bands of the selected candidate which can be used as an additional new technique to group quasars based on the fractal signature observed in their time series and determine whether quasars are non-linear physical systems or not. The Multifractal Detrended Moving Average algorithm (MFDMA) has been used to study the scaling in non-linear, complex and dynamic systems. To achieve this goal, we applied the backward (θ = 0) MFDMA method for one-dimensional signals. We observe weak multifractal (close to monofractal) behaviour in some of the time series of our candidate except in the mm, UV and X-ray bands. The non-linear temporal correlation is the main source of the observed multifractality in the time series whereas the heaviness of the distribution contributes less.

Developmental Evaluation: Applying Complexity Concepts to Enhance Innovation and Use

ERIC Educational Resources Information Center

Patton, Michael Quinn

2010-01-01

Developmental evaluation (DE) offers a powerful approach to monitoring and supporting social innovations by working in partnership with program decision makers. In this book, eminent authority shows how to conduct evaluations within a DE framework. Patton draws on insights about complex dynamic systems, uncertainty, nonlinearity, and emergence. He…

Nonlinear complexity of random visibility graph and Lempel-Ziv on multitype range-intensity interacting financial dynamics

NASA Astrophysics Data System (ADS)

Zhang, Yali; Wang, Jun

2017-09-01

In an attempt to investigate the nonlinear complex evolution of financial dynamics, a new financial price model - the multitype range-intensity contact (MRIC) financial model, is developed based on the multitype range-intensity interacting contact system, in which the interaction and transmission of different types of investment attitudes in a stock market are simulated by viruses spreading. Two new random visibility graph (VG) based analyses and Lempel-Ziv complexity (LZC) are applied to study the complex behaviors of return time series and the corresponding random sorted series. The VG method is the complex network theory, and the LZC is a non-parametric measure of complexity reflecting the rate of new pattern generation of a series. In this work, the real stock market indices are considered to be comparatively studied with the simulation data of the proposed model. Further, the numerical empirical study shows the similar complexity behaviors between the model and the real markets, the research confirms that the financial model is reasonable to some extent.

Final Report, DOE Early Career Award: Predictive modeling of complex physical systems: new tools for statistical inference, uncertainty quantification, and experimental design

DOE Office of Scientific and Technical Information (OSTI.GOV)

Marzouk, Youssef

Predictive simulation of complex physical systems increasingly rests on the interplay of experimental observations with computational models. Key inputs, parameters, or structural aspects of models may be incomplete or unknown, and must be developed from indirect and limited observations. At the same time, quantified uncertainties are needed to qualify computational predictions in the support of design and decision-making. In this context, Bayesian statistics provides a foundation for inference from noisy and limited data, but at prohibitive computional expense. This project intends to make rigorous predictive modeling *feasible* in complex physical systems, via accelerated and scalable tools for uncertainty quantification, Bayesianmore » inference, and experimental design. Specific objectives are as follows: 1. Develop adaptive posterior approximations and dimensionality reduction approaches for Bayesian inference in high-dimensional nonlinear systems. 2. Extend accelerated Bayesian methodologies to large-scale {\\em sequential} data assimilation, fully treating nonlinear models and non-Gaussian state and parameter distributions. 3. Devise efficient surrogate-based methods for Bayesian model selection and the learning of model structure. 4. Develop scalable simulation/optimization approaches to nonlinear Bayesian experimental design, for both parameter inference and model selection. 5. Demonstrate these inferential tools on chemical kinetic models in reacting flow, constructing and refining thermochemical and electrochemical models from limited data. Demonstrate Bayesian filtering on canonical stochastic PDEs and in the dynamic estimation of inhomogeneous subsurface properties and flow fields.« less

Closed-Loop Control of Complex Networks: A Trade-Off between Time and Energy

NASA Astrophysics Data System (ADS)

Sun, Yong-Zheng; Leng, Si-Yang; Lai, Ying-Cheng; Grebogi, Celso; Lin, Wei

2017-11-01

Controlling complex nonlinear networks is largely an unsolved problem at the present. Existing works focus either on open-loop control strategies and their energy consumptions or on closed-loop control schemes with an infinite-time duration. We articulate a finite-time, closed-loop controller with an eye toward the physical and mathematical underpinnings of the trade-off between the control time and energy as well as their dependence on the network parameters and structure. The closed-loop controller is tested on a large number of real systems including stem cell differentiation, food webs, random ecosystems, and spiking neuronal networks. Our results represent a step forward in developing a rigorous and general framework to control nonlinear dynamical networks with a complex topology.

Pattern formation based on complex coupling mechanism in dielectric barrier discharge

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liu, Weibo; College of Aeronautical Engineering, Binzhou University, Binzhou 256603; Dong, Lifang, E-mail: donglfhbu@163.com, E-mail: pyy1616@163.com

2016-08-15

The pattern formation of cinque-dice square superlattice pattern (CDSSP) is investigated based on the complex coupling mechanism in a dielectric barrier discharge (DBD) system. The spatio-temporal structure of CDSSP obtained by using an intensified-charge coupled device indicates that CDSSP is an interleaving of two kinds of subpatterns (mixture of rectangle and square, and dot-line square) which discharge twice in one half voltage, respectively. Selected by the complex coupling of two subpatterns, the CDSSP can be formed and shows good stability. This investigation based on gas discharge theory together with nonlinear theory may provide a deeper understanding for the nonlinear characteristicsmore » and even the formation mechanism of patterns in DBD.« less

Convergence to equilibrium of renormalised solutions to nonlinear chemical reaction–diffusion systems

NASA Astrophysics Data System (ADS)

Fellner, Klemens; Tang, Bao Quoc

2018-06-01

The convergence to equilibrium for renormalised solutions to nonlinear reaction-diffusion systems is studied. The considered reaction-diffusion systems arise from chemical reaction networks with mass action kinetics and satisfy the complex balanced condition. By applying the so-called entropy method, we show that if the system does not have boundary equilibria, i.e. equilibrium states lying on the boundary of R_+^N, then any renormalised solution converges exponentially to the complex balanced equilibrium with a rate, which can be computed explicitly up to a finite-dimensional inequality. This inequality is proven via a contradiction argument and thus not explicitly. An explicit method of proof, however, is provided for a specific application modelling a reversible enzyme reaction by exploiting the specific structure of the conservation laws. Our approach is also useful to study the trend to equilibrium for systems possessing boundary equilibria. More precisely, to show the convergence to equilibrium for systems with boundary equilibria, we establish a sufficient condition in terms of a modified finite-dimensional inequality along trajectories of the system. By assuming this condition, which roughly means that the system produces too much entropy to stay close to a boundary equilibrium for infinite time, the entropy method shows exponential convergence to equilibrium for renormalised solutions to complex balanced systems with boundary equilibria.

Nonlinear dynamics of global atmospheric and earth system processes

NASA Technical Reports Server (NTRS)

Zhang, Taiping; Verbitsky, Mikhail; Saltzman, Barry; Mann, Michael E.; Park, Jeffrey; Lall, Upmanu

1995-01-01

During the grant period, the authors continued ongoing studies aimed at enhancing their understanding of the operation of the atmosphere as a complex nonlinear system interacting with the hydrosphere, biosphere, and cryosphere in response to external radiative forcing. Five papers were completed with support from the grant, representing contributions in three main areas of study: (1) theoretical studies of the interactive atmospheric response to changed biospheric boundary conditions measurable from satellites; (2) statistical-observational studies of global-scale temperature variability on interannual to century time scales; and (3) dynamics of long-term earth system changes associated with ice sheet surges.

A nonlinear dynamical system for combustion instability in a pulse model combustor

NASA Astrophysics Data System (ADS)

Takagi, Kazushi; Gotoda, Hiroshi

2016-11-01

We theoretically and numerically study the bifurcation phenomena of nonlinear dynamical system describing combustion instability in a pulse model combustor on the basis of dynamical system theory and complex network theory. The dynamical behavior of pressure fluctuations undergoes a significant transition from steady-state to deterministic chaos via the period-doubling cascade process known as Feigenbaum scenario with decreasing the characteristic flow time. Recurrence plots and recurrence networks analysis we adopted in this study can quantify the significant changes in dynamic behavior of combustion instability that cannot be captured in the bifurcation diagram.

The Emergence of Temporal Structures in Dynamical Systems

NASA Astrophysics Data System (ADS)

Mainzer, Klaus

2010-10-01

Dynamical systems in classical, relativistic and quantum physics are ruled by laws with time reversibility. Complex dynamical systems with time-irreversibility are known from thermodynamics, biological evolution, growth of organisms, brain research, aging of people, and historical processes in social sciences. Complex systems are systems that compromise many interacting parts with the ability to generate a new quality of macroscopic collective behavior the manifestations of which are the spontaneous emergence of distinctive temporal, spatial or functional structures. But, emergence is no mystery. In a general meaning, the emergence of macroscopic features results from the nonlinear interactions of the elements in a complex system. Mathematically, the emergence of irreversible structures is modelled by phase transitions in non-equilibrium dynamics of complex systems. These methods have been modified even for chemical, biological, economic and societal applications (e.g., econophysics). Emergence of irreversible structures can also be simulated by computational systems. The question arises how the emergence of irreversible structures is compatible with the reversibility of fundamental physical laws. It is argued that, according to quantum cosmology, cosmic evolution leads from symmetry to complexity of irreversible structures by symmetry breaking and phase transitions. Thus, arrows of time and aging processes are not only subjective experiences or even contradictions to natural laws, but they can be explained by quantum cosmology and the nonlinear dynamics of complex systems. Human experiences and religious concepts of arrows of time are considered in a modern scientific framework. Platonic ideas of eternity are at least understandable with respect to mathematical invariance and symmetry of physical laws. Heraclit’s world of change and dynamics can be mapped onto our daily real-life experiences of arrows of time.

A new nonlinear model for pitch perception

NASA Astrophysics Data System (ADS)

Cartwright, Julyan H. E.; González, Diego L.; Piro, Oreste

The ability of the auditory system to perceive the fundamental frequency of a sound even when this frequency is removed from the stimulus is an interesting phenomenon related to the pitch of complex sounds. This capability is known as residue or virtual pitch perception and was first reported last century in the pioneering work of Seebeck. It is residue perception that allows one to listen to music with small transistor radios, which in general have a very poor and sometimes negligible response to low frequencies. The first attempt, due to von Helmholtz, to explain the residue as a nonlinear effect in the ear considered it to originate from difference combination tones. But later experiments showed that the residue does not coincide with a difference combination tone, and nonlinear theories were abandoned. However, in this paper we use recent results from the theory of nonlinear dynamical systems to show that physical frequencies produced by generic nonlinear oscillators acted upon by two independent periodic excitations can reproduce with great precision most of the experimental data about the residue.

Towards systemic theories in biological psychiatry.

PubMed

Bender, W; Albus, M; Möller, H-J; Tretter, F

2006-02-01

Although still rather controversial, empirical data on the neurobiology of schizophrenia have reached a degree of complexity that makes it hard to obtain a coherent picture of the malfunctions of the brain in schizophrenia. Theoretical neuropsychiatry should therefore use the tools of theoretical sciences like cybernetics, informatics, computational neuroscience or systems science. The methodology of systems science permits the modeling of complex dynamic nonlinear systems. Such procedures might help us to understand brain functions and the disorders and actions of psychiatric drugs better.

Wind energy system time-domain (WEST) analyzers

NASA Technical Reports Server (NTRS)

Dreier, M. E.; Hoffman, J. A.

1981-01-01

A portable analyzer which simulates in real time the complex nonlinear dynamics of horizontal axis wind energy systems was constructed. Math models for an aeroelastic rotor featuring nonlinear aerodynamic and inertial terms were implemented with high speed digital controllers and analog calculation. This model was combined with other math models of elastic supports, control systems, a power train and gimballed rotor kinematics. A stroboscopic display system graphically depicting distributed blade loads, motion, and other aerodynamic functions on a cathode ray tube is included. Limited correlation efforts showed good comparison between the results of this analyzer and other sophisticated digital simulations. The digital simulation results were successfully correlated with test data.

Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials

NASA Astrophysics Data System (ADS)

Yang, Jianke; Nixon, Sean

2016-11-01

Stability of soliton families in one-dimensional nonlinear Schrödinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets (λ , - λ ,λ* , -λ*), similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non- PT-symmetric systems, and it has far-reaching consequences on the stability behaviors of solitons.

An Analytical Dynamics Approach to the Control of Mechanical Systems

NASA Astrophysics Data System (ADS)

Mylapilli, Harshavardhan

A new and novel approach to the control of nonlinear mechanical systems is presented in this study. The approach is inspired by recent results in analytical dynamics that deal with the theory of constrained motion. The control requirements on the dynamical system are viewed from an analytical dynamics perspective and the theory of constrained motion is used to recast these control requirements as constraints on the dynamical system. Explicit closed form expressions for the generalized nonlinear control forces are obtained by using the fundamental equation of mechanics. The control so obtained is optimal at each instant of time and causes the constraints to be exactly satisfied. No linearizations and/or approximations of the nonlinear dynamical system are made, and no a priori structure is imposed on the nature of nonlinear controller. Three examples dealing with highly nonlinear complex dynamical systems that are chosen from diverse areas of discrete and continuum mechanics are presented to demonstrate the control approach. The first example deals with the energy control of underactuated inhomogeneous nonlinear lattices (or chains), the second example deals with the synchronization of the motion of multiple coupled slave gyros with that of a master gyro, and the final example deals with the control of incompressible hyperelastic rubber-like thin cantilever beams. Numerical simulations accompanying these examples show the ease, simplicity and the efficacy with which the control methodology can be applied and the accuracy with which the desired control objectives can be met.

Spontaneous switching of frequency-locking by periodic stimulus in oscillators of plasmodium of the true slime mold.

PubMed

Takamatsu, A; Yamamoto, T; Fujii, T

2004-01-01

Microfabrication technique was used to construct a model system with a living cell of plasmodium of the true slime mold, Physarum polycephalum, a living coupled oscillator system. Its parameters can be systematically controlled as in computer simulations, so that results are directly comparable to those of general mathematical models. As the first step, we investigated responses in oscillatory cells, the oscillators of the plasmodium, to periodic stimuli by temperature changes to elucidate characteristics of the cells as nonlinear systems whose internal dynamics are unknown because of their complexity. We observed that the forced oscillator of the plasmodium show 1:1, 2:1, 3:1 frequency locking inside so-called Arnold tongues regions as well as in other nonlinear systems such as chemical systems and other biological systems. In addition, we found spontaneous switching behavior from certain frequency locking states to other states, even under certain fixed parameters. This technique can be applied to more complex systems with multiple elements, such as coupled oscillator systems, and would be useful to investigate complicated phenomena in biological systems such as information processing.

Nonlinear analysis of dynamic signature

NASA Astrophysics Data System (ADS)

Rashidi, S.; Fallah, A.; Towhidkhah, F.

2013-12-01

Signature is a long trained motor skill resulting in well combination of segments like strokes and loops. It is a physical manifestation of complex motor processes. The problem, generally stated, is that how relative simplicity in behavior emerges from considerable complexity of perception-action system that produces behavior within an infinitely variable biomechanical and environmental context. To solve this problem, we present evidences which indicate that motor control dynamic in signing process is a chaotic process. This chaotic dynamic may explain a richer array of time series behavior in motor skill of signature. Nonlinear analysis is a powerful approach and suitable tool which seeks for characterizing dynamical systems through concepts such as fractal dimension and Lyapunov exponent. As a result, they can be analyzed in both horizontal and vertical for time series of position and velocity. We observed from the results that noninteger values for the correlation dimension indicates low dimensional deterministic dynamics. This result could be confirmed by using surrogate data tests. We have also used time series to calculate the largest Lyapunov exponent and obtain a positive value. These results constitute significant evidence that signature data are outcome of chaos in a nonlinear dynamical system of motor control.

Nonlinear random response prediction using MSC/NASTRAN

NASA Technical Reports Server (NTRS)

Robinson, J. H.; Chiang, C. K.; Rizzi, S. A.

1993-01-01

An equivalent linearization technique was incorporated into MSC/NASTRAN to predict the nonlinear random response of structures by means of Direct Matrix Abstract Programming (DMAP) modifications and inclusion of the nonlinear differential stiffness module inside the iteration loop. An iterative process was used to determine the rms displacements. Numerical results obtained for validation on simple plates and beams are in good agreement with existing solutions in both the linear and linearized regions. The versatility of the implementation will enable the analyst to determine the nonlinear random responses for complex structures under combined loads. The thermo-acoustic response of a hexagonal thermal protection system panel is used to highlight some of the features of the program.

Linear analysis using secants for materials with temperature dependent nonlinear elastic modulus and thermal expansion properties

NASA Astrophysics Data System (ADS)

Pepi, John W.

2017-08-01

Thermally induced stress is readily calculated for linear elastic material properties using Hooke's law in which, for situations where expansion is constrained, stress is proportional to the product of the material elastic modulus and its thermal strain. When material behavior is nonlinear, one needs to make use of nonlinear theory. However, we can avoid that complexity in some situations. For situations in which both elastic modulus and coefficient of thermal expansion vary with temperature, solutions can be formulated using secant properties. A theoretical approach is thus presented to calculate stresses for nonlinear, neo-Hookean, materials. This is important for high acuity optical systems undergoing large temperature extremes.

Fuzzy Adaptive Output Feedback Control of Uncertain Nonlinear Systems With Prescribed Performance.

PubMed

Zhang, Jin-Xi; Yang, Guang-Hong

2018-05-01

This paper investigates the tracking control problem for a family of strict-feedback systems in the presence of unknown nonlinearities and immeasurable system states. A low-complexity adaptive fuzzy output feedback control scheme is proposed, based on a backstepping method. In the control design, a fuzzy adaptive state observer is first employed to estimate the unmeasured states. Then, a novel error transformation approach together with a new modification mechanism is introduced to guarantee the finite-time convergence of the output error to a predefined region and ensure the closed-loop stability. Compared with the existing methods, the main advantages of our approach are that: 1) without using extra command filters or auxiliary dynamic surface control techniques, the problem of explosion of complexity can still be addressed and 2) the design procedures are independent of the initial conditions. Finally, two practical examples are performed to further illustrate the above theoretic findings.

Statistical Features of Complex Systems ---Toward Establishing Sociological Physics---

NASA Astrophysics Data System (ADS)

Kobayashi, Naoki; Kuninaka, Hiroto; Wakita, Jun-ichi; Matsushita, Mitsugu

2011-07-01

Complex systems have recently attracted much attention, both in natural sciences and in sociological sciences. Members constituting a complex system evolve through nonlinear interactions among each other. This means that in a complex system the multiplicative experience or, so to speak, the history of each member produces its present characteristics. If attention is paid to any statistical property in any complex system, the lognormal distribution is the most natural and appropriate among the standard or ``normal'' statistics to overview the whole system. In fact, the lognormality emerges rather conspicuously when we examine, as familiar and typical examples of statistical aspects in complex systems, the nursing-care period for the aged, populations of prefectures and municipalities, and our body height and weight. Many other examples are found in nature and society. On the basis of these observations, we discuss the possibility of sociological physics.

The Control Based on Internal Average Kinetic Energy in Complex Environment for Multi-robot System

NASA Astrophysics Data System (ADS)

Yang, Mao; Tian, Yantao; Yin, Xianghua

In this paper, reference trajectory is designed according to minimum energy consumed for multi-robot system, which nonlinear programming and cubic spline interpolation are adopted. The control strategy is composed of two levels, which lower-level is simple PD control and the upper-level is based on the internal average kinetic energy for multi-robot system in the complex environment with velocity damping. Simulation tests verify the effectiveness of this control strategy.

The brain as a dynamic physical system.

PubMed

McKenna, T M; McMullen, T A; Shlesinger, M F

1994-06-01

The brain is a dynamic system that is non-linear at multiple levels of analysis. Characterization of its non-linear dynamics is fundamental to our understanding of brain function. Identifying families of attractors in phase space analysis, an approach which has proven valuable in describing non-linear mechanical and electrical systems, can prove valuable in describing a range of behaviors and associated neural activity including sensory and motor repertoires. Additionally, transitions between attractors may serve as useful descriptors for analysing state changes in neurons and neural ensembles. Recent observations of synchronous neural activity, and the emerging capability to record the spatiotemporal dynamics of neural activity by voltage-sensitive dyes and electrode arrays, provide opportunities for observing the population dynamics of neural ensembles within a dynamic systems context. New developments in the experimental physics of complex systems, such as the control of chaotic systems, selection of attractors, attractor switching and transient states, can be a source of powerful new analytical tools and insights into the dynamics of neural systems.

Observer-Based Adaptive Fault-Tolerant Tracking Control of Nonlinear Nonstrict-Feedback Systems.

PubMed

Wu, Chengwei; Liu, Jianxing; Xiong, Yongyang; Wu, Ligang

2017-06-28

This paper studies an output-based adaptive fault-tolerant control problem for nonlinear systems with nonstrict-feedback form. Neural networks are utilized to identify the unknown nonlinear characteristics in the system. An observer and a general fault model are constructed to estimate the unavailable states and describe the fault, respectively. Adaptive parameters are constructed to overcome the difficulties in the design process for nonstrict-feedback systems. Meanwhile, dynamic surface control technique is introduced to avoid the problem of ''explosion of complexity''. Furthermore, based on adaptive backstepping control method, an output-based adaptive neural tracking control strategy is developed for the considered system against actuator fault, which can ensure that all the signals in the resulting closed-loop system are bounded, and the system output signal can be regulated to follow the response of the given reference signal with a small error. Finally, the simulation results are provided to validate the effectiveness of the control strategy proposed in this paper.

A study of the parallel algorithm for large-scale DC simulation of nonlinear systems

NASA Astrophysics Data System (ADS)

Cortés Udave, Diego Ernesto; Ogrodzki, Jan; Gutiérrez de Anda, Miguel Angel

Newton-Raphson DC analysis of large-scale nonlinear circuits may be an extremely time consuming process even if sparse matrix techniques and bypassing of nonlinear models calculation are used. A slight decrease in the time required for this task may be enabled on multi-core, multithread computers if the calculation of the mathematical models for the nonlinear elements as well as the stamp management of the sparse matrix entries are managed through concurrent processes. This numerical complexity can be further reduced via the circuit decomposition and parallel solution of blocks taking as a departure point the BBD matrix structure. This block-parallel approach may give a considerable profit though it is strongly dependent on the system topology and, of course, on the processor type. This contribution presents the easy-parallelizable decomposition-based algorithm for DC simulation and provides a detailed study of its effectiveness.

From the nonlinear Fokker-Planck equation to the Vlasov description and back: Confined interacting particles with drag

NASA Astrophysics Data System (ADS)

Plastino, A. R.; Curado, E. M. F.; Nobre, F. D.; Tsallis, C.

2018-02-01

Nonlinear Fokker-Planck equations endowed with power-law diffusion terms have proven to be valuable tools for the study of diverse complex systems in physics, biology, and other fields. The nonlinearity appearing in these evolution equations can be interpreted as providing an effective description of a system of particles interacting via short-range forces while performing overdamped motion under the effect of an external confining potential. This point of view has been recently applied to the study of thermodynamical features of interacting vortices in type II superconductors. In the present work we explore an embedding of the nonlinear Fokker-Planck equation within a Vlasov equation, thus incorporating inertial effects to the concomitant particle dynamics. Exact time-dependent solutions of the q -Gaussian form (with compact support) are obtained for the Vlasov equation in the case of quadratic confining potentials.

K-means-clustering-based fiber nonlinearity equalization techniques for 64-QAM coherent optical communication system.

PubMed

Zhang, Junfeng; Chen, Wei; Gao, Mingyi; Shen, Gangxiang

2017-10-30

In this work, we proposed two k-means-clustering-based algorithms to mitigate the fiber nonlinearity for 64-quadrature amplitude modulation (64-QAM) signal, the training-sequence assisted k-means algorithm and the blind k-means algorithm. We experimentally demonstrated the proposed k-means-clustering-based fiber nonlinearity mitigation techniques in 75-Gb/s 64-QAM coherent optical communication system. The proposed algorithms have reduced clustering complexity and low data redundancy and they are able to quickly find appropriate initial centroids and select correctly the centroids of the clusters to obtain the global optimal solutions for large k value. We measured the bit-error-ratio (BER) performance of 64-QAM signal with different launched powers into the 50-km single mode fiber and the proposed techniques can greatly mitigate the signal impairments caused by the amplified spontaneous emission noise and the fiber Kerr nonlinearity and improve the BER performance.

Sensitivity analysis and nonlinearity assessment of steam cracking furnace process

NASA Astrophysics Data System (ADS)

Rosli, M. N.; Sudibyo, Aziz, N.

2017-11-01

In this paper, sensitivity analysis and nonlinearity assessment of cracking furnace process are presented. For the sensitivity analysis, the fractional factorial design method is employed as a method to analyze the effect of input parameters, which consist of four manipulated variables and two disturbance variables, to the output variables and to identify the interaction between each parameter. The result of the factorial design method is used as a screening method to reduce the number of parameters, and subsequently, reducing the complexity of the model. It shows that out of six input parameters, four parameters are significant. After the screening is completed, step test is performed on the significant input parameters to assess the degree of nonlinearity of the system. The result shows that the system is highly nonlinear with respect to changes in an air-to-fuel ratio (AFR) and feed composition.

Exact states in waveguides with periodically modulated nonlinearity

NASA Astrophysics Data System (ADS)

Ding, E.; Chan, H. N.; Chow, K. W.; Nakkeeran, K.; Malomed, B. A.

2017-09-01

We introduce a one-dimensional model based on the nonlinear Schrödinger/Gross-Pitaevskii equation where the local nonlinearity is subject to spatially periodic modulation in terms of the Jacobi {dn} function, with three free parameters including the period, amplitude, and internal form-factor. An exact periodic solution is found for each set of parameters and, which is more important for physical realizations, we solve the inverse problem and predict the period and amplitude of the modulation that yields a particular exact spatially periodic state. A numerical stability analysis demonstrates that the periodic states become modulationally unstable for large periods, and regain stability in the limit of an infinite period, which corresponds to a bright soliton pinned to a localized nonlinearity-modulation pattern. The exact dark-bright soliton complex in a coupled system with a localized modulation structure is also briefly considered. The system can be realized in planar optical waveguides and cigar-shaped atomic Bose-Einstein condensates.

Scaling of chaos in strongly nonlinear lattices.

PubMed

Mulansky, Mario

2014-06-01

Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

Economic Decision Making: Application of the Theory of Complex Systems

NASA Astrophysics Data System (ADS)

Kitt, Robert

In this chapter the complex systems are discussed in the context of economic and business policy and decision making. It will be showed and motivated that social systems are typically chaotic, non-linear and/or non-equilibrium and therefore complex systems. It is discussed that the rapid change in global consumer behaviour is underway, that further increases the complexity in business and management. For policy making under complexity, following principles are offered: openness and international competition, tolerance and variety of ideas, self-reliability and low dependence on external help. The chapter contains four applications that build on the theoretical motivation of complexity in social systems. The first application demonstrates that small economies have good prospects to gain from the global processes underway, if they can demonstrate production flexibility, reliable business ethics and good risk management. The second application elaborates on and discusses the opportunities and challenges in decision making under complexity from macro and micro economic perspective. In this environment, the challenges for corporate management are being also permanently changed: the balance between short term noise and long term chaos whose attractor includes customers, shareholders and employees must be found. The emergence of chaos in economic relationships is demonstrated by a simple system of differential equations that relate the stakeholders described above. The chapter concludes with two financial applications: about debt and risk management. The non-equilibrium economic establishment leads to additional problems by using excessive borrowing; unexpected downturns in economy can more easily kill companies. Finally, the demand for quantitative improvements in risk management is postulated. Development of the financial markets has triggered non-linearity to spike in prices of various production articles such as agricultural and other commodities that has added market risk management to the business model of many companies.

Exploring the sustainability of industrial production and energy generation with a model system

EPA Science Inventory

The importance and complexity of sustainability has been well recognized and a formal study of sustainability based on system theory approaches is imperative as many of the relationships between the various components of the system could be non-linear, intertwined, and non-intuit...

The Chaos Theory of Careers.

ERIC Educational Resources Information Center

Pryor, Robert G. L.; Bright, Jim

2003-01-01

Four theoretical streams--contexualism/ecology, systems theory, realism/constructivism, and chaos theory--contributed to a theory of individuals as complex, unique, nonlinear, adaptive chaotic and open systems. Individuals use purposive action to construct careers but can make maladaptive and inappropriate choices. (Contains 42 references.) (SK)

Adaptive fuzzy dynamic surface control of nonlinear systems with input saturation and time-varying output constraints

NASA Astrophysics Data System (ADS)

Edalati, L.; Khaki Sedigh, A.; Aliyari Shooredeli, M.; Moarefianpour, A.

2018-02-01

This paper deals with the design of adaptive fuzzy dynamic surface control for uncertain strict-feedback nonlinear systems with asymmetric time-varying output constraints in the presence of input saturation. To approximate the unknown nonlinear functions and overcome the problem of explosion of complexity, a Fuzzy logic system is combined with the dynamic surface control in the backstepping design technique. To ensure the output constraints satisfaction, an asymmetric time-varying Barrier Lyapunov Function (BLF) is used. Moreover, by applying the minimal learning parameter technique, the number of the online parameters update for each subsystem is reduced to 2. Hence, the semi-globally uniformly ultimately boundedness (SGUUB) of all the closed-loop signals with appropriate tracking error convergence is guaranteed. The effectiveness of the proposed control is demonstrated by two simulation examples.

Automatic simplification of systems of reaction-diffusion equations by a posteriori analysis.

PubMed

Maybank, Philip J; Whiteley, Jonathan P

2014-02-01

Many mathematical models in biology and physiology are represented by systems of nonlinear differential equations. In recent years these models have become increasingly complex in order to explain the enormous volume of data now available. A key role of modellers is to determine which components of the model have the greatest effect on a given observed behaviour. An approach for automatically fulfilling this role, based on a posteriori analysis, has recently been developed for nonlinear initial value ordinary differential equations [J.P. Whiteley, Model reduction using a posteriori analysis, Math. Biosci. 225 (2010) 44-52]. In this paper we extend this model reduction technique for application to both steady-state and time-dependent nonlinear reaction-diffusion systems. Exemplar problems drawn from biology are used to demonstrate the applicability of the technique. Copyright © 2014 Elsevier Inc. All rights reserved.

Multi-linear model set design based on the nonlinearity measure and H-gap metric.

PubMed

Shaghaghi, Davood; Fatehi, Alireza; Khaki-Sedigh, Ali

2017-05-01

This paper proposes a model bank selection method for a large class of nonlinear systems with wide operating ranges. In particular, nonlinearity measure and H-gap metric are used to provide an effective algorithm to design a model bank for the system. Then, the proposed model bank is accompanied with model predictive controllers to design a high performance advanced process controller. The advantage of this method is the reduction of excessive switch between models and also decrement of the computational complexity in the controller bank that can lead to performance improvement of the control system. The effectiveness of the method is verified by simulations as well as experimental studies on a pH neutralization laboratory apparatus which confirms the efficiency of the proposed algorithm. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Nonlinear amplification of coherent waves in media with soliton-type refractive index pattern.

PubMed

Bugaychuk, S; Conte, R

2012-08-01

We derive the complex Ginzburg-Landau equation for the dynamical self-diffraction of optical waves in a nonlinear cavity. The case of the reflection geometry of wave interaction as well as a medium that possesses the cubic nonlinearity (including a local and a nonlocal nonlinear responses) and the relaxation is considered. A stable localized spatial structure in the form of a "dark" dissipative soliton is formed in the cavity in the steady state. The envelope of the intensity pattern, as well as of the dynamical grating amplitude, takes the shape of a tanh function. The obtained complex Ginzburg-Landau equation describes the dynamics of this envelope; at the same time, the evolution of this spatial structure changes the parameters of the output waves. New effects are predicted in this system due to the transformation of the dissipative soliton which takes place during the interaction of a pulse with a continuous wave, such as retention of the pulse shape during the transmission of impulses in a long nonlinear cavity, and giant amplification of a seed pulse, which takes energy due to redistribution of the pump continuous energy into the signal.

The Complexity Trap

DTIC Science & Technology

2012-01-01

proactively and effectively to today’s international environment, prioritization is the key first step —and precisely the opposite reaction to the complacency...formidable than just endless grains of sand.”32 This is not to deny the possibility of nonlinear phenomena, butterfly effects, self-organizing systems...The first step is replac- ing the current reactive worship of complexity with proactive prioritization. To escape the complexity trap, let us dare

Applying Chaos Theory to Lesson Planning and Delivery

ERIC Educational Resources Information Center

Cvetek, Slavko

2008-01-01

In this article, some of the ways in which thinking about chaos theory can help teachers and student-teachers to accept uncertainty and randomness as natural conditions in the classroom are considered. Building on some key features of complex systems commonly attributed to chaos theory (e.g. complexity, nonlinearity, sensitivity to initial…

Forum: The challenge of global change

NASA Astrophysics Data System (ADS)

Roederer, Juan G.

1990-09-01

How can we sustain a public sense of the common danger of global change while remaining honest in view of the realities of scientific uncertainty? How can we nurture this sense of common danger without making statements based on half-baked ideas, statistically unreliable results, or oversimplified models? How can we strike a balance between the need to overstate a case to attract the attention of the media and the obligation to adhere strictly to the ethos of science?The task of achieving a scientific understanding of the inner workings of the terrestrial environment is one of the most difficult and ambitious endeavors of humankind. It is full of traps, temptations and deceptions for the participating scientists. We are dealing with a horrendously complex, strongly interactive, highly non-linear system. Lessons learned from disciplines such as plasma physics and solid state physics which have been dealing with complex non-linear systems for decades, are not very encouraging. The first thing one learns is that there are intrinsic, physical limits to the quantitative predictability of a complex system that have nothing to do with the particular techniques employed to model it.

Single axis control of ball position in magnetic levitation system using fuzzy logic control

NASA Astrophysics Data System (ADS)

Sahoo, Narayan; Tripathy, Ashis; Sharma, Priyaranjan

2018-03-01

This paper presents the design and real time implementation of Fuzzy logic control(FLC) for the control of the position of a ferromagnetic ball by manipulating the current flowing in an electromagnet that changes the magnetic field acting on the ball. This system is highly nonlinear and open loop unstable. Many un-measurable disturbances are also acting on the system, making the control of it highly complex but interesting for any researcher in control system domain. First the system is modelled using the fundamental laws, which gives a nonlinear equation. The nonlinear model is then linearized at an operating point. Fuzzy logic controller is designed after studying the system in closed loop under PID control action. The controller is then implemented in real time using Simulink real time environment. The controller is tuned manually to get a stable and robust performance. The set point tracking performance of FLC and PID controllers were compared and analyzed.

Flow-pattern identification and nonlinear dynamics of gas-liquid two-phase flow in complex networks.

PubMed

Gao, Zhongke; Jin, Ningde

2009-06-01

The identification of flow pattern is a basic and important issue in multiphase systems. Because of the complexity of phase interaction in gas-liquid two-phase flow, it is difficult to discern its flow pattern objectively. In this paper, we make a systematic study on the vertical upward gas-liquid two-phase flow using complex network. Three unique network construction methods are proposed to build three types of networks, i.e., flow pattern complex network (FPCN), fluid dynamic complex network (FDCN), and fluid structure complex network (FSCN). Through detecting the community structure of FPCN by the community-detection algorithm based on K -mean clustering, useful and interesting results are found which can be used for identifying five vertical upward gas-liquid two-phase flow patterns. To investigate the dynamic characteristics of gas-liquid two-phase flow, we construct 50 FDCNs under different flow conditions, and find that the power-law exponent and the network information entropy, which are sensitive to the flow pattern transition, can both characterize the nonlinear dynamics of gas-liquid two-phase flow. Furthermore, we construct FSCN and demonstrate how network statistic can be used to reveal the fluid structure of gas-liquid two-phase flow. In this paper, from a different perspective, we not only introduce complex network theory to the study of gas-liquid two-phase flow but also indicate that complex network may be a powerful tool for exploring nonlinear time series in practice.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Scholbrock, A. K.; Fleming, P. A.; Fingersh, L. J.

Wind turbines are complex, nonlinear, dynamic systems driven by aerodynamic, gravitational, centrifugal, and gyroscopic forces. The aerodynamics of wind turbines are nonlinear, unsteady, and complex. Turbine rotors are subjected to a chaotic three-dimensional (3-D) turbulent wind inflow field with imbedded coherent vortices that drive fatigue loads and reduce lifetime. In order to reduce cost of energy, future large multimegawatt turbines must be designed with lighter weight structures, using active controls to mitigate fatigue loads, maximize energy capture, and add active damping to maintain stability for these dynamically active structures operating in a complex environment. Researchers at the National Renewable Energymore » Laboratory (NREL) and University of Stuttgart are designing, implementing, and testing advanced feed-back and feed-forward controls in order to reduce the cost of energy for wind turbines.« less

Modified multiple time scale method for solving strongly nonlinear damped forced vibration systems

NASA Astrophysics Data System (ADS)

Razzak, M. A.; Alam, M. Z.; Sharif, M. N.

2018-03-01

In this paper, modified multiple time scale (MTS) method is employed to solve strongly nonlinear forced vibration systems. The first-order approximation is only considered in order to avoid complexicity. The formulations and the determination of the solution procedure are very easy and straightforward. The classical multiple time scale (MS) and multiple scales Lindstedt-Poincare method (MSLP) do not give desire result for the strongly damped forced vibration systems with strong damping effects. The main aim of this paper is to remove these limitations. Two examples are considered to illustrate the effectiveness and convenience of the present procedure. The approximate external frequencies and the corresponding approximate solutions are determined by the present method. The results give good coincidence with corresponding numerical solution (considered to be exact) and also provide better result than other existing results. For weak nonlinearities with weak damping effect, the absolute relative error measures (first-order approximate external frequency) in this paper is only 0.07% when amplitude A = 1.5 , while the relative error gives MSLP method is surprisingly 28.81%. Furthermore, for strong nonlinearities with strong damping effect, the absolute relative error found in this article is only 0.02%, whereas the relative error obtained by MSLP method is 24.18%. Therefore, the present method is not only valid for weakly nonlinear damped forced systems, but also gives better result for strongly nonlinear systems with both small and strong damping effect.

Complex Systems

PubMed Central

Goldberger, Ary L.

2006-01-01

Physiologic systems in health and disease display an extraordinary range of temporal behaviors and structural patterns that defy understanding based on linear constructs, reductionist strategies, and classical homeostasis. Application of concepts and computational tools derived from the contemporary study of complex systems, including nonlinear dynamics, fractals and “chaos theory,” is having an increasing impact on biology and medicine. This presentation provides a brief overview of an emerging area of biomedical research, including recent applications to cardiopulmonary medicine and chronic obstructive lung disease. PMID:16921107

Resilience | Science Inventory | US EPA

EPA Pesticide Factsheets

Resilience is an important framework for understanding and managing complex systems of people and nature that are subject to abrupt and nonlinear change. The idea of ecological resilience was slow to gain acceptance in the scientific community, taking thirty years to become widely accepted (Gunderson 2000, cited under Original Definition). Currently, the concept is commonplace in academics, management, and policy. Although the idea has quantitative roots in the ecological sciences and was proposed as a measurable quality of ecosystems, the broad use of resilience led to an expansion of definitions and applications. Holling’s original definition, presented in 1973 (Holling 1973, cited under Original Definition), was simply the amount of disturbance that a system can withstand before it shifts into an alternative stability domain. Ecological resilience, therefore, emphasizes that the dynamics of complex systems are nonlinear, meaning that these systems can transition, often abruptly, between dynamic states with substantially different structures, functions, and processes. The transition of ecological systems from one state to another frequently has important repercussions for humans. Recent definitions are more normative and qualitative, especially in the social sciences, and a competing definition, that of engineering resilience, is still often used. Resilience is an emergent phenomenon of complex systems, which means it cannot be deduced from the behavior of t

Characterizing Feedback Control Mechanisms in Nonlinear Microbial Models of Soil Organic Matter Decomposition by Stability Analysis

NASA Astrophysics Data System (ADS)

Georgiou, K.; Tang, J.; Riley, W. J.; Torn, M. S.

2014-12-01

Soil organic matter (SOM) decomposition is regulated by biotic and abiotic processes. Feedback interactions between such processes may act to dampen oscillatory responses to perturbations from equilibrium. Indeed, although biological oscillations have been observed in small-scale laboratory incubations, the overlying behavior at the plot-scale exhibits a relatively stable response to disturbances in input rates and temperature. Recent studies have demonstrated the ability of microbial models to capture nonlinear feedbacks in SOM decomposition that linear Century-type models are unable to reproduce, such as soil priming in response to increased carbon input. However, these microbial models often exhibit strong oscillatory behavior that is deemed unrealistic. The inherently nonlinear dynamics of SOM decomposition have important implications for global climate-carbon and carbon-concentration feedbacks. It is therefore imperative to represent these dynamics in Earth System Models (ESMs) by introducing sub-models that accurately represent microbial and abiotic processes. In the present study we explore, both analytically and numerically, four microbe-enabled model structures of varying levels of complexity. The most complex model combines microbial physiology, a non-linear mineral sorption isotherm, and enzyme dynamics. Based on detailed stability analysis of the nonlinear dynamics, we calculate the system modes as functions of model parameters. This dependence provides insight into the source of state oscillations. We find that feedback mechanisms that emerge from careful representation of enzyme and mineral interactions, with parameter values in a prescribed range, are critical for both maintaining system stability and capturing realistic responses to disturbances. Corroborating and expanding upon the results of recent studies, we explain the emergence of oscillatory responses and discuss the appropriate microbe-enabled model structure for inclusion in ESMs.

Constant envelope OFDM scheme for 6PolSK-QPSK

NASA Astrophysics Data System (ADS)

Li, Yupeng; Ding, Ding

2018-03-01

A constant envelope OFDM scheme with phase modulator (PM-CE-OFDM) for 6PolSK-QPSK modulation was demonstrated. Performance under large fiber launch power is measured to check its advantages in counteracting fiber nonlinear impairments. In our simulation, PM-CE-OFDM, RF-assisted constant envelope OFDM (RF-CE-OFDM) and conventional OFDM (Con-OFDM) are transmitted through 80 km standard single mode fiber (SSMF) single channel and WDM system. Simulation results confirm that PM-CE-OFDM has best performance in resisting fiber nonlinearity. In addition, benefiting from the simple system structure, the complexity and cost of PM-CE-OFDM system could be reduced effectively.

Further Results of Soft-Inplane Tiltrotor Aeromechanics Investigation Using Two Multibody Analyses

NASA Technical Reports Server (NTRS)

Masarati, Pierangelo; Quaranta, Giuseppe; Piatak, David J.; Singleton, Jeffrey D.

2004-01-01

This investigation focuses on the development of multibody analytical models to predict the dynamic response, aeroelastic stability, and blade loading of a soft-inplane tiltrotor wind-tunnel model. Comprehensive rotorcraft-based multibody analyses enable modeling of the rotor system to a high level of detail such that complex mechanics and nonlinear effects associated with control system geometry and joint deadband may be considered. The influence of these and other nonlinear effects on the aeromechanical behavior of the tiltrotor model are examined. A parametric study of the design parameters which may have influence on the aeromechanics of the soft-inplane rotor system are also included in this investigation.

Tour time in a two-route traffic system controlled by signals

NASA Astrophysics Data System (ADS)

Nagatani, Takashi; Naito, Yuichi

2011-11-01

We study the dynamic behavior of vehicular traffic in a two-route system with a series of signals (traffic lights) at low density where the number of signals on route A is different from that on route B. We investigate the dependence of the tour time on the route for some strategies of signal control. The nonlinear dynamic model of a two-route traffic system controlled by signals is presented by nonlinear maps. The vehicular traffic exhibits a very complex behavior, depending on the cycle time, the phase difference, and the irregularity. The dependence of the tour time on the route choice is clarified for the signal strategies.

High-resolution broadband terahertz spectroscopy via electronic heterodyne detection of photonically generated terahertz frequency comb.

PubMed

Pavelyev, D G; Skryl, A S; Bakunov, M I

2014-10-01

We report an alternative approach to the terahertz frequency-comb spectroscopy (TFCS) based on nonlinear mixing of a photonically generated terahertz pulse train with a continuous wave signal from an electronic synthesizer. A superlattice is used as a nonlinear mixer. Unlike the standard TFCS technique, this approach does not require a complex double-laser system but retains the advantages of TFCS-high spectral resolution and wide bandwidth.

Nonlinear dynamics in the study of birdsong

NASA Astrophysics Data System (ADS)

Mindlin, Gabriel B.

2017-09-01

Birdsong, a rich and complex behavior, is a stellar model to understand a variety of biological problems, from motor control to learning. It also enables us to study how behavior emerges when a nervous system, a biomechanical device and the environment interact. In this review, I will show that many questions in the field can benefit from the approach of nonlinear dynamics, and how birdsong can inspire new directions for research in dynamics.

Nonlinear Relaxation in Population Dynamics

NASA Astrophysics Data System (ADS)

Cirone, Markus A.; de Pasquale, Ferdinando; Spagnolo, Bernardo

We analyze the nonlinear relaxation of a complex ecosystem composed of many interacting species. The ecological system is described by generalized Lotka-Volterra equations with a multiplicative noise. The transient dynamics is studied in the framework of the mean field theory and with random interaction between the species. We focus on the statistical properties of the asymptotic behaviour of the time integral of the ith population and on the distribution of the population and of the local field.

On the nonlinear stability of the unsteady, viscous flow of an incompressible fluid in a curved pipe

NASA Technical Reports Server (NTRS)

Shortis, Trudi A.; Hall, Philip

1995-01-01

The stability of the flow of an incompressible, viscous fluid through a pipe of circular cross-section curved about a central axis is investigated in a weakly nonlinear regime. A sinusoidal pressure gradient with zero mean is imposed, acting along the pipe. A WKBJ perturbation solution is constructed, taking into account the need for an inner solution in the vicinity of the outer bend, which is obtained by identifying the saddle point of the Taylor number in the complex plane of the cross-sectional angle co-ordinate. The equation governing the nonlinear evolution of the leading order vortex amplitude is thus determined. The stability analysis of this flow to periodic disturbances leads to a partial differential system dependent on three variables, and since the differential operators in this system are periodic in time, Floquet theory may be applied to reduce this system to a coupled infinite system of ordinary differential equations, together with homogeneous uncoupled boundary conditions. The eigenvalues of this system are calculated numerically to predict a critical Taylor number consistent with the analysis of Papageorgiou. A discussion of how nonlinear effects alter the linear stability analysis is also given, and the nature of the instability determined.

Atomic switch networks as complex adaptive systems

NASA Astrophysics Data System (ADS)

Scharnhorst, Kelsey S.; Carbajal, Juan P.; Aguilera, Renato C.; Sandouk, Eric J.; Aono, Masakazu; Stieg, Adam Z.; Gimzewski, James K.

2018-03-01

Complexity is an increasingly crucial aspect of societal, environmental and biological phenomena. Using a dense unorganized network of synthetic synapses it is shown that a complex adaptive system can be physically created on a microchip built especially for complex problems. These neuro-inspired atomic switch networks (ASNs) are a dynamic system with inherent and distributed memory, recurrent pathways, and up to a billion interacting elements. We demonstrate key parameters describing self-organized behavior such as non-linearity, power law dynamics, and multistate switching regimes. Device dynamics are then investigated using a feedback loop which provides control over current and voltage power-law behavior. Wide ranging prospective applications include understanding and eventually predicting future events that display complex emergent behavior in the critical regime.

A 1.26 μW Cytomimetic IC Emulating Complex Nonlinear Mammalian Cell Cycle Dynamics: Synthesis, Simulation and Proof-of-Concept Measured Results.

PubMed

Houssein, Alexandros; Papadimitriou, Konstantinos I; Drakakis, Emmanuel M

2015-08-01

Cytomimetic circuits represent a novel, ultra low-power, continuous-time, continuous-value class of circuits, capable of mapping on silicon cellular and molecular dynamics modelled by means of nonlinear ordinary differential equations (ODEs). Such monolithic circuits are in principle able to emulate on chip, single or multiple cell operations in a highly parallel fashion. Cytomimetic topologies can be synthesized by adopting the Nonlinear Bernoulli Cell Formalism (NBCF), a mathematical framework that exploits the striking similarities between the equations describing weakly-inverted Metal-Oxide Semiconductor (MOS) devices and coupled nonlinear ODEs, typically appearing in models of naturally encountered biochemical systems. The NBCF maps biological state variables onto strictly positive subthreshold MOS circuit currents. This paper presents the synthesis, the simulation and proof-of-concept chip results corresponding to the emulation of a complex cellular network mechanism, the skeleton model for the network of Cyclin-dependent Kinases (CdKs) driving the mammalian cell cycle. This five variable nonlinear biological model, when appropriate model parameter values are assigned, can exhibit multiple oscillatory behaviors, varying from simple periodic oscillations, to complex oscillations such as quasi-periodicity and chaos. The validity of our approach is verified by simulated results with realistic process parameters from the commercially available AMS 0.35 μm technology and by chip measurements. The fabricated chip occupies an area of 2.27 mm2 and consumes a power of 1.26 μW from a power supply of 3 V. The presented cytomimetic topology follows closely the behavior of its biological counterpart, exhibiting similar time-dependent solutions of the Cdk complexes, the transcription factors and the proteins.

A new approach for designing self-organizing systems and application to adaptive control

NASA Technical Reports Server (NTRS)

Ramamoorthy, P. A.; Zhang, Shi; Lin, Yueqing; Huang, Song

1993-01-01

There is tremendous interest in the design of intelligent machines capable of autonomous learning and skillful performance under complex environments. A major task in designing such systems is to make the system plastic and adaptive when presented with new and useful information and stable in response to irrelevant events. A great body of knowledge, based on neuro-physiological concepts, has evolved as a possible solution to this problem. Adaptive resonance theory (ART) is a classical example under this category. The system dynamics of an ART network is described by a set of differential equations with nonlinear functions. An approach for designing self-organizing networks characterized by nonlinear differential equations is proposed.

Artificial Neural Networks

NASA Technical Reports Server (NTRS)

Niebur, Dagmar

1995-01-01

Electric power systems represent complex systems involving many electrical components whoseoperation has to be planned, analyzed, monitored and controlled. The time-scale of tasks in electricpower systems extends from long term planning years ahead to milliseconds in the area of control. The behavior of power systems is highly non-linear. Monitoring and control involves several hundred variables which are only partly available by measurements.

Improving dynamic performances of PWM-driven servo-pneumatic systems via a novel pneumatic circuit.

PubMed

Taghizadeh, Mostafa; Ghaffari, Ali; Najafi, Farid

2009-10-01

In this paper, the effect of pneumatic circuit design on the input-output behavior of PWM-driven servo-pneumatic systems is investigated and their control performances are improved using linear controllers instead of complex and costly nonlinear ones. Generally, servo-pneumatic systems are well known for their nonlinear behavior. However, PWM-driven servo-pneumatic systems have the advantage of flexibility in the design of pneumatic circuits which affects the input-output linearity of the whole system. A simple pneumatic circuit with only one fast switching valve is designed which leads to a quasi-linear input-output relation. The quasi-linear behavior of the proposed circuit is verified both experimentally and by simulations. Closed loop position control experiments are then carried out using linear P- and PD-controllers. Since the output position is noisy and cannot be directly differentiated, a Kalman filter is designed to estimate the velocity of the cylinder. Highly improved tracking performances are obtained using these linear controllers, compared to previous works with nonlinear controllers.

Conceptualising population health: from mechanistic thinking to complexity science.

PubMed

Jayasinghe, Saroj

2011-01-20

The mechanistic interpretation of reality can be traced to the influential work by René Descartes and Sir Isaac Newton. Their theories were able to accurately predict most physical phenomena relating to motion, optics and gravity. This paradigm had at least three principles and approaches: reductionism, linearity and hierarchy. These ideas appear to have influenced social scientists and the discourse on population health. In contrast, Complexity Science takes a more holistic view of systems. It views natural systems as being 'open', with fuzzy borders, constantly adapting to cope with pressures from the environment. These are called Complex Adaptive Systems (CAS). The sub-systems within it lack stable hierarchies, and the roles of agency keep changing. The interactions with the environment and among sub-systems are non-linear interactions and lead to self-organisation and emergent properties. Theoretical frameworks such as epi+demos+cracy and the ecosocial approach to health have implicitly used some of these concepts of interacting dynamic sub-systems. Using Complexity Science we can view population health outcomes as an emergent property of CAS, which has numerous dynamic non-linear interactions among its interconnected sub-systems or agents. In order to appreciate these sub-systems and determinants, one should acquire a basic knowledge of diverse disciplines and interact with experts from different disciplines. Strategies to improve health should be multi-pronged, and take into account the diversity of actors, determinants and contexts. The dynamic nature of the system requires that the interventions are constantly monitored to provide early feedback to a flexible system that takes quick corrections.

Paucity of attractors in nonlinear systems driven with complex signals.

PubMed

Pethel, Shawn D; Blakely, Jonathan N

2011-04-01

We study the probability of multistability in a quadratic map driven repeatedly by a random signal of length N, where N is taken as a measure of the signal complexity. We first establish analytically that the number of coexisting attractors is bounded above by N. We then numerically estimate the probability p of a randomly chosen signal resulting in a multistable response as a function of N. Interestingly, with increasing drive signal complexity the system exhibits a paucity of attractors. That is, almost any drive signal beyond a certain complexity level will result in a single attractor response (p=0). This mechanism may play a role in allowing sensitive multistable systems to respond consistently to external influences.

A general U-block model-based design procedure for nonlinear polynomial control systems

NASA Astrophysics Data System (ADS)

Zhu, Q. M.; Zhao, D. Y.; Zhang, Jianhua

2016-10-01

The proposition of U-model concept (in terms of 'providing concise and applicable solutions for complex problems') and a corresponding basic U-control design algorithm was originated in the first author's PhD thesis. The term of U-model appeared (not rigorously defined) for the first time in the first author's other journal paper, which established a framework for using linear polynomial control system design approaches to design nonlinear polynomial control systems (in brief, linear polynomial approaches → nonlinear polynomial plants). This paper represents the next milestone work - using linear state-space approaches to design nonlinear polynomial control systems (in brief, linear state-space approaches → nonlinear polynomial plants). The overall aim of the study is to establish a framework, defined as the U-block model, which provides a generic prototype for using linear state-space-based approaches to design the control systems with smooth nonlinear plants/processes described by polynomial models. For analysing the feasibility and effectiveness, sliding mode control design approach is selected as an exemplary case study. Numerical simulation studies provide a user-friendly step-by-step procedure for the readers/users with interest in their ad hoc applications. In formality, this is the first paper to present the U-model-oriented control system design in a formal way and to study the associated properties and theorems. The previous publications, in the main, have been algorithm-based studies and simulation demonstrations. In some sense, this paper can be treated as a landmark for the U-model-based research from intuitive/heuristic stage to rigour/formal/comprehensive studies.

Nonlinear and adaptive control

NASA Technical Reports Server (NTRS)

Athans, Michael

1989-01-01

The primary thrust of the research was to conduct fundamental research in the theories and methodologies for designing complex high-performance multivariable feedback control systems; and to conduct feasibiltiy studies in application areas of interest to NASA sponsors that point out advantages and shortcomings of available control system design methodologies.

Volterra series based blind equalization for nonlinear distortions in short reach optical CAP system

NASA Astrophysics Data System (ADS)

Tao, Li; Tan, Hui; Fang, Chonghua; Chi, Nan

2016-12-01

In this paper, we propose a blind Volterra series based nonlinear equalization (VNLE) with low complexity for the nonlinear distortion mitigation in short reach optical carrierless amplitude and phase (CAP) modulation system. The principle of the blind VNLE is presented and the performance of its blind adaptive algorithms including the modified cascaded multi-mode algorithm (MCMMA) and direct detection LMS (DD-LMS) are investigated experimentally. Compared to the conventional VNLE using training symbols before demodulation, it is performed after matched filtering and downsampling, so shorter memory length is required but similar performance improvement is observed. About 1 dB improvement is observed at BER of 3.8×10-3 for 40 Gb/s CAP32 signal over 40 km standard single mode fiber.

Directed dynamical influence is more detectable with noise

PubMed Central

Jiang, Jun-Jie; Huang, Zi-Gang; Huang, Liang; Liu, Huan; Lai, Ying-Cheng

2016-01-01

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence. PMID:27066763

Directed dynamical influence is more detectable with noise.

PubMed

Jiang, Jun-Jie; Huang, Zi-Gang; Huang, Liang; Liu, Huan; Lai, Ying-Cheng

2016-04-12

Successful identification of directed dynamical influence in complex systems is relevant to significant problems of current interest. Traditional methods based on Granger causality and transfer entropy have issues such as difficulty with nonlinearity and large data requirement. Recently a framework based on nonlinear dynamical analysis was proposed to overcome these difficulties. We find, surprisingly, that noise can counterintuitively enhance the detectability of directed dynamical influence. In fact, intentionally injecting a proper amount of asymmetric noise into the available time series has the unexpected benefit of dramatically increasing confidence in ascertaining the directed dynamical influence in the underlying system. This result is established based on both real data and model time series from nonlinear ecosystems. We develop a physical understanding of the beneficial role of noise in enhancing detection of directed dynamical influence.

Untangling Brain-Wide Dynamics in Consciousness by Cross-Embedding

PubMed Central

Tajima, Satohiro; Yanagawa, Toru; Fujii, Naotaka; Toyoizumi, Taro

2015-01-01

Brain-wide interactions generating complex neural dynamics are considered crucial for emergent cognitive functions. However, the irreducible nature of nonlinear and high-dimensional dynamical interactions challenges conventional reductionist approaches. We introduce a model-free method, based on embedding theorems in nonlinear state-space reconstruction, that permits a simultaneous characterization of complexity in local dynamics, directed interactions between brain areas, and how the complexity is produced by the interactions. We demonstrate this method in large-scale electrophysiological recordings from awake and anesthetized monkeys. The cross-embedding method captures structured interaction underlying cortex-wide dynamics that may be missed by conventional correlation-based analysis, demonstrating a critical role of time-series analysis in characterizing brain state. The method reveals a consciousness-related hierarchy of cortical areas, where dynamical complexity increases along with cross-area information flow. These findings demonstrate the advantages of the cross-embedding method in deciphering large-scale and heterogeneous neuronal systems, suggesting a crucial contribution by sensory-frontoparietal interactions to the emergence of complex brain dynamics during consciousness. PMID:26584045

The topology of non-linear global carbon dynamics: from tipping points to planetary boundaries

NASA Astrophysics Data System (ADS)

Anderies, J. M.; Carpenter, S. R.; Steffen, Will; Rockström, Johan

2013-12-01

We present a minimal model of land use and carbon cycle dynamics and use it to explore the relationship between non-linear dynamics and planetary boundaries. Only the most basic interactions between land cover and terrestrial, atmospheric, and marine carbon stocks are considered in the model. Our goal is not to predict global carbon dynamics as it occurs in the actual Earth System. Rather, we construct a conceptually reasonable heuristic model of a feedback system between different carbon stocks that captures the qualitative features of the actual Earth System and use it to explore the topology of the boundaries of what can be called a ‘safe operating space’ for humans. The model analysis illustrates the existence of dynamic, non-linear tipping points in carbon cycle dynamics and the potential complexity of planetary boundaries. Finally, we use the model to illustrate some challenges associated with navigating planetary boundaries.

Nonlinear adhesion dynamics of confined lipid membranes

NASA Astrophysics Data System (ADS)

To, Tung; Le Goff, Thomas; Pierre-Louis, Olivier

Lipid membranes, which are ubiquitous objects in biological environments are often confined. For example, they can be sandwiched between a substrate and the cytoskeleton between cell adhesion, or between other membranes in stacks, or in the Golgi apparatus. We present a study of the nonlinear dynamics of membranes in a model system, where the membrane is confined between two flat walls. The dynamics derived from the lubrication approximation is highly nonlinear and nonlocal. The solution of this model in one dimension exhibits frozen states due to oscillatory interactions between membranes caused by the bending rigidity. We develope a kink model for these phenomena based on the historical work of Kawasaki and Otha. In two dimensions, the dynamics is more complex, and depends strongly on the amount of excess area in the system. We discuss the relevance of our findings for experiments on model membranes, and for biological systems. Supported by the grand ANR Biolub.

Lifespan differences in nonlinear dynamics during rest and auditory oddball performance.

PubMed

Müller, Viktor; Lindenberger, Ulman

2012-07-01

Electroencephalographic recordings (EEG) were used to assess age-associated differences in nonlinear brain dynamics during both rest and auditory oddball performance in children aged 9.0-12.8 years, younger adults, and older adults. We computed nonlinear coupling dynamics and dimensional complexity, and also determined spectral alpha power as an indicator of cortical reactivity. During rest, both nonlinear coupling and spectral alpha power decreased with age, whereas dimensional complexity increased. In contrast, when attending to the deviant stimulus, nonlinear coupling increased with age, and complexity decreased. Correlational analyses showed that nonlinear measures assessed during auditory oddball performance were reliably related to an independently assessed measure of perceptual speed. We conclude that cortical dynamics during rest and stimulus processing undergo substantial reorganization from childhood to old age, and propose that lifespan age differences in nonlinear dynamics during stimulus processing reflect lifespan changes in the functional organization of neuronal cell assemblies. © 2012 Blackwell Publishing Ltd.

Optimal Energy Measurement in Nonlinear Systems: An Application of Differential Geometry

NASA Technical Reports Server (NTRS)

Fixsen, Dale J.; Moseley, S. H.; Gerrits, T.; Lita, A.; Nam, S. W.

2014-01-01

Design of TES microcalorimeters requires a tradeoff between resolution and dynamic range. Often, experimenters will require linearity for the highest energy signals, which requires additional heat capacity be added to the detector. This results in a reduction of low energy resolution in the detector. We derive and demonstrate an algorithm that allows operation far into the nonlinear regime with little loss in spectral resolution. We use a least squares optimal filter that varies with photon energy to accommodate the nonlinearity of the detector and the non-stationarity of the noise. The fitting process we use can be seen as an application of differential geometry. This recognition provides a set of well-developed tools to extend our work to more complex situations. The proper calibration of a nonlinear microcalorimeter requires a source with densely spaced narrow lines. A pulsed laser multi-photon source is used here, and is seen to be a powerful tool for allowing us to develop practical systems with significant detector nonlinearity. The combination of our analysis techniques and the multi-photon laser source create a powerful tool for increasing the performance of future TES microcalorimeters.

Functional complexity and ecosystem stability: an experimental approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Van Voris, P.; O'Neill, R.V.; Shugart, H.H.

1978-01-01

The complexity-stability hypothesis was experimentally tested using intact terrestrial microcosms. Functional complexity was defined as the number and significance of component interactions (i.e., population interactions, physical-chemical reactions, biological turnover rates) influenced by nonlinearities, feedbacks, and time delays. It was postulated that functional complexity could be nondestructively measured through analysis of a signal generated from the system. Power spectral analysis of hourly CO/sub 2/ efflux, from eleven old-field microcosms, was analyzed for the number of low frequency peaks and used to rank the functional complexity of each system. Ranking of ecosystem stability was based on the capacity of the system tomore » retain essential nutrients and was measured by net loss of Ca after the system was stressed. Rank correlation supported the hypothesis that increasing ecosystem functional complexity leads to increasing ecosystem stability. The results indicated that complex functional dynamics can serve to stabilize the system. The results also demonstrated that microcosms are useful tools for system-level investigations.« less

Superstructure-based Design and Optimization of Batch Biodiesel Production Using Heterogeneous Catalysts

NASA Astrophysics Data System (ADS)

Nuh, M. Z.; Nasir, N. F.

2017-08-01

Biodiesel as a fuel comprised of mono alkyl esters of long chain fatty acids derived from renewable lipid feedstock, such as vegetable oil and animal fat. Biodiesel production is complex process which need systematic design and optimization. However, no case study using the process system engineering (PSE) elements which are superstructure optimization of batch process, it involves complex problems and uses mixed-integer nonlinear programming (MINLP). The PSE offers a solution to complex engineering system by enabling the use of viable tools and techniques to better manage and comprehend the complexity of the system. This study is aimed to apply the PSE tools for the simulation of biodiesel process and optimization and to develop mathematical models for component of the plant for case A, B, C by using published kinetic data. Secondly, to determine economic analysis for biodiesel production, focusing on heterogeneous catalyst. Finally, the objective of this study is to develop the superstructure for biodiesel production by using heterogeneous catalyst. The mathematical models are developed by the superstructure and solving the resulting mixed integer non-linear model and estimation economic analysis by using MATLAB software. The results of the optimization process with the objective function of minimizing the annual production cost by batch process from case C is 23.2587 million USD. Overall, the implementation a study of process system engineering (PSE) has optimized the process of modelling, design and cost estimation. By optimizing the process, it results in solving the complex production and processing of biodiesel by batch.

Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems.

PubMed

McMahon, Christopher J; Toomey, Joshua P; Kane, Deb M

2017-01-01

We have analysed large data sets consisting of tens of thousands of time series from three Type B laser systems: a semiconductor laser in a photonic integrated chip, a semiconductor laser subject to optical feedback from a long free-space-external-cavity, and a solid-state laser subject to optical injection from a master laser. The lasers can deliver either constant, periodic, pulsed, or chaotic outputs when parameters such as the injection current and the level of external perturbation are varied. The systems represent examples of experimental nonlinear systems more generally and cover a broad range of complexity including systematically varying complexity in some regions. In this work we have introduced a new procedure for semi-automatically interrogating experimental laser system output power time series to calculate the correlation dimension (CD) using the commonly adopted Grassberger-Proccacia algorithm. The new CD procedure is called the 'minimum gradient detection algorithm'. A value of minimum gradient is returned for all time series in a data set. In some cases this can be identified as a CD, with uncertainty. Applying the new 'minimum gradient detection algorithm' CD procedure, we obtained robust measurements of the correlation dimension for many of the time series measured from each laser system. By mapping the results across an extended parameter space for operation of each laser system, we were able to confidently identify regions of low CD (CD < 3) and assign these robust values for the correlation dimension. However, in all three laser systems, we were not able to measure the correlation dimension at all parts of the parameter space. Nevertheless, by mapping the staged progress of the algorithm, we were able to broadly classify the dynamical output of the lasers at all parts of their respective parameter spaces. For two of the laser systems this included displaying regions of high-complexity chaos and dynamic noise. These high-complexity regions are differentiated from regions where the time series are dominated by technical noise. This is the first time such differentiation has been achieved using a CD analysis approach. More can be known of the CD for a system when it is interrogated in a mapping context, than from calculations using isolated time series. This has been shown for three laser systems and the approach is expected to be useful in other areas of nonlinear science where large data sets are available and need to be semi-automatically analysed to provide real dimensional information about the complex dynamics. The CD/minimum gradient algorithm measure provides additional information that complements other measures of complexity and relative complexity, such as the permutation entropy; and conventional physical measurements.

Insights on correlation dimension from dynamics mapping of three experimental nonlinear laser systems

PubMed Central

McMahon, Christopher J.; Toomey, Joshua P.

2017-01-01

Background We have analysed large data sets consisting of tens of thousands of time series from three Type B laser systems: a semiconductor laser in a photonic integrated chip, a semiconductor laser subject to optical feedback from a long free-space-external-cavity, and a solid-state laser subject to optical injection from a master laser. The lasers can deliver either constant, periodic, pulsed, or chaotic outputs when parameters such as the injection current and the level of external perturbation are varied. The systems represent examples of experimental nonlinear systems more generally and cover a broad range of complexity including systematically varying complexity in some regions. Methods In this work we have introduced a new procedure for semi-automatically interrogating experimental laser system output power time series to calculate the correlation dimension (CD) using the commonly adopted Grassberger-Proccacia algorithm. The new CD procedure is called the ‘minimum gradient detection algorithm’. A value of minimum gradient is returned for all time series in a data set. In some cases this can be identified as a CD, with uncertainty. Findings Applying the new ‘minimum gradient detection algorithm’ CD procedure, we obtained robust measurements of the correlation dimension for many of the time series measured from each laser system. By mapping the results across an extended parameter space for operation of each laser system, we were able to confidently identify regions of low CD (CD < 3) and assign these robust values for the correlation dimension. However, in all three laser systems, we were not able to measure the correlation dimension at all parts of the parameter space. Nevertheless, by mapping the staged progress of the algorithm, we were able to broadly classify the dynamical output of the lasers at all parts of their respective parameter spaces. For two of the laser systems this included displaying regions of high-complexity chaos and dynamic noise. These high-complexity regions are differentiated from regions where the time series are dominated by technical noise. This is the first time such differentiation has been achieved using a CD analysis approach. Conclusions More can be known of the CD for a system when it is interrogated in a mapping context, than from calculations using isolated time series. This has been shown for three laser systems and the approach is expected to be useful in other areas of nonlinear science where large data sets are available and need to be semi-automatically analysed to provide real dimensional information about the complex dynamics. The CD/minimum gradient algorithm measure provides additional information that complements other measures of complexity and relative complexity, such as the permutation entropy; and conventional physical measurements. PMID:28837602

Nonlinear optical properties and excited state dynamics of sandwich-type mixed (phthalocyaninato)(Schiff-base) triple-decker complexes: Effect of rare earth atom

NASA Astrophysics Data System (ADS)

Li, Zhongguo; Gao, Feng; Xiao, Zhengguo; Wu, Xingzhi; Zuo, Jinglin; Song, Yinglin

2018-07-01

The third-order nonlinear optical properties of two di-lanthanide (Ln = Tb and Dy) sandwich complexes with mixed phthalocyanine and Schiff-base ligands were studied using Z-scan technique at 532 nm with 20 ps and 4 ns pulses. Both complexes exhibit reverse saturable absorption and self-focusing effect in ps regime, while the second-order hyperpolarizability decreases from Dy to Tb. Interestingly, the Tb triple-decker complexes show larger nonlinear absorption than Dy complexes on ns timescale. The time-resolved pump-probe measurements demonstrate that the nonlinear optical response was caused by excited-state mechanism related to the five-level model, while the singlet state lifetime of Dy complexes is 3 times shorter than that of Tb complexes. Our results indicate the lanthanide ions play a critical role in the photo-physical properties of triple-decker phthalocyanine complexes for their application as optical limiting materials.

Model-based approach to study the impact of biofuels on the sustainability of an ecological system

EPA Science Inventory

The importance and complexity of sustainability have been well recognized and a formal study of sustainability based on system theory approaches is imperative as many of the relationships between various components of the ecosystem could be nonlinear, intertwined and non-intuitiv...

Model based approach to Study the Impact of Biofuels on the Sustainability of an Ecological System

EPA Science Inventory

The importance and complexity of sustainability has been well recognized and a formal study of sustainability based on system theory approaches is imperative as many of the relationships between various components of the ecosystem could be nonlinear, intertwined and non intuitive...

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane.

PubMed

Liu, T Y; Chiu, T L; Clarkson, P A; Chow, K W

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

A connection between the maximum displacements of rogue waves and the dynamics of poles in the complex plane

NASA Astrophysics Data System (ADS)

Liu, T. Y.; Chiu, T. L.; Clarkson, P. A.; Chow, K. W.

2017-09-01

Rogue waves of evolution systems are displacements which are localized in both space and time. The locations of the points of maximum displacements of the wave profiles may correlate with the trajectories of the poles of the exact solutions from the perspective of complex variables through analytic continuation. More precisely, the location of the maximum height of the rogue wave in laboratory coordinates (real space and time) is conjectured to be equal to the real part of the pole of the exact solution, if the spatial coordinate is allowed to be complex. This feature can be verified readily for the Peregrine breather (lowest order rogue wave) of the nonlinear Schrödinger equation. This connection is further demonstrated numerically here for more complicated scenarios, namely the second order rogue wave of the Boussinesq equation (for bidirectional long waves in shallow water), an asymmetric second order rogue wave for the nonlinear Schrödinger equation (as evolution system for slowly varying wave packets), and a symmetric second order rogue wave of coupled Schrödinger systems. Furthermore, the maximum displacements in physical space occur at a time instant where the trajectories of the poles in the complex plane reverse directions. This property is conjectured to hold for many other systems, and will help to determine the maximum amplitudes of rogue waves.

Regression of non-linear coupling of noise in LIGO detectors

NASA Astrophysics Data System (ADS)

Da Silva Costa, C. F.; Billman, C.; Effler, A.; Klimenko, S.; Cheng, H.-P.

2018-03-01

In 2015, after their upgrade, the advanced Laser Interferometer Gravitational-Wave Observatory (LIGO) detectors started acquiring data. The effort to improve their sensitivity has never stopped since then. The goal to achieve design sensitivity is challenging. Environmental and instrumental noise couple to the detector output with different, linear and non-linear, coupling mechanisms. The noise regression method we use is based on the Wiener–Kolmogorov filter, which uses witness channels to make noise predictions. We present here how this method helped to determine complex non-linear noise couplings in the output mode cleaner and in the mirror suspension system of the LIGO detector.

Monitoring a Complex Physical System using a Hybrid Dynamic Bayes Net

NASA Technical Reports Server (NTRS)

Lerner, Uri; Moses, Brooks; Scott, Maricia; McIlraith, Sheila; Keller, Daphne

2005-01-01

The Reverse Water Gas Shift system (RWGS) is a complex physical system designed to produce oxygen from the carbon dioxide atmosphere on Mars. If sent to Mars, it would operate without human supervision, thus requiring a reliable automated system for monitoring and control. The RWGS presents many challenges typical of real-world systems, including: noisy and biased sensors, nonlinear behavior, effects that are manifested over different time granularities, and unobservability of many important quantities. In this paper we model the RWGS using a hybrid (discrete/continuous) Dynamic Bayesian Network (DBN), where the state at each time slice contains 33 discrete and 184 continuous variables. We show how the system state can be tracked using probabilistic inference over the model. We discuss how to deal with the various challenges presented by the RWGS, providing a suite of techniques that are likely to be useful in a wide range of applications. In particular, we describe a general framework for dealing with nonlinear behavior using numerical integration techniques, extending the successful Unscented Filter. We also show how to use a fixed-point computation to deal with effects that develop at different time scales, specifically rapid changes occuring during slowly changing processes. We test our model using real data collected from the RWGS, demonstrating the feasibility of hybrid DBNs for monitoring complex real-world physical systems.

Double symbolic joint entropy in nonlinear dynamic complexity analysis

NASA Astrophysics Data System (ADS)

Yao, Wenpo; Wang, Jun

2017-07-01

Symbolizations, the base of symbolic dynamic analysis, are classified as global static and local dynamic approaches which are combined by joint entropy in our works for nonlinear dynamic complexity analysis. Two global static methods, symbolic transformations of Wessel N. symbolic entropy and base-scale entropy, and two local ones, namely symbolizations of permutation and differential entropy, constitute four double symbolic joint entropies that have accurate complexity detections in chaotic models, logistic and Henon map series. In nonlinear dynamical analysis of different kinds of heart rate variability, heartbeats of healthy young have higher complexity than those of the healthy elderly, and congestive heart failure (CHF) patients are lowest in heartbeats' joint entropy values. Each individual symbolic entropy is improved by double symbolic joint entropy among which the combination of base-scale and differential symbolizations have best complexity analysis. Test results prove that double symbolic joint entropy is feasible in nonlinear dynamic complexity analysis.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations.

PubMed

Hu, Eric Y; Bouteiller, Jean-Marie C; Song, Dong; Baudry, Michel; Berger, Theodore W

2015-01-01

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations.

Volterra representation enables modeling of complex synaptic nonlinear dynamics in large-scale simulations

PubMed Central

Hu, Eric Y.; Bouteiller, Jean-Marie C.; Song, Dong; Baudry, Michel; Berger, Theodore W.

2015-01-01

Chemical synapses are comprised of a wide collection of intricate signaling pathways involving complex dynamics. These mechanisms are often reduced to simple spikes or exponential representations in order to enable computer simulations at higher spatial levels of complexity. However, these representations cannot capture important nonlinear dynamics found in synaptic transmission. Here, we propose an input-output (IO) synapse model capable of generating complex nonlinear dynamics while maintaining low computational complexity. This IO synapse model is an extension of a detailed mechanistic glutamatergic synapse model capable of capturing the input-output relationships of the mechanistic model using the Volterra functional power series. We demonstrate that the IO synapse model is able to successfully track the nonlinear dynamics of the synapse up to the third order with high accuracy. We also evaluate the accuracy of the IO synapse model at different input frequencies and compared its performance with that of kinetic models in compartmental neuron models. Our results demonstrate that the IO synapse model is capable of efficiently replicating complex nonlinear dynamics that were represented in the original mechanistic model and provide a method to replicate complex and diverse synaptic transmission within neuron network simulations. PMID:26441622

Nonlinear dynamics of the human lumbar intervertebral disc.

PubMed

Marini, Giacomo; Huber, Gerd; Püschel, Klaus; Ferguson, Stephen J

2015-02-05

Systems with a quasi-static response similar to the axial response of the intervertebral disc (i.e. progressive stiffening) often present complex dynamics, characterized by peculiar nonlinearities in the frequency response. However, such characteristics have not been reported for the dynamic response of the disc. The accurate understanding of disc dynamics is essential to investigate the unclear correlation between whole body vibration and low back pain. The present study investigated the dynamic response of the disc, including its potential nonlinear response, over a range of loading conditions. Human lumbar discs were tested by applying a static preload to the top and a sinusoidal displacement at the bottom of the disc. The frequency of the stimuli was set to increase linearly from a low frequency to a high frequency limit and back down. In general, the response showed nonlinear and asymmetric characteristics. For each test, the disc had different response in the frequency-increasing compared to the frequency-decreasing sweep. In particular, the system presented abrupt changes of the oscillation amplitude at specific frequencies, which differed between the two sweeps. This behaviour indicates that the system oscillation has a different equilibrium condition depending on the path followed by the stimuli. Preload and amplitude of the oscillation directly influenced the disc response by changing the nonlinear dynamics and frequency of the jump-phenomenon. These results show that the characterization of the dynamic response of physiological systems should be readdressed to determine potential nonlinearities. Their direct effect on the system function should be further investigated. Copyright © 2014 Elsevier Ltd. All rights reserved.

Limitations and tradeoffs in synchronization of large-scale networks with uncertain links

PubMed Central

Diwadkar, Amit; Vaidya, Umesh

2016-01-01

The synchronization of nonlinear systems connected over large-scale networks has gained popularity in a variety of applications, such as power grids, sensor networks, and biology. Stochastic uncertainty in the interconnections is a ubiquitous phenomenon observed in these physical and biological networks. We provide a size-independent network sufficient condition for the synchronization of scalar nonlinear systems with stochastic linear interactions over large-scale networks. This sufficient condition, expressed in terms of nonlinear dynamics, the Laplacian eigenvalues of the nominal interconnections, and the variance and location of the stochastic uncertainty, allows us to define a synchronization margin. We provide an analytical characterization of important trade-offs between the internal nonlinear dynamics, network topology, and uncertainty in synchronization. For nearest neighbour networks, the existence of an optimal number of neighbours with a maximum synchronization margin is demonstrated. An analytical formula for the optimal gain that produces the maximum synchronization margin allows us to compare the synchronization properties of various complex network topologies. PMID:27067994

A class of high resolution explicit and implicit shock-capturing methods

NASA Technical Reports Server (NTRS)

Yee, H. C.

1989-01-01

An attempt is made to give a unified and generalized formulation of a class of high resolution, explicit and implicit shock capturing methods, and to illustrate their versatility in various steady and unsteady complex shock wave computations. Included is a systematic review of the basic design principle of the various related numerical methods. Special emphasis is on the construction of the basis nonlinear, spatially second and third order schemes for nonlinear scalar hyperbolic conservation laws and the methods of extending these nonlinear scalar schemes to nonlinear systems via the approximate Riemann solvers and the flux vector splitting approaches. Generalization of these methods to efficiently include equilibrium real gases and large systems of nonequilibrium flows are discussed. Some issues concerning the applicability of these methods that were designed for homogeneous hyperbolic conservation laws to problems containing stiff source terms and shock waves are also included. The performance of some of these schemes is illustrated by numerical examples for 1-, 2- and 3-dimensional gas dynamics problems.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series.

PubMed

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Evaluation of nonlinearity and validity of nonlinear modeling for complex time series

NASA Astrophysics Data System (ADS)

Suzuki, Tomoya; Ikeguchi, Tohru; Suzuki, Masuo

2007-10-01

Even if an original time series exhibits nonlinearity, it is not always effective to approximate the time series by a nonlinear model because such nonlinear models have high complexity from the viewpoint of information criteria. Therefore, we propose two measures to evaluate both the nonlinearity of a time series and validity of nonlinear modeling applied to it by nonlinear predictability and information criteria. Through numerical simulations, we confirm that the proposed measures effectively detect the nonlinearity of an observed time series and evaluate the validity of the nonlinear model. The measures are also robust against observational noises. We also analyze some real time series: the difference of the number of chickenpox and measles patients, the number of sunspots, five Japanese vowels, and the chaotic laser. We can confirm that the nonlinear model is effective for the Japanese vowel /a/, the difference of the number of measles patients, and the chaotic laser.

Nonlinear viscosity in brane-world cosmology with a Gauss–Bonnet term

NASA Astrophysics Data System (ADS)

Debnath, P. S.; Beesham, A.; Paul, B. C.

2018-06-01

Cosmological solutions are obtained with nonlinear bulk viscous cosmological fluid in the Randall–Sundrum type II (RS) brane-world model with or without Gauss–Bonnet (GB) terms. To describe such a viscous fluid, we consider the nonlinear transport equation which may be used far from equilibrium during inflation or reheating. Cosmological models are explored for both (i) power law and (ii) exponential evolution of the early universe in the presence of an imperfect fluid described by the non-linear Israel and Stewart theory (nIS). We obtain analytic solutions and the complex field equations are also analyzed numerically to study the evolution of the universe. The stability analysis of the equilibrium points of the dynamical system associated with the evolution of the nonlinear bulk viscous fluid in the RS Brane in the presence (or absence) of a GB term are also studied.

Phenomenal enhancement of optical nonlinearity in PTZ-I based ZnS/ZnSe nanocomposites

NASA Astrophysics Data System (ADS)

Divyasree, M. C.; Shiju, E.; Vijisha, M. V.; Ramesan, M. T.; Chandrasekharan, K.

2018-05-01

The enhanced nonlinear optical properties of phenothiazine-iodine (PTZ-I) charge transfer complex (CTC) on composite formation with ZnS/ZnSe nanostructures are reported. The interaction between the components was confirmed by the FTIR spectra. Structural and morphological changes on nanocomposite formation were analyzed by scanning electron microscopy and X-ray diffraction spectra. The absorption and emission features of both the nanocomposites and their constituent components were studied. Nonlinear optical properties of all the samples in nanosecond regime were investigated by the Z-scan technique using Nd: YAG laser with 532 nm wavelength and 7 ns pulse width. The optical nonlinearity of PTZ-I CTC was found to be improved considerably on composite formation and the new systems can be proposed as excellent candidates for photonic devices. Enhanced optical nonlinearity of the composites could be attributed to charge/energy transfer mechanism between PTZ-I CTC and the nanostructures.

Traditional Knowledge of Western Herbal Medicine and Complex Systems Science

PubMed Central

Niemeyer, Kathryn; Bell, Iris R.; Koithan, Mary

2013-01-01

Traditional knowledge of Western herbal medicine (WHM) supports experiential approaches to healing that have evolved over time. This is evident in the use of polyherb formulations comprised of crude plant parts, individually tailored to treat the cause of dysfunction and imbalance by addressing the whole person holistically. The challenge for WHM is to integrate science with traditional knowledge that is a foundation of the practice of WHM. The purpose of this paper is to provide a plausible theoretical hypothesis by applying complex systems science to WHM, illustrating how medicinal plants are complex, adaptive, environmentally interactive systems exhibiting synergy and nonlinear healing causality. This paper explores the conceptual congruence between medicinal plants and humans as complex systems coherently coupled through recurrent interaction. Complex systems science provides the theoretical tenets that explain traditional knowledge of medicinal plants while supporting clinical practice and expanding research and documentation of WHM. PMID:24058898

Traditional Knowledge of Western Herbal Medicine and Complex Systems Science.

PubMed

Niemeyer, Kathryn; Bell, Iris R; Koithan, Mary

2013-09-01

Traditional knowledge of Western herbal medicine (WHM) supports experiential approaches to healing that have evolved over time. This is evident in the use of polyherb formulations comprised of crude plant parts, individually tailored to treat the cause of dysfunction and imbalance by addressing the whole person holistically. The challenge for WHM is to integrate science with traditional knowledge that is a foundation of the practice of WHM. The purpose of this paper is to provide a plausible theoretical hypothesis by applying complex systems science to WHM, illustrating how medicinal plants are complex, adaptive, environmentally interactive systems exhibiting synergy and nonlinear healing causality. This paper explores the conceptual congruence between medicinal plants and humans as complex systems coherently coupled through recurrent interaction. Complex systems science provides the theoretical tenets that explain traditional knowledge of medicinal plants while supporting clinical practice and expanding research and documentation of WHM.

Batch-mode Reinforcement Learning for improved hydro-environmental systems management

NASA Astrophysics Data System (ADS)

Castelletti, A.; Galelli, S.; Restelli, M.; Soncini-Sessa, R.

2010-12-01

Despite the great progresses made in the last decades, the optimal management of hydro-environmental systems still remains a very active and challenging research area. The combination of multiple, often conflicting interests, high non-linearities of the physical processes and the management objectives, strong uncertainties in the inputs, and high dimensional state makes the problem challenging and intriguing. Stochastic Dynamic Programming (SDP) is one of the most suitable methods for designing (Pareto) optimal management policies preserving the original problem complexity. However, it suffers from a dual curse, which, de facto, prevents its practical application to even reasonably complex water systems. (i) Computational requirement grows exponentially with state and control dimension (Bellman's curse of dimensionality), so that SDP can not be used with water systems where the state vector includes more than few (2-3) units. (ii) An explicit model of each system's component is required (curse of modelling) to anticipate the effects of the system transitions, i.e. any information included into the SDP framework can only be either a state variable described by a dynamic model or a stochastic disturbance, independent in time, with the associated pdf. Any exogenous information that could effectively improve the system operation cannot be explicitly considered in taking the management decision, unless a dynamic model is identified for each additional information, thus adding to the problem complexity through the curse of dimensionality (additional state variables). To mitigate this dual curse, the combined use of batch-mode Reinforcement Learning (bRL) and Dynamic Model Reduction (DMR) techniques is explored in this study. bRL overcomes the curse of modelling by replacing explicit modelling with an external simulator and/or historical observations. The curse of dimensionality is averted using a functional approximation of the SDP value function based on proper non-linear regressors. DMR reduces the complexity and the associated computational requirements of non-linear distributed process based models, making them suitable for being included into optimization schemes. Results from real world applications of the approach are also presented, including reservoir operation with both quality and quantity targets.

Resilience

EPA Science Inventory

Resilience is an important framework for understanding and managing complex systems of people and nature that are subject to abrupt and nonlinear change. The idea of ecological resilience was slow to gain acceptance in the scientific community, taking thirty years to become widel...

The Coupled Harmonic Oscillator: Not Just for Seniors Anymore.

ERIC Educational Resources Information Center

Preyer, Norris W.

1996-01-01

Presents experiments that use Microcomputer Based Laboratory (MBL) techniques to enable freshmen physics students to investigate complex systems, such as nonlinear oscillators or coupled harmonic oscillators, at a level appropriate for an independent project. (JRH)

An application of sample entropy to precipitation in Paraíba State, Brazil

NASA Astrophysics Data System (ADS)

Xavier, Sílvio Fernando Alves; da Silva Jale, Jader; Stosic, Tatijana; dos Santos, Carlos Antonio Costa; Singh, Vijay P.

2018-05-01

A climate system is characterized to be a complex non-linear system. In order to describe the complex characteristics of precipitation series in Paraíba State, Brazil, we aim the use of sample entropy, a kind of entropy-based algorithm, to evaluate the complexity of precipitation series. Sixty-nine meteorological stations are distributed over four macroregions: Zona da Mata, Agreste, Borborema, and Sertão. The results of the analysis show that intricacies of monthly average precipitation have differences in the macroregions. Sample entropy is able to reflect the dynamic change of precipitation series providing a new way to investigate complexity of hydrological series. The complexity exhibits areal variation of local water resource systems which can influence the basis for utilizing and developing resources in dry areas.

Microcontroller-based real-time QRS detection.

PubMed

Sun, Y; Suppappola, S; Wrublewski, T A

1992-01-01

The authors describe the design of a system for real-time detection of QRS complexes in the electrocardiogram based on a single-chip microcontroller (Motorola 68HC811). A systematic analysis of the instrumentation requirements for QRS detection and of the various design techniques is also given. Detection algorithms using different nonlinear transforms for the enhancement of QRS complexes are evaluated by using the ECG database of the American Heart Association. The results show that the nonlinear transform involving multiplication of three adjacent, sign-consistent differences in the time domain gives a good performance and a quick response. When implemented with an appropriate sampling rate, this algorithm is also capable of rejecting pacemaker spikes. The eight-bit single-chip microcontroller provides sufficient throughput and shows a satisfactory performance. Implementation of multiple detection algorithms in the same system improves flexibility and reliability. The low chip count in the design also favors maintainability and cost-effectiveness.

Complex Dynamics of Wetland Ecosystem with Nonlinear Harvesting: Application to Chilika Lake in Odisha, India

NASA Astrophysics Data System (ADS)

Upadhyay, Ranjit Kumar; Tiwari, S. K.; Roy, Parimita

2015-06-01

In this paper, an attempt has been made to study the spatial and temporal dynamical interactions among the species of wetland ecosystem through a mathematical model. The model represents the population dynamics of phytoplankton, zooplankton and fish species found in Chilika lake, Odisha, India. Nonlinear stability analysis of both the temporal and spatial models has been carried out. Maximum sustainable yield and optimal harvesting policy have been studied for a nonspatial model system. Numerical simulation has been performed to figure out the parameters responsible for the complex dynamics of the wetland system. Significant outcomes of our numerical findings and their interpretations from an ecological point of view are provided in this paper. Numerical simulation of spatial model exhibits some interesting and beautiful patterns. We have also pointed out the parameters that are responsible for the good health of wetland ecosystem.

Adaptive control for a class of nonlinear complex dynamical systems with uncertain complex parameters and perturbations

PubMed Central

Liu, Jian; Liu, Kexin; Liu, Shutang

2017-01-01

In this paper, adaptive control is extended from real space to complex space, resulting in a new control scheme for a class of n-dimensional time-dependent strict-feedback complex-variable chaotic (hyperchaotic) systems (CVCSs) in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature. In detail, we have developed a unified framework for designing the adaptive complex scalar controller to ensure this type of CVCSs asymptotically stable and for selecting complex update laws to estimate unknown complex parameters. In particular, combining Lyapunov functions dependent on complex-valued vectors and back-stepping technique, sufficient criteria on stabilization of CVCSs are derived in the sense of Wirtinger calculus in complex space. Finally, numerical simulation is presented to validate our theoretical results. PMID:28467431

Adaptive control for a class of nonlinear complex dynamical systems with uncertain complex parameters and perturbations.

PubMed

Liu, Jian; Liu, Kexin; Liu, Shutang

2017-01-01

In this paper, adaptive control is extended from real space to complex space, resulting in a new control scheme for a class of n-dimensional time-dependent strict-feedback complex-variable chaotic (hyperchaotic) systems (CVCSs) in the presence of uncertain complex parameters and perturbations, which has not been previously reported in the literature. In detail, we have developed a unified framework for designing the adaptive complex scalar controller to ensure this type of CVCSs asymptotically stable and for selecting complex update laws to estimate unknown complex parameters. In particular, combining Lyapunov functions dependent on complex-valued vectors and back-stepping technique, sufficient criteria on stabilization of CVCSs are derived in the sense of Wirtinger calculus in complex space. Finally, numerical simulation is presented to validate our theoretical results.

Topological nature of nonlinear optical effects in solids.

PubMed

Morimoto, Takahiro; Nagaosa, Naoto

2016-05-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials.

Topological nature of nonlinear optical effects in solids

PubMed Central

Morimoto, Takahiro; Nagaosa, Naoto

2016-01-01

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by strong light irradiation to materials that results in nonlinear polarizations in the electric field. These are of great importance in studying the physics of excited states of the system as well as for applications to optical devices and solar cells. Nonlinear properties of materials are usually described by nonlinear susceptibilities, which have complex expressions including many matrix elements and energy denominators. On the other hand, a nonequilibrium steady state under an electric field periodic in time has a concise description in terms of the Floquet bands of electrons dressed by photons. We show theoretically, using the Floquet formalism, that various nonlinear optical effects, such as the shift current in noncentrosymmetric materials, photovoltaic Hall response, and photo-induced change of order parameters under the continuous irradiation of monochromatic light, can be described in a unified fashion by topological quantities involving the Berry connection and Berry curvature. We found that vector fields defined with the Berry connections in the space of momentum and/or parameters govern the nonlinear responses. This topological view offers a route to designing nonlinear optical materials. PMID:27386523

Nonlinear bleaching, absorption, and scattering of 532-nm-irradiated plasmonic nanoparticles

DOE Office of Scientific and Technical Information (OSTI.GOV)

Liberman, V.; Sworin, M.; Kingsborough, R. P.

2013-02-07

Single-pulse irradiation of Au and Ag suspensions of nanospheres and nanodisks with 532-nm 4-ns pulses has identified complex optical nonlinearities while minimizing material damage. For all materials tested, we observe competition between saturable absorption (SA) and reverse SA (RSA), with RSA behavior dominating for intensities above {approx}50 MW/cm{sup 2}. Due to reduced laser damage in single-pulse experiments, the observed intrinsic nonlinear absorption coefficients are the highest reported to date for Au nanoparticles. We find size dependence to the nonlinear absorption enhancement for Au nanoparticles, peaking in magnitude for 80-nm nanospheres and falling off at larger sizes. The nonlinear absorption coefficientsmore » for Au and Ag spheres are comparable in magnitude. On the other hand, the nonlinear absorption for Ag disks, when corrected for volume fraction, is several times higher. These trends in nonlinear absorption are correlated to local electric field enhancement through quasi-static mean-field theory. Through variable size aperture measurements, we also separate nonlinear scattering from nonlinear absorption. For all materials tested, we find that nonlinear scattering is highly directional and that its magnitude is comparable to that of nonlinear absorption. These results indicate methods to improve the efficacy of plasmonic nanoparticles as optical limiters in pulsed laser systems.« less

Two-step sensitivity testing of parametrized and regionalized life cycle assessments: methodology and case study.

PubMed

Mutel, Christopher L; de Baan, Laura; Hellweg, Stefanie

2013-06-04

Comprehensive sensitivity analysis is a significant tool to interpret and improve life cycle assessment (LCA) models, but is rarely performed. Sensitivity analysis will increase in importance as inventory databases become regionalized, increasing the number of system parameters, and parametrized, adding complexity through variables and nonlinear formulas. We propose and implement a new two-step approach to sensitivity analysis. First, we identify parameters with high global sensitivities for further examination and analysis with a screening step, the method of elementary effects. Second, the more computationally intensive contribution to variance test is used to quantify the relative importance of these parameters. The two-step sensitivity test is illustrated on a regionalized, nonlinear case study of the biodiversity impacts from land use of cocoa production, including a worldwide cocoa products trade model. Our simplified trade model can be used for transformable commodities where one is assessing market shares that vary over time. In the case study, the highly uncertain characterization factors for the Ivory Coast and Ghana contributed more than 50% of variance for almost all countries and years examined. The two-step sensitivity test allows for the interpretation, understanding, and improvement of large, complex, and nonlinear LCA systems.

Parameter estimation procedure for complex non-linear systems: calibration of ASM No. 1 for N-removal in a full-scale oxidation ditch.

PubMed

Abusam, A; Keesman, K J; van Straten, G; Spanjers, H; Meinema, K

2001-01-01

When applied to large simulation models, the process of parameter estimation is also called calibration. Calibration of complex non-linear systems, such as activated sludge plants, is often not an easy task. On the one hand, manual calibration of such complex systems is usually time-consuming, and its results are often not reproducible. On the other hand, conventional automatic calibration methods are not always straightforward and often hampered by local minima problems. In this paper a new straightforward and automatic procedure, which is based on the response surface method (RSM) for selecting the best identifiable parameters, is proposed. In RSM, the process response (output) is related to the levels of the input variables in terms of a first- or second-order regression model. Usually, RSM is used to relate measured process output quantities to process conditions. However, in this paper RSM is used for selecting the dominant parameters, by evaluating parameters sensitivity in a predefined region. Good results obtained in calibration of ASM No. 1 for N-removal in a full-scale oxidation ditch proved that the proposed procedure is successful and reliable.

A NASTRAN/TREETOPS solution to a flexible, multi-body dynamics and controls problem on a UNIX workstation

NASA Technical Reports Server (NTRS)

Benavente, Javier E.; Luce, Norris R.

1989-01-01

Demands for nonlinear time history simulations of large, flexible multibody dynamic systems has created a need for efficient interfaces between finite-element modeling programs and time-history simulations. One such interface, TREEFLX, an interface between NASTRAN and TREETOPS, a nonlinear dynamics and controls time history simulation for multibody structures, is presented and demonstrated via example using the proposed Space Station Mobile Remote Manipulator System (MRMS). The ability to run all three programs (NASTRAN, TREEFLX and TREETOPS), in addition to other programs used for controller design and model reduction (such as DMATLAB and TREESEL, both described), under a UNIX Workstation environment demonstrates the flexibility engineers now have in designing, developing and testing control systems for dynamically complex systems.

Implications of complex adaptive systems theory for interpreting research about health care organizations.

PubMed

Jordon, Michelle; Lanham, Holly Jordan; Anderson, Ruth A; McDaniel, Reuben R

2010-02-01

Data about health care organizations (HCOs) are not useful until they are interpreted. Such interpretations are influenced by the theoretical lenses used by the researcher. Our purpose was to suggest the usefulness of theories of complex adaptive systems (CASs) in guiding research interpretation. Specifically, we addressed two questions: (1) What are the implications for interpreting research observations in HCOs of the fact that we are observing relationships among diverse agents? (2) What are the implications for interpreting research observations in HCOs of the fact that we are observing relationships among agents that learn? We defined diversity and learning and the implications of the non-linear relationships among agents from a CAS perspective. We then identified some common analytical practices that were problematic and may lead to conceptual and methodological errors. Then we described strategies for interpreting the results of research observations. We suggest that the task of interpreting research observations of HCOs could be improved if researchers take into account that the systems they study are CASs with non-linear relationships among diverse, learning agents. Our analysis points out how interpretation of research results might be shaped by the fact that HCOs are CASs. We described how learning is, in fact, the result of interactions among diverse agents and that learning can, by itself, reduce or increase agent diversity. We encouraged researchers to be persistent in their attempts to reason about complex systems and learn to attend not only to structures, but also to processes and functions of complex systems.

Complexity Variability Assessment of Nonlinear Time-Varying Cardiovascular Control

NASA Astrophysics Data System (ADS)

Valenza, Gaetano; Citi, Luca; Garcia, Ronald G.; Taylor, Jessica Noggle; Toschi, Nicola; Barbieri, Riccardo

2017-02-01

The application of complex systems theory to physiology and medicine has provided meaningful information about the nonlinear aspects underlying the dynamics of a wide range of biological processes and their disease-related aberrations. However, no studies have investigated whether meaningful information can be extracted by quantifying second-order moments of time-varying cardiovascular complexity. To this extent, we introduce a novel mathematical framework termed complexity variability, in which the variance of instantaneous Lyapunov spectra estimated over time serves as a reference quantifier. We apply the proposed methodology to four exemplary studies involving disorders which stem from cardiology, neurology and psychiatry: Congestive Heart Failure (CHF), Major Depression Disorder (MDD), Parkinson’s Disease (PD), and Post-Traumatic Stress Disorder (PTSD) patients with insomnia under a yoga training regime. We show that complexity assessments derived from simple time-averaging are not able to discern pathology-related changes in autonomic control, and we demonstrate that between-group differences in measures of complexity variability are consistent across pathologies. Pathological states such as CHF, MDD, and PD are associated with an increased complexity variability when compared to healthy controls, whereas wellbeing derived from yoga in PTSD is associated with lower time-variance of complexity.

Developing a local least-squares support vector machines-based neuro-fuzzy model for nonlinear and chaotic time series prediction.

PubMed

Miranian, A; Abdollahzade, M

2013-02-01

Local modeling approaches, owing to their ability to model different operating regimes of nonlinear systems and processes by independent local models, seem appealing for modeling, identification, and prediction applications. In this paper, we propose a local neuro-fuzzy (LNF) approach based on the least-squares support vector machines (LSSVMs). The proposed LNF approach employs LSSVMs, which are powerful in modeling and predicting time series, as local models and uses hierarchical binary tree (HBT) learning algorithm for fast and efficient estimation of its parameters. The HBT algorithm heuristically partitions the input space into smaller subdomains by axis-orthogonal splits. In each partitioning, the validity functions automatically form a unity partition and therefore normalization side effects, e.g., reactivation, are prevented. Integration of LSSVMs into the LNF network as local models, along with the HBT learning algorithm, yield a high-performance approach for modeling and prediction of complex nonlinear time series. The proposed approach is applied to modeling and predictions of different nonlinear and chaotic real-world and hand-designed systems and time series. Analysis of the prediction results and comparisons with recent and old studies demonstrate the promising performance of the proposed LNF approach with the HBT learning algorithm for modeling and prediction of nonlinear and chaotic systems and time series.

A Simplified Model of ARIS for Optimal Controller Design

NASA Technical Reports Server (NTRS)

Beech, Geoffrey S.; Hampton, R. David; Kross, Denny (Technical Monitor)

2001-01-01

Many space-science experiments require active vibration isolation. Boeing's Active Rack Isolation System (ARIS) isolates experiments at the rack (vs. experiment or sub-experiment) level, with multi e experiments per rack. An ARIS-isolated rack typically employs eight actuators and thirteen umbilicals; the umbilicals provide services such as power, data transmission, and cooling. Hampton, et al., used "Kane's method" to develop an analytical, nonlinear, rigid-body model of ARIS that includes full actuator dynamics (inertias). This model, less the umbilicals, was first implemented for simulation by Beech and Hampton; they developed and tested their model using two commercial-off-the-shelf (COTS) software packages. Rupert, et al., added umbilical-transmitted disturbances to this nonlinear model. Because the nonlinear model, even for the untethered system, is both exceedingly complex and "encapsulated" inside these COTS tools, it is largely inaccessible to ARIS controller designers. This paper shows that ISPR rattle-space constraints and small ARIS actuator masses permit considerable model simplification, without significant loss of fidelity. First, for various loading conditions, comparisons are made between the dynamic responses of the nonlinear model (untethered) and a truth model. Then comparisons are made among nonlinear, linearized, and linearized reduced-mass models. It is concluded that these three models all capture the significant system rigid-body dynamics, with the third being preferred due to its relative simplicity.

Wideband electromagnetic energy harvesting from ambient vibrations

NASA Astrophysics Data System (ADS)

Mallick, Dhiman; Podder, Pranay; Roy, Saibal

2015-06-01

Different bandwidth widening schemes of electromagnetic energy harvesters have been reported in this work. The devices are fabricated on FR4 substrate using laser micromachining techniques. The linear device operate in a narrow band around the resonance; in order to tune resonant frequency of the device electrically, two different types of complex load topologies are adopted. Using capacitive load, the resonant frequency is tuned in the low frequency direction whereas using inductive load, the resonant frequency is tuned in the high frequency direction. An overall tuning range of ˜2.4 Hz is obtained at 0.3g though the output power dropped significantly over the tuning range. In order to improve the off-resonance performance, nonlinear oscillation based systems are adopted. A specially designed spring arm with fixed-guided configuration produced single well nonlinear monostable configuration. With increasing input acceleration, wider bandwidth is obtained with such a system as large displacement, stretching nonlinearity comes into play and 9.55 Hz bandwidth is obtained at 0.5g. The repulsive force between one static and one vibrating oppositely polarized magnets are used to generate bistable nonlinear potential system. The distance between the mentioned magnets is varied between 4 to 10 mm to produce tunable nonlinearity with a maximum half power bandwidth over 3 Hz at 0.5g.

Curl forces and the nonlinear Fokker-Planck equation.

PubMed

Wedemann, R S; Plastino, A R; Tsallis, C

2016-12-01

Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are q exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exist, the nonlinear Fokker-Planck equations satisfy an H theorem in terms of a free-energy-like quantity involving the S_{q} entropy. A particular two-dimensional model admitting analytical, time-dependent q-Gaussian solutions is discussed in detail. This model describes a system of particles with short-range interactions, performing overdamped motion under drag effects due to a rotating resisting medium. It is related to models that have been recently applied to the study of type-II superconductors. The relevance of the present developments to the study of complex systems in physics, astronomy, and biology is discussed.

Elegant Ince—Gaussian breathers in strongly nonlocal nonlinear media

NASA Astrophysics Data System (ADS)

Bai, Zhi-Yong; Deng, Dong-Mei; Guo, Qi

2012-06-01

A novel class of optical breathers, called elegant Ince—Gaussian breathers, are presented in this paper. They are exact analytical solutions to Snyder and Mitchell's mode in an elliptic coordinate system, and their transverse structures are described by Ince-polynomials with complex arguments and a Gaussian function. We provide convincing evidence for the correctness of the solutions and the existence of the breathers via comparing the analytical solutions with numerical simulation of the nonlocal nonlinear Schrödinger equation.

Antisynchronization of Two Complex Dynamical Networks

NASA Astrophysics Data System (ADS)

Banerjee, Ranjib; Grosu, Ioan; Dana, Syamal K.

A nonlinear type open-plus-closed-loop (OPCL) coupling is investi-gated for antisynchronization of two complex networks under unidirectional and bidirectional interactions where each node of the networks is considered as a continuous dynamical system. We present analytical results for antisynchroni-zation in identical networks. A numerical example is given for unidirectional coupling with each node represented by a spiking-bursting type Hindmarsh-Rose neuron model. Antisynchronization for mutual interaction is allowed only to inversion symmetric dynamical systems as chosen nodes.

Complex and Nonlinear Pedagogy and the Implications for Physical Education

ERIC Educational Resources Information Center

Chow, Jia Yi; Atencio, Matthew

2014-01-01

There is increasing support to describe and examine the teaching of game skills in physical education from a complex and nonlinear perspective. The emergence of game behaviours as a consequence of the dynamic interactions of the learner, the game environment and the task constraints within the game context highlights the nonlinear and complex…

A DST Model of Multilingualism and the Role of Metalinguistic Awareness

ERIC Educational Resources Information Center

Jessner, Ulrike

2008-01-01

This paper suggests that a dynamic systems theory (DST) provides an adequate conceptual metaphor for discussing multilingual development. Multilingual acquisition is a nonlinear and complex dynamic process depending on a number of interacting factors. Variability plays a crucial role in the multilingual system as it changes over time (Herdina &…

Modeling the cardiovascular system using a nonlinear additive autoregressive model with exogenous input

NASA Astrophysics Data System (ADS)

Riedl, M.; Suhrbier, A.; Malberg, H.; Penzel, T.; Bretthauer, G.; Kurths, J.; Wessel, N.

2008-07-01

The parameters of heart rate variability and blood pressure variability have proved to be useful analytical tools in cardiovascular physics and medicine. Model-based analysis of these variabilities additionally leads to new prognostic information about mechanisms behind regulations in the cardiovascular system. In this paper, we analyze the complex interaction between heart rate, systolic blood pressure, and respiration by nonparametric fitted nonlinear additive autoregressive models with external inputs. Therefore, we consider measurements of healthy persons and patients suffering from obstructive sleep apnea syndrome (OSAS), with and without hypertension. It is shown that the proposed nonlinear models are capable of describing short-term fluctuations in heart rate as well as systolic blood pressure significantly better than similar linear ones, which confirms the assumption of nonlinear controlled heart rate and blood pressure. Furthermore, the comparison of the nonlinear and linear approaches reveals that the heart rate and blood pressure variability in healthy subjects is caused by a higher level of noise as well as nonlinearity than in patients suffering from OSAS. The residue analysis points at a further source of heart rate and blood pressure variability in healthy subjects, in addition to heart rate, systolic blood pressure, and respiration. Comparison of the nonlinear models within and among the different groups of subjects suggests the ability to discriminate the cohorts that could lead to a stratification of hypertension risk in OSAS patients.

Complexity, Chaos, and Nonlinear Dynamics: A New Perspective on Career Development Theory

ERIC Educational Resources Information Center

Bloch, Deborah P.

2005-01-01

The author presents a theory of career development drawing on nonlinear dynamics and chaos and complexity theories. Career is presented as a complex adaptive entity, a fractal of the human entity. Characteristics of complex adaptive entities, including (a) autopiesis, or self-regeneration; (b) open exchange; (c) participation in networks; (d)…

Nonlinear decoding of a complex movie from the mammalian retina

PubMed Central

Deny, Stéphane; Martius, Georg

2018-01-01

Retina is a paradigmatic system for studying sensory encoding: the transformation of light into spiking activity of ganglion cells. The inverse problem, where stimulus is reconstructed from spikes, has received less attention, especially for complex stimuli that should be reconstructed “pixel-by-pixel”. We recorded around a hundred neurons from a dense patch in a rat retina and decoded movies of multiple small randomly-moving discs. We constructed nonlinear (kernelized and neural network) decoders that improved significantly over linear results. An important contribution to this was the ability of nonlinear decoders to reliably separate between neural responses driven by locally fluctuating light signals, and responses at locally constant light driven by spontaneous-like activity. This improvement crucially depended on the precise, non-Poisson temporal structure of individual spike trains, which originated in the spike-history dependence of neural responses. We propose a general principle by which downstream circuitry could discriminate between spontaneous and stimulus-driven activity based solely on higher-order statistical structure in the incoming spike trains. PMID:29746463

A Wavelet Bicoherence-Based Quadratic Nonlinearity Feature for Translational Axis Condition Monitoring

PubMed Central

Li, Yong; Wang, Xiufeng; Lin, Jing; Shi, Shengyu

2014-01-01

The translational axis is one of the most important subsystems in modern machine tools, as its degradation may result in the loss of the product qualification and lower the control precision. Condition-based maintenance (CBM) has been considered as one of the advanced maintenance schemes to achieve effective, reliable and cost-effective operation of machine systems, however, current vibration-based maintenance schemes cannot be employed directly in the translational axis system, due to its complex structure and the inefficiency of commonly used condition monitoring features. In this paper, a wavelet bicoherence-based quadratic nonlinearity feature is proposed for translational axis condition monitoring by using the torque signature of the drive servomotor. Firstly, the quadratic nonlinearity of the servomotor torque signature is discussed, and then, a biphase randomization wavelet bicoherence is introduced for its quadratic nonlinear detection. On this basis, a quadratic nonlinearity feature is proposed for condition monitoring of the translational axis. The properties of the proposed quadratic nonlinearity feature are investigated by simulations. Subsequently, this feature is applied to the real-world servomotor torque data collected from the X-axis on a high precision vertical machining centre. All the results show that the performance of the proposed feature is much better than that of original condition monitoring features. PMID:24473281

The sleeping brain as a complex system.

PubMed

Olbrich, Eckehard; Achermann, Peter; Wennekers, Thomas

2011-10-13

'Complexity science' is a rapidly developing research direction with applications in a multitude of fields that study complex systems consisting of a number of nonlinear elements with interesting dynamics and mutual interactions. This Theme Issue 'The complexity of sleep' aims at fostering the application of complexity science to sleep research, because the brain in its different sleep stages adopts different global states that express distinct activity patterns in large and complex networks of neural circuits. This introduction discusses the contributions collected in the present Theme Issue. We highlight the potential and challenges of a complex systems approach to develop an understanding of the brain in general and the sleeping brain in particular. Basically, we focus on two topics: the complex networks approach to understand the changes in the functional connectivity of the brain during sleep, and the complex dynamics of sleep, including sleep regulation. We hope that this Theme Issue will stimulate and intensify the interdisciplinary communication to advance our understanding of the complex dynamics of the brain that underlies sleep and consciousness.

Automated Design of Complex Dynamic Systems

PubMed Central

Hermans, Michiel; Schrauwen, Benjamin; Bienstman, Peter; Dambre, Joni

2014-01-01

Several fields of study are concerned with uniting the concept of computation with that of the design of physical systems. For example, a recent trend in robotics is to design robots in such a way that they require a minimal control effort. Another example is found in the domain of photonics, where recent efforts try to benefit directly from the complex nonlinear dynamics to achieve more efficient signal processing. The underlying goal of these and similar research efforts is to internalize a large part of the necessary computations within the physical system itself by exploiting its inherent non-linear dynamics. This, however, often requires the optimization of large numbers of system parameters, related to both the system's structure as well as its material properties. In addition, many of these parameters are subject to fabrication variability or to variations through time. In this paper we apply a machine learning algorithm to optimize physical dynamic systems. We show that such algorithms, which are normally applied on abstract computational entities, can be extended to the field of differential equations and used to optimize an associated set of parameters which determine their behavior. We show that machine learning training methodologies are highly useful in designing robust systems, and we provide a set of both simple and complex examples using models of physical dynamical systems. Interestingly, the derived optimization method is intimately related to direct collocation a method known in the field of optimal control. Our work suggests that the application domains of both machine learning and optimal control have a largely unexplored overlapping area which envelopes a novel design methodology of smart and highly complex physical systems. PMID:24497969

Down syndrome's brain dynamics: analysis of fractality in resting state.

PubMed

Hemmati, Sahel; Ahmadlou, Mehran; Gharib, Masoud; Vameghi, Roshanak; Sajedi, Firoozeh

2013-08-01

To the best knowledge of the authors there is no study on nonlinear brain dynamics of down syndrome (DS) patients, whereas brain is a highly complex and nonlinear system. In this study, fractal dimension of EEG, as a key characteristic of brain dynamics, showing irregularity and complexity of brain dynamics, was used for evaluation of the dynamical changes in the DS brain. The results showed higher fractality of the DS brain in almost all regions compared to the normal brain, which indicates less centrality and higher irregular or random functioning of the DS brain regions. Also, laterality analysis of the frontal lobe showed that the normal brain had a right frontal laterality of complexity whereas the DS brain had an inverse pattern (left frontal laterality). Furthermore, the high accuracy of 95.8 % obtained by enhanced probabilistic neural network classifier showed the potential of nonlinear dynamic analysis of the brain for diagnosis of DS patients. Moreover, the results showed that the higher EEG fractality in DS is associated with the higher fractality in the low frequencies (delta and theta), in broad regions of the brain, and the high frequencies (beta and gamma), majorly in the frontal regions.

Rogue-wave pattern transition induced by relative frequency.

PubMed

Zhao, Li-Chen; Xin, Guo-Guo; Yang, Zhan-Ying

2014-08-01

We revisit a rogue wave in a two-mode nonlinear fiber whose dynamics is described by two-component coupled nonlinear Schrödinger equations. The relative frequency between two modes can induce different rogue wave patterns transition. In particular, we find a four-petaled flower structure rogue wave can exist in the two-mode coupled system, which possesses an asymmetric spectrum distribution. Furthermore, spectrum analysis is performed on these different type rogue waves, and the spectrum relations between them are discussed. We demonstrate qualitatively that different modulation instability gain distribution can induce different rogue wave excitation patterns. These results would deepen our understanding of rogue wave dynamics in complex systems.

Examples of the nonlinear dynamics of ballistic capture and escape in the earth-moon system

NASA Technical Reports Server (NTRS)

Belbruno, Edward A.

1990-01-01

An example of a trajectory is given which is initially captured in an elliptic resonant orbit about the earth and then ballistically escapes the earth-moon system. This is demonstrated by a numerical example in three-dimensions using a planetary ephemeris. Another example shows a mechanism of how an elliptic orbit about the earth can increase its energy by performing a complex nonlinear transition to an elliptic orbit of a larger semi-major axis. Capture is also considered. An application of ballistic capture at the moon via an unstable periodic orbit using the four-body sun-earth-moon-S/C interaction is described.

Low-Dimensional Models for Physiological Systems: Nonlinear Coupling of Gas and Liquid Flows

NASA Astrophysics Data System (ADS)

Staples, A. E.; Oran, E. S.; Boris, J. P.; Kailasanath, K.

2006-11-01

Current computational models of biological organisms focus on the details of a specific component of the organism. For example, very detailed models of the human heart, an aorta, a vein, or part of the respiratory or digestive system, are considered either independently from the rest of the body, or as interacting simply with other systems and components in the body. In actual biological organisms, these components and systems are strongly coupled and interact in complex, nonlinear ways leading to complicated global behavior. Here we describe a low-order computational model of two physiological systems, based loosely on a circulatory and respiratory system. Each system is represented as a one-dimensional fluid system with an interconnected series of mass sources, pumps, valves, and other network components, as appropriate, representing different physical organs and system components. Preliminary results from a first version of this model system are presented.

Balancing Broad Ideas with Context: An Evaluation of Student Accuracy in Describing Ecosystem Processes after a System-Level Intervention

ERIC Educational Resources Information Center

Jordan, Rebecca C.; Brooks, Wesley R.; Hmelo-Silver, Cindy; Eberbach, Catherine; Sinha, Suparna

2014-01-01

Promoting student understanding of ecosystem processes is critical to biological education. Yet, teaching complex life systems can be difficult because systems are dynamic and often behave in a non-linear manner. In this paper, we discuss assessment results from a middle school classroom intervention in which a conceptual representation framework…

Nonlinear resonances and antiresonances of a forced sonic vacuum

DOE PAGES

Pozharskiy, D.; Zhang, Y.; Williams, M. O.; ...

2015-12-23

We consider a harmonically driven acoustic medium in the form of a (finite length) highly nonlinear granular crystal with an amplitude- and frequency-dependent boundary drive. Despite the absence of a linear spectrum in the system, we identify resonant periodic propagation whereby the crystal responds at integer multiples of the drive period and observe that this can lead to local maxima of transmitted force at its fixed boundary. In addition, we identify and discuss minima of the transmitted force (“antiresonances”) between these resonances. Representative one-parameter complex bifurcation diagrams involve period doublings and Neimark-Sacker bifurcations as well as multiple isolas (e.g., ofmore » period-3, -4, or -5 solutions entrained by the forcing). We combine them in a more detailed, two-parameter bifurcation diagram describing the stability of such responses to both frequency and amplitude variations of the drive. This picture supports a notion of a (purely) “nonlinear spectrum” in a system which allows no sound wave propagation (due to zero sound speed: the so-called sonic vacuum). As a result, we rationalize this behavior in terms of purely nonlinear building blocks: apparent traveling and standing nonlinear waves.« less

Systems thinking.

PubMed

Cabrera, Derek; Colosi, Laura; Lobdell, Claire

2008-08-01

Evaluation is one of many fields where "systems thinking" is popular and is said to hold great promise. However, there is disagreement about what constitutes systems thinking. Its meaning is ambiguous, and systems scholars have made diverse and divergent attempts to describe it. Alternative origins include: von Bertalanffy, Aristotle, Lao Tsu or multiple aperiodic "waves." Some scholars describe it as synonymous with systems sciences (i.e., nonlinear dynamics, complexity, chaos). Others view it as taxonomy-a laundry list of systems approaches. Within so much noise, it is often difficult for evaluators to find the systems thinking signal. Recent work in systems thinking describes it as an emergent property of four simple conceptual patterns (rules). For an evaluator to become a "systems thinker", he or she need not spend years learning many methods or nonlinear sciences. Instead, with some practice, one can learn to apply these four simple rules to existing evaluation knowledge with transformative results.

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zuo, Peng; Fan, Zheng, E-mail: ZFAN@ntu.edu.sg; Zhou, Yu

2016-07-15

Nonlinear guided waves have been investigated widely in simple geometries, such as plates, pipe and shells, where analytical solutions have been developed. This paper extends the application of nonlinear guided waves to waveguides with arbitrary cross sections. The criteria for the existence of nonlinear guided waves were summarized based on the finite deformation theory and nonlinear material properties. Numerical models were developed for the analysis of nonlinear guided waves in complex geometries, including nonlinear Semi-Analytical Finite Element (SAFE) method to identify internal resonant modes in complex waveguides, and Finite Element (FE) models to simulate the nonlinear wave propagation at resonantmore » frequencies. Two examples, an aluminum plate and a steel rectangular bar, were studied using the proposed numerical model, demonstrating the existence of nonlinear guided waves in such structures and the energy transfer from primary to secondary modes.« less

Computer program determines chemical equilibria in complex systems

NASA Technical Reports Server (NTRS)

Gordon, S.; Zeleznik, F. J.

1966-01-01

Computer program numerically solves nonlinear algebraic equations for chemical equilibrium based on iteration equations independent of choice of components. This program calculates theoretical performance for frozen and equilibrium composition during expansion and Chapman-Jouguet flame properties, studies combustion, and designs hardware.

We should be using nonlinear indices when relating heart-rate dynamics to cognition and mood

PubMed Central

Young, Hayley; Benton, David

2015-01-01

Both heart rate (HR) and brain functioning involve the integrated output of a multitude of regulatory mechanisms, that are not quantified adequately by linear approximations such as means and standard deviations. It was therefore considered whether non-linear measures of HR complexity are more strongly associated with cognition and mood. Whilst resting, the inter-beat (R-R) time series of twenty-one males and twenty-four females were measured for five minutes. The data were summarised using time, frequency and nonlinear complexity measures. Attention, memory, reaction times, mood and cortisol levels were assessed. Nonlinear HR indices captured additional information, enabling a greater percentage of the variance in behaviour to be explained. On occasions non-linear indices were related to aspects for behaviour, for example focused attention and cortisol production, when time or frequency indices were not. These effects were sexually dimorphic with HR complexity being more strongly associated with the behaviour of females. It was concluded that nonlinear rather than linear methods of summarizing the HR times series offers a novel way of relating brain functioning and behaviour. It should be considered whether non-linear measures of HR complexity can be used as a biomarker of the integrated functioning of the brain. PMID:26565560

Nonlinear optical investigation of the Tris(2‧,2-bipyridyl)iron(II) tetrafluoroborate using z-scan technique

NASA Astrophysics Data System (ADS)

Zidan, M. D.; Al-Ktaifani, M. M.; Allahham, A.

2017-05-01

Z-scan measurements were performed with a CW diode laser at 635 nm to investigate the nonlinear optical properties of Tris(2‧,2-bipyridyl)iron(II) tetrafluoroborate in ethanol at two concentrations. Theoretical fit was carried out to evaluate the nonlinear absorption coefficient (β) and the negative nonlinear refractive index (n2) for the studied complex. Furthermore, the ground-state absorption cross sections (σg), the excited-state absorption cross sections (σex) and thermo-optic coefficient were also estimated. The investigations show large NLO response, which is predominantly associated with substantial conjugation between the aromatic ring π-electron system and d-electron set metal center. The obtained results give a strong indication that Tris(2‧,2-bipyridyl)iron(II) tetrafluoroborate have a potential application in optical domain.

Synchronization and Causality Across Time-scales: Complex Dynamics and Extremes in El Niño/Southern Oscillation

NASA Astrophysics Data System (ADS)

Jajcay, N.; Kravtsov, S.; Tsonis, A.; Palus, M.

2017-12-01

A better understanding of dynamics in complex systems, such as the Earth's climate is one of the key challenges for contemporary science and society. A large amount of experimental data requires new mathematical and computational approaches. Natural complex systems vary on many temporal and spatial scales, often exhibiting recurring patterns and quasi-oscillatory phenomena. The statistical inference of causal interactions and synchronization between dynamical phenomena evolving on different temporal scales is of vital importance for better understanding of underlying mechanisms and a key for modeling and prediction of such systems. This study introduces and applies information theory diagnostics to phase and amplitude time series of different wavelet components of the observed data that characterizes El Niño. A suite of significant interactions between processes operating on different time scales was detected, and intermittent synchronization among different time scales has been associated with the extreme El Niño events. The mechanisms of these nonlinear interactions were further studied in conceptual low-order and state-of-the-art dynamical, as well as statistical climate models. Observed and simulated interactions exhibit substantial discrepancies, whose understanding may be the key to an improved prediction. Moreover, the statistical framework which we apply here is suitable for direct usage of inferring cross-scale interactions in nonlinear time series from complex systems such as the terrestrial magnetosphere, solar-terrestrial interactions, seismic activity or even human brain dynamics.

Predictability of extremes in non-linear hierarchically organized systems

NASA Astrophysics Data System (ADS)

Kossobokov, V. G.; Soloviev, A.

2011-12-01

Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare phenomena of highly complex origin, by their nature, implies using problem oriented methods, which design breaks the limits of classical statistical or econometric applications. The unambiguously designed forecast/prediction algorithms of the "yes or no" variety, analyze the observable quantitative integrals and indicators available to a given date, then provides unambiguous answer to the question whether a critical transition should be expected or not in the next time interval. Since the predictability of an originating non-linear dynamical system is limited in principle, the probabilistic component of forecast/prediction algorithms is represented by the empirical probabilities of alarms, on one side, and failures-to-predict, on the other, estimated on control sets achieved in the retro- and prospective experiments. Predicting in advance is the only decisive test of forecast/predictions and the relevant on-going experiments are conducted in the case seismic extremes, recessions, and increases of unemployment rate. The results achieved in real-time testing keep being encouraging and confirm predictability of the extremes.

Modification of optical properties by adiabatic shifting of resonances in a four-level atom

NASA Astrophysics Data System (ADS)

Dutta, Bibhas Kumar; Panchadhyayee, Pradipta

2018-04-01

We describe the linear and nonlinear optical properties of a four-level atomic system, after reducing it to an effective two-level atomic model under the condition of adiabatic shifting of resonances driven by two coherent off-resonant fields. The reduced form of the Hamiltonian corresponding to the two-level system is obtained by employing an adiabatic elimination procedure in the rate equations of the probability amplitudes for the proposed four-level model. For a weak probe field operating in the system, the nonlinear dependence of complex susceptibility on the Rabi frequencies and the detuning parameters of the off-resonant driving fields makes it possible to exhibit coherent control of single-photon and two-photon absorption and transparency, the evolution of enhanced Self-Kerr nonlinearity and noticeable dispersive switching. We have shown how the quantum interference results in the generic four-level model at the adiabatic limit. The present scheme describes the appearance of single-photon transparency without invoking any exact two-photon resonance.

Growth and characterization of a third order nonlinear optical single crystal: Ethylenediamine-4-nitrophenolate monohydrate

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dhanalakshmi, B.; Ponnusamy, S., E-mail: suruponnus@gmail.com; Muthamizhchelvan, C.

2015-10-15

Highlights: • EDA4NPH crystal possesses negative nonlinear refractive index. • The crystal exhibits high third-order NLO susceptibility. • Wide transparency of the crystal makes it suitable for NLO applications. • Dielectric studies substantiate the suitability for electro-optic applications. • The crystal possesses suitable mechanical strength for device fabrication. - Abstract: Bulk crystals of the charge-transfer complex, ethylenediamine-4-nitrophenolate monohydrate, were grown by slow solvent evaporation method from aqueous solution at room temperature. The X-ray diffraction measurements showed that the crystal belongs to centrosymmetric space group C2/c of monoclinic system. The functional groups in the complex were identified using FTIR, FTRaman andmore » FTNMR analyses. The Z-scan measurements revealed the negative nonlinear refractive index of the crystal. The nonlinear absorption coefficient and third order nonlinear optical susceptibility calculated from the measurements were −3.5823 × 10{sup −3} cm/W and 2.3762 × 10{sup −6} esu respectively. The crystal was shown to be highly transparent above 366 nm by UV–vis spectroscopy and a yellow fluorescence was observed from PL spectrum. The TG–DTA and DSC analyses showed that the crystal is thermally stable up to 117.4 °C. The crystals were characterized by dielectric, etching and microhardness studies.« less

Rapid solution of large-scale systems of equations

NASA Technical Reports Server (NTRS)

Storaasli, Olaf O.

1994-01-01

The analysis and design of complex aerospace structures requires the rapid solution of large systems of linear and nonlinear equations, eigenvalue extraction for buckling, vibration and flutter modes, structural optimization and design sensitivity calculation. Computers with multiple processors and vector capabilities can offer substantial computational advantages over traditional scalar computer for these analyses. These computers fall into two categories: shared memory computers and distributed memory computers. This presentation covers general-purpose, highly efficient algorithms for generation/assembly or element matrices, solution of systems of linear and nonlinear equations, eigenvalue and design sensitivity analysis and optimization. All algorithms are coded in FORTRAN for shared memory computers and many are adapted to distributed memory computers. The capability and numerical performance of these algorithms will be addressed.

Single evolution equation in a light-matter pairing system

NASA Astrophysics Data System (ADS)

Bugaychuk, S.; Tobisch, E.

2018-03-01

The coupled system including wave mixing and nonlinear dynamics of a nonlocal optical medium is usually studied (1) numerically, with the medium being regarded as a black box, or (2) experimentally, making use of some empirical assumptions. In this paper we deduce for the first time a single evolution equation describing the dynamics of the pairing system as a holistic complex. For a non-degenerate set of parameters, we obtain the nonlinear Schrödinger equation with coefficients being written out explicitly. Analytical solutions of this equation can be experimentally realized in any photorefractive medium, e.g. in photorefractive, liquid or photonic crystals. For instance, a soliton-like solution can be used in dynamical holography for designing an artificial grating with maximal amplification of an image.

Cooperative Adaptive Output Regulation for Second-Order Nonlinear Multiagent Systems With Jointly Connected Switching Networks.

PubMed

Liu, Wei; Huang, Jie

2018-03-01

This paper studies the cooperative global robust output regulation problem for a class of heterogeneous second-order nonlinear uncertain multiagent systems with jointly connected switching networks. The main contributions consist of the following three aspects. First, we generalize the result of the adaptive distributed observer from undirected jointly connected switching networks to directed jointly connected switching networks. Second, by performing a new coordinate and input transformation, we convert our problem into the cooperative global robust stabilization problem of a more complex augmented system via the distributed internal model principle. Third, we solve the stabilization problem by a distributed state feedback control law. Our result is illustrated by the leader-following consensus problem for a group of Van der Pol oscillators.

Superdiffusive transport and energy localization in disordered granular crystals

DOE Office of Scientific and Technical Information (OSTI.GOV)

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition.more » Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m ~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.« less

Superdiffusive transport and energy localization in disordered granular crystals

DOE PAGES

Martinez, Alejandro J.; Kevrekidis, Panagiotis G.; Porter, Mason A.

2016-02-12

We study the spreading of initially localized excitations in one-dimensional disordered granular crystals. We thereby investigate localization phenomena in strongly nonlinear systems, which we demonstrate to be fundamentally different from localization in linear and weakly nonlinear systems. We conduct a thorough comparison of wave dynamics in chains with three different types of disorder: an uncorrelated (Anderson-like) disorder and two types of correlated disorders (which are produced by random dimer arrangements), and for two families of initial conditions: displacement perturbations and velocity perturbations. We find for strongly precompressed (i.e., weakly nonlinear) chains that the dynamics strongly depends on the initial condition.more » Furthermore, for displacement perturbations, the long-time asymptotic behavior of the second moment m ~2 has oscillations that depend on the type of disorder, with a complex trend that is markedly different from a power law and which is particularly evident for an Anderson-like disorder.« less

Nonlinear Adaptive PID Control for Greenhouse Environment Based on RBF Network

PubMed Central

Zeng, Songwei; Hu, Haigen; Xu, Lihong; Li, Guanghui

2012-01-01

This paper presents a hybrid control strategy, combining Radial Basis Function (RBF) network with conventional proportional, integral, and derivative (PID) controllers, for the greenhouse climate control. A model of nonlinear conservation laws of enthalpy and matter between numerous system variables affecting the greenhouse climate is formulated. RBF network is used to tune and identify all PID gain parameters online and adaptively. The presented Neuro-PID control scheme is validated through simulations of set-point tracking and disturbance rejection. We compare the proposed adaptive online tuning method with the offline tuning scheme that employs Genetic Algorithm (GA) to search the optimal gain parameters. The results show that the proposed strategy has good adaptability, strong robustness and real-time performance while achieving satisfactory control performance for the complex and nonlinear greenhouse climate control system, and it may provide a valuable reference to formulate environmental control strategies for actual application in greenhouse production. PMID:22778587

Fault detection and isolation for complex system

NASA Astrophysics Data System (ADS)

Jing, Chan Shi; Bayuaji, Luhur; Samad, R.; Mustafa, M.; Abdullah, N. R. H.; Zain, Z. M.; Pebrianti, Dwi

2017-07-01

Fault Detection and Isolation (FDI) is a method to monitor, identify, and pinpoint the type and location of system fault in a complex multiple input multiple output (MIMO) non-linear system. A two wheel robot is used as a complex system in this study. The aim of the research is to construct and design a Fault Detection and Isolation algorithm. The proposed method for the fault identification is using hybrid technique that combines Kalman filter and Artificial Neural Network (ANN). The Kalman filter is able to recognize the data from the sensors of the system and indicate the fault of the system in the sensor reading. Error prediction is based on the fault magnitude and the time occurrence of fault. Additionally, Artificial Neural Network (ANN) is another algorithm used to determine the type of fault and isolate the fault in the system.

Nonlinear spectroscopy of trapped ions

NASA Astrophysics Data System (ADS)

Schlawin, Frank; Gessner, Manuel; Mukamel, Shaul; Buchleitner, Andreas

2014-08-01

Nonlinear spectroscopy employs a series of laser pulses to interrogate dynamics in large interacting many-body systems, and it has become a highly successful method for experiments in chemical physics. Current quantum optical experiments approach system sizes and levels of complexity that require the development of efficient techniques to assess spectral and dynamical features with scalable experimental overhead. However, established methods from optical spectroscopy of macroscopic ensembles cannot be applied straightforwardly to few-atom systems. Based on the ideas proposed in M. Gessner et al., (arXiv:1312.3365), we develop a diagrammatic approach to construct nonlinear measurement protocols for controlled quantum systems, and we discuss experimental implementations with trapped ion technology in detail. These methods, in combination with distinct features of ultracold-matter systems, allow us to monitor and analyze excitation dynamics in both the electronic and vibrational degrees of freedom. They are independent of system size, and they can therefore reliably probe systems in which, e.g., quantum state tomography becomes prohibitively expensive. We propose signals that can probe steady-state currents, detect the influence of anharmonicities on phonon transport, and identify signatures of chaotic dynamics near a quantum phase transition in an Ising-type spin chain.

Analysis of complex neural circuits with nonlinear multidimensional hidden state models

PubMed Central

Friedman, Alexander; Slocum, Joshua F.; Tyulmankov, Danil; Gibb, Leif G.; Altshuler, Alex; Ruangwises, Suthee; Shi, Qinru; Toro Arana, Sebastian E.; Beck, Dirk W.; Sholes, Jacquelyn E. C.; Graybiel, Ann M.

2016-01-01

A universal need in understanding complex networks is the identification of individual information channels and their mutual interactions under different conditions. In neuroscience, our premier example, networks made up of billions of nodes dynamically interact to bring about thought and action. Granger causality is a powerful tool for identifying linear interactions, but handling nonlinear interactions remains an unmet challenge. We present a nonlinear multidimensional hidden state (NMHS) approach that achieves interaction strength analysis and decoding of networks with nonlinear interactions by including latent state variables for each node in the network. We compare NMHS to Granger causality in analyzing neural circuit recordings and simulations, improvised music, and sociodemographic data. We conclude that NMHS significantly extends the scope of analyses of multidimensional, nonlinear networks, notably in coping with the complexity of the brain. PMID:27222584

A Polynomial-Based Nonlinear Least Squares Optimized Preconditioner for Continuous and Discontinuous Element-Based Discretizations of the Euler Equations

DTIC Science & Technology

2014-01-01

system (here using left- preconditioning ) (KÃ)x = Kb̃, (3.1) where K is a low-order polynomial in à given by K = s(Ã) = m∑ i=0 kià i, (3.2) and has a... system with a complex spectrum, region E in the complex plane must be some convex form (e.g., an ellipse or polygon) that approximately encloses the...preconditioners with p = 2 and p = 20 on the spectrum of the preconditioned system matrices Kà and KH̃ for both CG Schur-complement form and DG form cases

A policy evaluation tool: Management of a multiaquifer system using controlled stream recharge

USGS Publications Warehouse

Danskin, Wesley R.; Gorelick, Steven M.

1985-01-01

A model for the optimal allocation of water resources was developed for a multiaquifer groundwater and surface water system near Livermore, California. The complex groundwater system was analyzed using a transient, quasi-three-dimensional model that considers the nonlinear behavior of the unconfined aquifer. The surface water system consists of a reservoir that discharges water to three streams which in turn recharge the upper aquifer. Nonlinear streamflow-recharge relationships were developed based upon synoptic field measurements of streamflow. The management model uses constrained optimization to minimize the cost of allocating surface water subject to physical and economic restrictions. Results indicate that a combined hydrologic and economic management model can be used to evaluate management practices of a complex hydrogeologic system. Questions can be posed which either would be impossible or extremely difficult to solve without the management model. We demonstrate the utility of such a model in three areas. First, the efficiency of intra-basin water allocations is evaluated. Second, critical factors that control management decisions of the basin are identified. Third, the influence of economic incentives that can best satisfy the conflicting objectives of various water users is explored.

Chaos as a psychological construct: historical roots, principal findings, and current growth directions.

PubMed

Guastello, Stephen J

2009-07-01

The landmarks in the use of chaos and related constructs in psychology were entwined with the growing use of other nonlinear dynamical constructs, especially catastrophes and self-organization. The growth in substantive applications of chaos in psychology is partially related to the development of methodologies that work within the constraints of psychological data. The psychological literature includes rigorous theory with testable propositions, lighter-weight metaphorical uses of the construct, and colloquial uses of "chaos" with no particular theoretical intent. The current state of the chaos construct and supporting empirical research in psychological theory is summarized in neuroscience, psychophysics, psychomotor skill and other learning phenomena, clinical and abnormal psychology, and group dynamics and organizational behavior. Trends indicate that human systems do not remain chaotic indefinitely; they eventually self-organize, and the concept of the complex adaptive system has become prominent. Chaotic turbulence is generally higher in healthy systems compared to unhealthy systems, although opposite appears true in mood disorders. Group dynamics research shows trends consistent with the complex adaptive system, whereas organizational behavior lags behind in empirical studies relative to the quantity of its theory. Future directions for research involving the chaos construct and other nonlinear dynamics are outlined.

Merging Developmental and Feminist Evaluation to Monitor and Evaluate Transformative Social Change

ERIC Educational Resources Information Center

Haylock, Laura; Miller, Carol

2016-01-01

Programs seeking to challenge and change gender and power relationships require a nimble, evolving monitoring, evaluation, and learning (MEL) system that helps make sense of how nonlinear complex social change happens. This article describes efforts by Oxfam Canada to develop such a system for a women's rights and gender equality program. The…

Biological system interactions.

PubMed Central

Adomian, G; Adomian, G E; Bellman, R E

1984-01-01

Mathematical modeling of cellular population growth, interconnected subsystems of the body, blood flow, and numerous other complex biological systems problems involves nonlinearities and generally randomness as well. Such problems have been dealt with by mathematical methods often changing the actual model to make it tractable. The method presented in this paper (and referenced works) allows much more physically realistic solutions. PMID:6585837

Generalized Projective Synchronization between Two Complex Networks with Time-Varying Coupling Delay

NASA Astrophysics Data System (ADS)

Sun, Mei; Zeng, Chang-Yan; Tian, Li-Xin

2009-01-01

Generalized projective synchronization (GPS) between two complex networks with time-varying coupling delay is investigated. Based on the Lyapunov stability theory, a nonlinear controller and adaptive updated laws are designed. Feasibility of the proposed scheme is proven in theory. Moreover, two numerical examples are presented, using the energy resource system and Lü's system [Physica A 382 (2007) 672] as the nodes of the networks. GPS between two energy resource complex networks with time-varying coupling delay is achieved. This study can widen the application range of the generalized synchronization methods and will be instructive for the demand-supply of energy resource in some regions of China.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2002-01-01

This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations

NASA Technical Reports Server (NTRS)

Yee, H. C.

2005-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations.

Building Blocks for Reliable Complex Nonlinear Numerical Simulations. Chapter 2

NASA Technical Reports Server (NTRS)

Yee, H. C.; Mansour, Nagi N. (Technical Monitor)

2001-01-01

This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.

Evaluation of integration methods for hybrid simulation of complex structural systems through collapse

NASA Astrophysics Data System (ADS)

Del Carpio R., Maikol; Hashemi, M. Javad; Mosqueda, Gilberto

2017-10-01

This study examines the performance of integration methods for hybrid simulation of large and complex structural systems in the context of structural collapse due to seismic excitations. The target application is not necessarily for real-time testing, but rather for models that involve large-scale physical sub-structures and highly nonlinear numerical models. Four case studies are presented and discussed. In the first case study, the accuracy of integration schemes including two widely used methods, namely, modified version of the implicit Newmark with fixed-number of iteration (iterative) and the operator-splitting (non-iterative) is examined through pure numerical simulations. The second case study presents the results of 10 hybrid simulations repeated with the two aforementioned integration methods considering various time steps and fixed-number of iterations for the iterative integration method. The physical sub-structure in these tests consists of a single-degree-of-freedom (SDOF) cantilever column with replaceable steel coupons that provides repeatable highlynonlinear behavior including fracture-type strength and stiffness degradations. In case study three, the implicit Newmark with fixed-number of iterations is applied for hybrid simulations of a 1:2 scale steel moment frame that includes a relatively complex nonlinear numerical substructure. Lastly, a more complex numerical substructure is considered by constructing a nonlinear computational model of a moment frame coupled to a hybrid model of a 1:2 scale steel gravity frame. The last two case studies are conducted on the same porotype structure and the selection of time steps and fixed number of iterations are closely examined in pre-test simulations. The generated unbalance forces is used as an index to track the equilibrium error and predict the accuracy and stability of the simulations.

Modeling Belt-Servomechanism by Chebyshev Functional Recurrent Neuro-Fuzzy Network

NASA Astrophysics Data System (ADS)

Huang, Yuan-Ruey; Kang, Yuan; Chu, Ming-Hui; Chang, Yeon-Pun

A novel Chebyshev functional recurrent neuro-fuzzy (CFRNF) network is developed from a combination of the Takagi-Sugeno-Kang (TSK) fuzzy model and the Chebyshev recurrent neural network (CRNN). The CFRNF network can emulate the nonlinear dynamics of a servomechanism system. The system nonlinearity is addressed by enhancing the input dimensions of the consequent parts in the fuzzy rules due to functional expansion of a Chebyshev polynomial. The back propagation algorithm is used to adjust the parameters of the antecedent membership functions as well as those of consequent functions. To verify the performance of the proposed CFRNF, the experiment of the belt servomechanism is presented in this paper. Both of identification methods of adaptive neural fuzzy inference system (ANFIS) and recurrent neural network (RNN) are also studied for modeling of the belt servomechanism. The analysis and comparison results indicate that CFRNF makes identification of complex nonlinear dynamic systems easier. It is verified that the accuracy and convergence of the CFRNF are superior to those of ANFIS and RNN by the identification results of a belt servomechanism.

Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application.

PubMed

Sakai, Kenshi; Upadhyaya, Shrinivasa K; Andrade-Sanchez, Pedro; Sviridova, Nina V

2017-03-01

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

Nonlinear dynamics of the complex multi-scale network

NASA Astrophysics Data System (ADS)

Makarov, Vladimir V.; Kirsanov, Daniil; Goremyko, Mikhail; Andreev, Andrey; Hramov, Alexander E.

2018-04-01

In this paper, we study the complex multi-scale network of nonlocally coupled oscillators for the appearance of chimera states. Chimera is a special state in which, in addition to the asynchronous cluster, there are also completely synchronous parts in the system. We show that the increase of nodes in subgroups leads to the destruction of the synchronous interaction within the common ring and to the narrowing of the chimera region.

PREFACE: XI Latin American Workshop on Nonlinear Phenomena

NASA Astrophysics Data System (ADS)

Anteneodo, Celia; da Luz, Marcos G. E.

2010-09-01

The XI Latin American Workshop on Nonlinear Phenomena (LAWNP) has been held in Búzios-RJ, Brazil, from 5-9 October 2009. This international conference is one in a series that have gathered biennially, over the past 21 years, physicists and other scientists who direct their work towards several aspects of nonlinear phenomena and complex systems. The main purpose of LAWNP meetings is to create a friendly and motivating environment, such that researchers from Latin America and from other parts of the globe can discuss not only their own latest results but also the trends and perspectives in this very interdisciplinary field of investigation. Hence, it constitutes a forum for promoting scientific collaboration and fomenting the emergence of new ideas, helping to advance the field. The XI edition (LAWNP'09) has gathered more than 230 scientists and students (most from Latin America), covering all of the world (27 different countries from North and South America, Asia, Europe, and Oceania). In total there were 18 plenary lectures, 80 parallel talks, and 140 poster contributions. A stimulating round-table discussion also took place devoted to the present and future of the Latin American Institutions in Complex Phenomena (a summary can be found at http://lawnp09.fis.puc-rio.br, in the Round-Table report link). The 2009 workshop was devoted to a wide scope of themes and points of view, pursuing to include the latest trends and developments in the science of nonlinearity. In this way, we have a great pleasure in publishing this Proceedings volume based on the high quality scientific works presented at LAWNP'09, covering already established methods as well as new approaches, discussing both theoretical and practical aspects, and addressing paradigmatic systems and also completely new problems, in nonlinearity and complexity. In fact, the present volume may be a very valuable reference for those interested in an overview on how nonlinear interactions can affect different phenomena in nature, addressing: classical and quantum chaos; instability and bifurcation; cooperative behavior; self-organization; pattern formation and synchronization; far-from-equilibrium and fluctuation dynamics; nonlinearity in fluid, plasmas, granular media, optics, and wave propagation; turbulence onset; and complexity in natural and social systems. The success of the conference was possible thanks to the financial support from many agencies, especially the Brazilian agencies Capes and CNPq, and the international agencies, Binational Itaupú, ICTP-Trieste, and CAIS-Albuquerque. Equally very important was the support by the organizer's institutions PUC-Rio de Janeiro and UFPR-Curitiba. We also must thank Journal of Physics: Conference Series, for believing in the success and scientific quality of the conference, and to the journal staff, specially Anete Ashton, for the kind and prompt help during the whole production process of this publication. Finally, and most important, we acknowledge all the participants of the LAWNP'09, whose interest and enthusiasm in advancing the science of nonlinearity constitutes the true moto making the present Proceedings a very valuable scientific contribution. Celia Anteneodo (PUC-Rio, Brazil) and Marcos G E da Luz (UFPR-Curitiba, Brazil) Conference Chairs Conference photograph Some of the conference participants. CAPES logo This issue was supported by CAPES (Agency for Evaluation and Support of Graduate Studies Programs), Brazilian govern entity devoted to the formation of human resources. CA would like to thank CAPES for financial support.

Dynamics of chromatic visual system processing differ in complexity between children and adults.

PubMed

Boon, Mei Ying; Suttle, Catherine M; Henry, Bruce I; Dain, Stephen J

2009-06-30

Measures of chromatic contrast sensitivity in children are lower than those of adults. This may be related to immaturities in signal processing at or near threshold. We have found that children's VEPs in response to low contrast supra-threshold chromatic stimuli are more intra-individually variable than those recorded from adults. Here, we report on linear and nonlinear analyses of chromatic VEPs recorded from children and adults. Two measures of signal-to-noise ratio are similar between the adults and children, suggesting that relatively high noise is unlikely to account for the poor clarity of negative and positive peak components in the children's VEPs. Nonlinear analysis indicates higher complexity of adults' than children's chromatic VEPs, at levels of chromatic contrast around and well above threshold.

Mode Reduction and Upscaling of Reactive Transport Under Incomplete Mixing

NASA Astrophysics Data System (ADS)

Lester, D. R.; Bandopadhyay, A.; Dentz, M.; Le Borgne, T.

2016-12-01

Upscaling of chemical reactions in partially-mixed fluid environments is a challenging problem due to the detailed interactions between inherently nonlinear reaction kinetics and complex spatio-temporal concentration distributions under incomplete mixing. We address this challenge via the development of an order reduction method for the advection-diffusion-reaction equation (ADRE) via projection of the reaction kinetics onto a small number N of leading eigenmodes of the advection-diffusion operator (the so-called "strange eigenmodes" of the flow) as an N-by-N nonlinear system, whilst mixing dynamics only are projected onto the remaining modes. For simple kinetics and moderate Péclet and Damkhöler numbers, this approach yields analytic solutions for the concentration mean, evolving spatio-temporal distribution and PDF in terms of the well-mixed reaction kinetics and mixing dynamics. For more complex kinetics or large Péclet or Damkhöler numbers only a small number of modes are required to accurately quantify the mixing and reaction dynamics in terms of the concentration field and PDF, facilitating greatly simplified approximation and analysis of reactive transport. Approximate solutions of this low-order nonlinear system provide quantiative predictions of the evolving concentration PDF. We demonstrate application of this method to a simple random flow and various mass-action reaction kinetics.

Time-periodic solutions of driven-damped trimer granular crystals

DOE PAGES

Charalampidis, E. G.; Li, F.; Chong, C.; ...

2015-01-01

In this work, we consider time-periodic structures of granular crystals consisting of alternate chrome steel (S) and tungsten carbide (W) spherical particles where each unit cell follows the pattern of a 2:1 trimer: S-W-S. The configuration at the left boundary is driven by a harmonic in-time actuation with given amplitude and frequency while the right one is a fixed wall. Similar to the case of a dimer chain, the combination of dissipation, driving of the boundary, and intrinsic nonlinearity leads to complex dynamics. For fixed driving frequencies in each of the spectral gaps, we find that the nonlinear surface modesmore » and the states dictated by the linear drive collide in a saddle-node bifurcation as the driving amplitude is increased, beyond which the dynamics of the system becomes chaotic. While the bifurcation structure is similar for solutions within the first and second gap, those in the first gap appear to be less robust. We also conduct a continuation in driving frequency, where it is apparent that the nonlinearity of the system results in a complex bifurcation diagram, involving an intricate set of loops of branches, especially within the spectral gap. The theoretical findings are qualitatively corroborated by the experimental full-field visualization of the time-periodic structures.« less

Reduced-order modeling of piezoelectric energy harvesters with nonlinear circuits under complex conditions

NASA Astrophysics Data System (ADS)

Xiang, Hong-Jun; Zhang, Zhi-Wei; Shi, Zhi-Fei; Li, Hong

2018-04-01

A fully coupled modeling approach is developed for piezoelectric energy harvesters in this work based on the use of available robust finite element packages and efficient reducing order modeling techniques. At first, the harvester is modeled using finite element packages. The dynamic equilibrium equations of harvesters are rebuilt by extracting system matrices from the finite element model using built-in commands without any additional tools. A Krylov subspace-based scheme is then applied to obtain a reduced-order model for improving simulation efficiency but preserving the key features of harvesters. Co-simulation of the reduced-order model with nonlinear energy harvesting circuits is achieved in a system level. Several examples in both cases of harmonic response and transient response analysis are conducted to validate the present approach. The proposed approach allows to improve the simulation efficiency by several orders of magnitude. Moreover, the parameters used in the equivalent circuit model can be conveniently obtained by the proposed eigenvector-based model order reduction technique. More importantly, this work establishes a methodology for modeling of piezoelectric energy harvesters with any complicated mechanical geometries and nonlinear circuits. The input load may be more complex also. The method can be employed by harvester designers to optimal mechanical structures or by circuit designers to develop novel energy harvesting circuits.

Poverty, disease, and the ecology of complex systems.

PubMed

Ngonghala, Calistus N; Pluciński, Mateusz M; Murray, Megan B; Farmer, Paul E; Barrett, Christopher B; Keenan, Donald C; Bonds, Matthew H

2014-04-01

Understanding why some human populations remain persistently poor remains a significant challenge for both the social and natural sciences. The extremely poor are generally reliant on their immediate natural resource base for subsistence and suffer high rates of mortality due to parasitic and infectious diseases. Economists have developed a range of models to explain persistent poverty, often characterized as poverty traps, but these rarely account for complex biophysical processes. In this Essay, we argue that by coupling insights from ecology and economics, we can begin to model and understand the complex dynamics that underlie the generation and maintenance of poverty traps, which can then be used to inform analyses and possible intervention policies. To illustrate the utility of this approach, we present a simple coupled model of infectious diseases and economic growth, where poverty traps emerge from nonlinear relationships determined by the number of pathogens in the system. These nonlinearities are comparable to those often incorporated into poverty trap models in the economics literature, but, importantly, here the mechanism is anchored in core ecological principles. Coupled models of this sort could be usefully developed in many economically important biophysical systems--such as agriculture, fisheries, nutrition, and land use change--to serve as foundations for deeper explorations of how fundamental ecological processes influence structural poverty and economic development.

Wave theory of turbulence in compressible media

NASA Technical Reports Server (NTRS)

Kentzer, C. P.

1975-01-01

An acoustical theory of turbulence was developed to aid in the study of the generation of sound in turbulent flows. The statistical framework adopted is a quantum-like wave dynamical formulation in terms of complex distribution functions. This formulation results in nonlinear diffusion-type transport equations for the probability densities of the five modes of wave propagation: two vorticity modes, one entropy mode, and two acoustic modes. This system of nonlinear equations is closed and complete. The technique of analysis was chosen such that direct applications to practical problems can be obtained with relative ease.

Towards fully analog hardware reservoir computing for speech recognition

NASA Astrophysics Data System (ADS)

Smerieri, Anteo; Duport, François; Paquot, Yvan; Haelterman, Marc; Schrauwen, Benjamin; Massar, Serge

2012-09-01

Reservoir computing is a very recent, neural network inspired unconventional computation technique, where a recurrent nonlinear system is used in conjunction with a linear readout to perform complex calculations, leveraging its inherent internal dynamics. In this paper we show the operation of an optoelectronic reservoir computer in which both the nonlinear recurrent part and the readout layer are implemented in hardware for a speech recognition application. The performance obtained is close to the one of to state-of-the-art digital reservoirs, while the analog architecture opens the way to ultrafast computation.

Nonlinear Dynamics on Interconnected Networks

NASA Astrophysics Data System (ADS)

Arenas, Alex; De Domenico, Manlio

2016-06-01

Networks of dynamical interacting units can represent many complex systems, from the human brain to transportation systems and societies. The study of these complex networks, when accounting for different types of interactions has become a subject of interest in the last few years, especially because its representational power in the description of users' interactions in diverse online social platforms (Facebook, Twitter, Instagram, etc.) [1], or in representing different transportation modes in urban networks [2,3]. The general name coined for these networks is multilayer networks, where each layer accounts for a type of interaction (see Fig. 1).

Nonlinear dynamics of planetary gears using analytical and finite element models

NASA Astrophysics Data System (ADS)

Ambarisha, Vijaya Kumar; Parker, Robert G.

2007-05-01

Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.

A design pathfinder with material correlation points for inflatable systems

NASA Astrophysics Data System (ADS)

Fulcher, Jared Terrell

The incorporation of inflatable structures into aerospace systems can produce significant advantages in stowed volume to mechanical effectiveness and overall weight. Many applications of these ultra-lightweight systems are designed to precisely control internal or external surfaces, or both, to achieve desired performance. The modeling of these structures becomes complex due to the material nonlinearities inherent to the majority of construction materials used in inflatable structures. Furthermore, accurately modeling the response and behavior of the interfacing boundaries that are common to many inflatable systems will lead to better understanding of the entire class of structures. The research presented involved using nonlinear finite element simulations correlated with photogrammetry testing to develop a procedure for defining material properties for commercially available polyurethane-coated woven nylon fabric, which is representative of coated materials that have been proven materials for use in many inflatable systems. Further, the new material model was used to design and develop an inflatable pathfinder system which employs only internal pressure to control an assembly of internal membranes. This canonical inflatable system will be used for exploration and development of general understanding of efficient design methodology and analysis of future systems. Canonical structures are incorporated into the design of the phased pathfinder system to allow for more universal insight. Nonlinear finite element simulations were performed to evaluate the effect of various boundary conditions, loading configurations, and material orientations on the geometric precision of geometries representing typical internal/external surfaces commonly incorporated into inflatable pathfinder system. The response of the inflatable system to possible damage was also studied using nonlinear finite element simulations. Development of a correlated material model for analysis of the inflatable pathfinder system has improved the efficiency of design and analysis techniques of future inflatable structures. KEYWORDS: Nonlinear Finite Element, Inflatable Structures, Gossamer Space Systems, Photogrammetry Measurements, Coated Woven Fabric.

Using fuzzy models in machining control system and assessment of sustainability

NASA Astrophysics Data System (ADS)

Grinek, A. V.; Boychuk, I. P.; Dantsevich, I. M.

2018-03-01

Description of the complex relationship of the optimum velocity with the temperature-strength state in the cutting zone for machining a fuzzy model is proposed. The fuzzy-logical conclusion allows determining the processing speed, which ensures effective, from the point of view of ensuring the quality of the surface layer, the temperature in the cutting zone and the maximum allowable cutting force. A scheme for stabilizing the temperature-strength state in the cutting zone using a nonlinear fuzzy PD–controller is proposed. The stability of the nonlinear system is estimated with the help of grapho–analytical realization of the method of harmonic balance and by modeling in MatLab.

Decentralized adaptive control of robot manipulators with robust stabilization design

NASA Technical Reports Server (NTRS)

Yuan, Bau-San; Book, Wayne J.

1988-01-01

Due to geometric nonlinearities and complex dynamics, a decentralized technique for adaptive control for multilink robot arms is attractive. Lyapunov-function theory for stability analysis provides an approach to robust stabilization. Each joint of the arm is treated as a component subsystem. The adaptive controller is made locally stable with servo signals including proportional and integral gains. This results in the bound on the dynamical interactions with other subsystems. A nonlinear controller which stabilizes the system with uniform boundedness is used to improve the robustness properties of the overall system. As a result, the robot tracks the reference trajectories with convergence. This strategy makes computation simple and therefore facilitates real-time implementation.

Modulation format dependence of digital nonlinearity compensation performance in optical fibre communication systems.

PubMed

Xu, Tianhua; Shevchenko, Nikita A; Lavery, Domaniç; Semrau, Daniel; Liga, Gabriele; Alvarado, Alex; Killey, Robert I; Bayvel, Polina

2017-02-20

The relationship between modulation format and the performance of multi-channel digital back-propagation (MC-DBP) in ideal Nyquist-spaced optical communication systems is investigated. It is found that the nonlinear distortions behave independent of modulation format in the case of full-field DBP, in contrast to the cases of electronic dispersion compensation and partial-bandwidth DBP. It is shown that the minimum number of steps per span required for MC-DBP depends on the chosen modulation format. For any given target information rate, there exists a possible trade-off between modulation format and back-propagated bandwidth, which could be used to reduce the computational complexity requirement of MC-DBP.

Towards a unifying theory for the first-, second-, and third-order molecular (non)linear optical response

NASA Astrophysics Data System (ADS)

Pérez-Moreno, Javier; Clays, Koen; Kuzyk, Mark G.

2010-05-01

We present a procedure for the modeling of the dispersion of the nonlinear optical response of complex molecular structures that is based strictly on the results from experimental characterization. We show how under some general conditions, the use of the Thomas-Kuhn sum-rules leads to a successful modeling of the nonlinear response of complex molecular structures.

Regime shifts and panarchies in regional scale social-ecological water systems

EPA Science Inventory

In this article we summarize histories of nonlinear, complex interactions among societal, legal, and ecosystem dynamics in six North American water basins, as they respond to changing climate. These case studies were chosen to explore the conditions for emergence of adaptive gove...

Nonlinear Stage of Modulation Instability for a Fifth-Order Nonlinear Schrödinger Equation

NASA Astrophysics Data System (ADS)

Jia, Hui-Xian; Shan, Dong-Ming

2017-10-01

In this article, a fifth-order nonlinear Schrödinger equation, which can be used to characterise the solitons in the optical fibre and inhomogeneous Heisenberg ferromagnetic spin system, has been investigated. Akhmediev breather, Kuzentsov soliton, and generalised soliton have all been attained via the Darbox transformation. Propagation and interaction for three-type breathers have been studied: the types of breather are determined by the module and complex angle of parameter ξ; interaction between Akhmediev breather and generalised soliton displays a phase shift, whereas the others do not. Modulation instability of the generalised solitons have been analysed: a small perturbation can develop into a rogue wave, which is consistent with the results of rogue wave solutions.

Higher-order modulation instability in nonlinear fiber optics.

PubMed

Erkintalo, Miro; Hammani, Kamal; Kibler, Bertrand; Finot, Christophe; Akhmediev, Nail; Dudley, John M; Genty, Goëry

2011-12-16

We report theoretical, numerical, and experimental studies of higher-order modulation instability in the focusing nonlinear Schrödinger equation. This higher-order instability arises from the nonlinear superposition of elementary instabilities, associated with initial single breather evolution followed by a regime of complex, yet deterministic, pulse splitting. We analytically describe the process using the Darboux transformation and compare with experiments in optical fiber. We show how a suitably low frequency modulation on a continuous wave field induces higher-order modulation instability splitting with the pulse characteristics at different phases of evolution related by a simple scaling relationship. We anticipate that similar processes are likely to be observed in many other systems including plasmas, Bose-Einstein condensates, and deep water waves. © 2011 American Physical Society

Landscape change in the southern Piedmont: challenges, solutions, and uncertainty across scales

USGS Publications Warehouse

Conroy, M.J.; Allen, Craig R.; Peterson, J.T.; Pritchard, L.J.; Moore, C.T.

2003-01-01

The southern Piedmont of the southeastern United States epitomizes the complex and seemingly intractable problems and hard decisions that result from uncontrolled urban and suburban sprawl. Here we consider three recurrent themes in complicated problems involving complex systems: (1) scale dependencies and cross-scale, often nonlinear relationships; (2) resilience, in particular the potential for complex systems to move to alternate stable states with decreased ecological and/or economic value; and (3) uncertainty in the ability to understand and predict outcomes, perhaps particularly those that occur as a result of human impacts. We consider these issues in the context of landscape-level decision making, using as an example water resources and lotic systems in the Piedmont region of the southeastern United States.

Towards the map of quantum gravity

NASA Astrophysics Data System (ADS)

Mielczarek, Jakub; Trześniewski, Tomasz

2018-06-01

In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between loop quantum gravity, causal dynamical triangulations, Hořava-Lifshitz gravity, asymptotic safety scenario, Quantum Graphity, deformations of relativistic symmetries and nonlinear phase space models are discussed. The main focus is on quantum deformations of the Hypersurface Deformations Algebra and Poincaré algebra, nonlinear structure of phase space, the running dimension of spacetime and nontrivial phase diagram of quantum gravity. We present an attempt to arrange the observed relations in the form of a graph, highlighting different aspects of quantum gravity. The analysis is performed in the spirit of a mind map, which represents the architectural approach to the studied theory, being a natural way to describe the properties of a complex system. We hope that the constructed graphs (maps) will turn out to be helpful in uncovering the global picture of quantum gravity as a particular complex system and serve as a useful guide for the researchers.

Observation of optical solitons in PT-symmetric lattices

PubMed Central

Wimmer, Martin; Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; Christodoulides, Demetrios N.; Peschel, Ulf

2015-01-01

Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated. PMID:26215165

Information flow to assess cardiorespiratory interactions in patients on weaning trials.

PubMed

Vallverdú, M; Tibaduisa, O; Clariá, F; Hoyer, D; Giraldo, B; Benito, S; Caminal, P

2006-01-01

Nonlinear processes of the autonomic nervous system (ANS) can produce breath-to-breath variability in the pattern of breathing. In order to provide assess to these nonlinear processes, nonlinear statistical dependencies between heart rate variability and respiratory pattern variability are analyzed. In this way, auto-mutual information and cross-mutual information concepts are applied. This information flow analysis is presented as a short-term non linear analysis method to investigate the information flow interactions in patients on weaning trials. 78 patients from mechanical ventilation were studied: Group A of 28 patients that failed to maintain spontaneous breathing and were reconnected; Group B of 50 patients with successful trials. The results show lower complexity with an increase of information flow in group A than in group B. Furthermore, a more (weakly) coupled nonlinear oscillator behavior is observed in the series of group A than in B.

Observation of optical solitons in PT-symmetric lattices

NASA Astrophysics Data System (ADS)

Wimmer, Martin; Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; Christodoulides, Demetrios N.; Peschel, Ulf

2015-07-01

Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated.

A geometrical approach to control and controllability of nonlinear dynamical networks

PubMed Central

Wang, Le-Zhi; Su, Ri-Qi; Huang, Zi-Gang; Wang, Xiao; Wang, Wen-Xu; Grebogi, Celso; Lai, Ying-Cheng

2016-01-01

In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains an outstanding problem. Here we develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically meaningful, we consider restricted parameter perturbation by imposing two constraints: it must be experimentally realizable and applied only temporarily. We introduce the concept of attractor network, which allows us to formulate a quantifiable controllability framework for nonlinear dynamical networks: a network is more controllable if the attractor network is more strongly connected. We test our control framework using examples from various models of experimental gene regulatory networks and demonstrate the beneficial role of noise in facilitating control. PMID:27076273

N-SCAN: new vibromodulation system for detection and monitoring of cracks and other contact-type defects

NASA Astrophysics Data System (ADS)

Donskoy, Dmitri; Ekimov, Alexander; Luzzato, Emile; Lottiaux, Jean-Louis; Stoupin, Stanislav; Zagrai, Andrei

2003-08-01

In recent years, innovative vibro-modulation technique has been introduced for detection of contact-type interfaces such as cracks, debondings, and delaminations. The technique utilizes the effect of nonlinear interaction of ultrasound and vibrations at the interface of the defect. Vibration varies on the contact area of the interface modulating passing through ultrasonic wave. The modulation manifests itself as additional side-band spectral components with the combination frequencies in the spectrum of the received signal. The presence of these components allows for detection and differentiation of the contact-type defects from other structural and material inhomogeneities. Vibro-modulation technique has been implemented in N-SCAN damage detection system. The system consists of a digital synthesizer, high and low frequency amplifiers, a magnetostrictive shaker, ultrasonic transducers and a PC-based data acquisition/processing station with N-SCAN software. The ability of the system to detect contact-type defects was experimentally verified using specimens of simple and complex geometries made of steel, aluminum, composites and other structural materials. N-SCAN proved to be very effective for nondestructive testing of full-scale structures ranging from 24 foot-long gun barrels to stainless steel pipes used in nuclear power plants. Among advantages of the system are applicability for the wide range of structural materials and for structures with complex geometries, real time data processing, convenient interface for system operation, simplicity of interpretation of results, no need for sensor scanning along structure, onsite inspection of large structures at a fraction of time as compared with conventional techniques. This paper describes the basic principles of nonlinear vibro-modulation NDE technique, some theoretical background for nonlinear interaction and justification of signal processing algorithm. It is also presents examples of practical implementation and application of the technique.

Forward design of a complex enzyme cascade reaction

PubMed Central

Hold, Christoph; Billerbeck, Sonja; Panke, Sven

2016-01-01

Enzymatic reaction networks are unique in that one can operate a large number of reactions under the same set of conditions concomitantly in one pot, but the nonlinear kinetics of the enzymes and the resulting system complexity have so far defeated rational design processes for the construction of such complex cascade reactions. Here we demonstrate the forward design of an in vitro 10-membered system using enzymes from highly regulated biological processes such as glycolysis. For this, we adapt the characterization of the biochemical system to the needs of classical engineering systems theory: we combine online mass spectrometry and continuous system operation to apply standard system theory input functions and to use the detailed dynamic system responses to parameterize a model of sufficient quality for forward design. This allows the facile optimization of a 10-enzyme cascade reaction for fine chemical production purposes. PMID:27677244

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacón, L., E-mail: chacon@lanl.gov; Chen, G.; Knoll, D.A.

We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLOmore » approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.« less

Multiscale high-order/low-order (HOLO) algorithms and applications

NASA Astrophysics Data System (ADS)

Chacón, L.; Chen, G.; Knoll, D. A.; Newman, C.; Park, H.; Taitano, W.; Willert, J. A.; Womeldorff, G.

2017-02-01

We review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. The HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.

Non—Linear Flood Assessment with Neural Network

NASA Astrophysics Data System (ADS)

Murariu, Gabriel; Puscasu, Gheorghe; Gogoncea, Vlad

2010-01-01

In our days, theoretical investigations are used in obtaining the mathematical model for the studied systems or processes. In general, the dynamics of the system are deeply nonlinear, complex or unknown. Generally speaking, such complex structure is a set of interconnected components. The common approach is therefore to start from measurements of the behavior of the system and the external influences (inputs) and try to determine a mathematical relation between them without going into the details of what is actually happening inside the system. Such strategy had known a great success during the time and it was applied for a large class of multifaceted processes. Accepting this approach, there could be investigated the climatic phenomena. In this paper is presented, in a comparative way, a non-linear water flood assessment made in a very sensitive area of the Lower Danube zone where, in the past years, a series of climatic problems have been happening. In these conditions, climatic risk factor management is a necessity. In a regular way, there could be considered and designed nonlinear models for the climatic factors' analysis by using a huge historical evidence data archive. In a previous paper we reached a notable intermediary result basing on a mathematical model constructed on internal recurrent neural network structure. Such approach had been presented considering the internal state estimation when no measurements coming from the sensors are available for system states. A modified backpropagation algorithm had been introduced in order to train the internal recurrent neural networks for nonlinear system identification. In this paper is exposed a comparative study between a numerical advances based on fluid dynamics' equations and our previous approach, based on internal recurrent neural networks (IRNN). The numerical approaching was made in order to succeed in building a physics model of a water flow evaluation and further, to achieve including the rainfall contributions. This condition is necessary for prediction and it is the first step toward a DSS—Decision Support System in the area. The relationship between the simulated results and the registered data allows considering our particular method to be useful for considered water flood assessment.

Thermodynamic study of complex formation between Ce3+ and cryptand 222 in some binary mixed nonaqueous solvents

NASA Astrophysics Data System (ADS)

Rounaghi, G. H.; Dolatshahi, S.; Tarahomi, S.

2014-12-01

The stoichiometry, stability and the thermodynamic parameters of complex formation between cerium(III) cation and cryptand 222 (4,7,13,16,21,24-hexaoxa-1,10-diazabycyclo[8.8.8]-hexacosane) were studied by conductometric titration method in some binary solvent mixtures of dimethylformamide (DMF), 1,2-dichloroethane (DCE), ethyl acetate (EtOAc) and methyl acetate (MeOAc) with methanol (MeOH), at 288, 298, 308, and 318 K. A model based on 1: 1 stoichiometry has been used to analyze the conductivity data. The data have been fitted according to a non-linear least-squares analysis that provide the stability constant, K f, for the cation-ligand inclusion complex. The results revealed that the stability order of [Ce(cryptand 222)]3+ complex changes with the nature and composition of the solvent system. A non-linear relationship was observed between the stability constant (log K f) of [Ce(cryptand 222)]3+ complex versus the composition of the binary mixed solvent. Standard thermodynamic values were obtained from temperature dependence of the stability constant of the complex, show that the studied complexation process is mainly entropy governed and are influenced by the nature and composition of the binary mixed solvent solutions.

External Aiding Methods for IMU-Based Navigation

DTIC Science & Technology

2016-11-26

Carlo simulation and particle filtering . This approach allows for the utilization of highly complex systems in a black box configuration with minimal...alternative method, which has the advantage of being less computationally demanding, is to use a Kalman filtering -based approach. The particular...Kalman filtering -based approach used here is known as linear covariance analysis. In linear covariance analysis, the nonlinear systems describing the

Fuzzy logic based robotic controller

NASA Technical Reports Server (NTRS)

Attia, F.; Upadhyaya, M.

1994-01-01

Existing Proportional-Integral-Derivative (PID) robotic controllers rely on an inverse kinematic model to convert user-specified cartesian trajectory coordinates to joint variables. These joints experience friction, stiction, and gear backlash effects. Due to lack of proper linearization of these effects, modern control theory based on state space methods cannot provide adequate control for robotic systems. In the presence of loads, the dynamic behavior of robotic systems is complex and nonlinear, especially where mathematical modeling is evaluated for real-time operators. Fuzzy Logic Control is a fast emerging alternative to conventional control systems in situations where it may not be feasible to formulate an analytical model of the complex system. Fuzzy logic techniques track a user-defined trajectory without having the host computer to explicitly solve the nonlinear inverse kinematic equations. The goal is to provide a rule-based approach, which is closer to human reasoning. The approach used expresses end-point error, location of manipulator joints, and proximity to obstacles as fuzzy variables. The resulting decisions are based upon linguistic and non-numerical information. This paper presents a solution to the conventional robot controller which is independent of computationally intensive kinematic equations. Computer simulation results of this approach as obtained from software implementation are also discussed.

Developments of a new data acquisition system at ANNRI

NASA Astrophysics Data System (ADS)

Nakao, T.; Terada, K.; Kimura, A.; Nakamura, S.; Iwamoto, O.; Harada, H.; Katabuchi, T.; Igashira, M.; Hori, J.

2017-09-01

A new data acquisition system (DAQ system) has been developed at the Accurate Neutron-Nucleus Reaction Measurement Instrument (ANNRI) facility in the Japan Proton Accelerator Research Complex, Materials and Life Science Experimental Facility (J-PARC/MLF). DAQ systems for both the Ge detector system and the Li-glass detector system were tested by using a gold sample. The applicability of the time-of-flight method was checked. System performance was evaluated on the basis of digital conversion nonlinearity, energy resolution, multi-channel coincidence and dead time.

Decomposition of the complex system into nonlinear spatio-temporal modes: algorithm and application to climate data mining

NASA Astrophysics Data System (ADS)

Feigin, Alexander; Gavrilov, Andrey; Loskutov, Evgeny; Mukhin, Dmitry

2015-04-01

Proper decomposition of the complex system into well separated "modes" is a way to reveal and understand the mechanisms governing the system behaviour as well as discover essential feedbacks and nonlinearities. The decomposition is also natural procedure that provides to construct adequate and concurrently simplest models of both corresponding sub-systems, and of the system in whole. In recent works two new methods of decomposition of the Earth's climate system into well separated modes were discussed. The first method [1-3] is based on the MSSA (Multichannel Singular Spectral Analysis) [4] for linear expanding vector (space-distributed) time series and makes allowance delayed correlations of the processes recorded in spatially separated points. The second one [5-7] allows to construct nonlinear dynamic modes, but neglects delay of correlations. It was demonstrated [1-3] that first method provides effective separation of different time scales, but prevent from correct reduction of data dimension: slope of variance spectrum of spatio-temporal empirical orthogonal functions that are "structural material" for linear spatio-temporal modes, is too flat. The second method overcomes this problem: variance spectrum of nonlinear modes falls essentially sharply [5-7]. However neglecting time-lag correlations brings error of mode selection that is uncontrolled and increases with growth of mode time scale. In the report we combine these two methods in such a way that the developed algorithm allows constructing nonlinear spatio-temporal modes. The algorithm is applied for decomposition of (i) multi hundreds years globally distributed data generated by the INM RAS Coupled Climate Model [8], and (ii) 156 years time series of SST anomalies distributed over the globe [9]. We compare efficiency of different methods of decomposition and discuss the abilities of nonlinear spatio-temporal modes for construction of adequate and concurrently simplest ("optimal") models of climate systems. 1. Feigin A.M., Mukhin D., Gavrilov A., Volodin E.M., and Loskutov E.M. (2013) "Separation of spatial-temporal patterns ("climatic modes") by combined analysis of really measured and generated numerically vector time series", AGU 2013 Fall Meeting, Abstract NG33A-1574. 2. Alexander Feigin, Dmitry Mukhin, Andrey Gavrilov, Evgeny Volodin, and Evgeny Loskutov (2014) "Approach to analysis of multiscale space-distributed time series: separation of spatio-temporal modes with essentially different time scales", Geophysical Research Abstracts, Vol. 16, EGU2014-6877. 3. Dmitry Mukhin, Dmitri Kondrashov, Evgeny Loskutov, Andrey Gavrilov, Alexander Feigin, and Michael Ghil (2014) "Predicting critical transitions in ENSO models, Part II: Spatially dependent models", Journal of Climate (accepted, doi: 10.1175/JCLI-D-14-00240.1). 4. Ghil, M., R. M. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, et al. (2002) "Advanced spectral methods for climatic time series", Rev. Geophys. 40(1), 3.1-3.41. 5. Dmitry Mukhin, Andrey Gavrilov, Evgeny M Loskutov and Alexander M Feigin (2014) "Nonlinear Decomposition of Climate Data: a New Method for Reconstruction of Dynamical Modes", AGU 2014 Fall Meeting, Abstract NG43A-3752. 6. Andrey Gavrilov, Dmitry Mukhin, Evgeny Loskutov, and Alexander Feigin (2015) "Empirical decomposition of climate data into nonlinear dynamic modes", Geophysical Research Abstracts, Vol. 17, EGU2015-627. 7. Dmitry Mukhin, Andrey Gavrilov, Evgeny Loskutov, Alexander Feigin, and Juergen Kurths (2015) "Reconstruction of principal dynamical modes from climatic variability: nonlinear approach", Geophysical Research Abstracts, Vol. 17, EGU2015-5729. 8. http://83.149.207.89/GCM_DATA_PLOTTING/GCM_INM_DATA_XY_en.htm. 9. http://iridl.ldeo.columbia.edu/SOURCES/.KAPLAN/.EXTENDED/.v2/.ssta/.

Sensitivity and Nonlinearity of Thermoacoustic Oscillations

NASA Astrophysics Data System (ADS)

Juniper, Matthew P.; Sujith, R. I.

2018-01-01

Nine decades of rocket engine and gas turbine development have shown that thermoacoustic oscillations are difficult to predict but can usually be eliminated with relatively small ad hoc design changes. These changes can, however, be ruinously expensive to devise. This review explains why linear and nonlinear thermoacoustic behavior is so sensitive to parameters such as operating point, fuel composition, and injector geometry. It shows how nonperiodic behavior arises in experiments and simulations and discusses how fluctuations in thermoacoustic systems with turbulent reacting flow, which are usually filtered or averaged out as noise, can reveal useful information. Finally, it proposes tools to exploit this sensitivity in the future: adjoint-based sensitivity analysis to optimize passive control designs and complex systems theory to warn of impending thermoacoustic oscillations and to identify the most sensitive elements of a thermoacoustic system.

Chaotic Motions in the Real Fuzzy Electronic Circuits

DTIC Science & Technology

2012-12-30

field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good sources to be...Takagi-Sugeno (T-S) fuzzy chaotic systems on electronic circuit. In the research field of secure communications, the original source should be blended ...model. The overall fuzzy model of the system is achieved by fuzzy blending of the linear system models. Consider a continuous-time nonlinear dynamic

Estimating the Volterra Series Transfer Function over coherent optical OFDM for efficient monitoring of the fiber channel nonlinearity.

PubMed

Shulkind, Gal; Nazarathy, Moshe

2012-12-17

We present an efficient method for system identification (nonlinear channel estimation) of third order nonlinear Volterra Series Transfer Function (VSTF) characterizing the four-wave-mixing nonlinear process over a coherent OFDM fiber link. Despite the seemingly large number of degrees of freedom in the VSTF (cubic in the number of frequency points) we identified a compressed VSTF representation which does not entail loss of information. Additional slightly lossy compression may be obtained by discarding very low power VSTF coefficients associated with regions of destructive interference in the FWM phased array effect. Based on this two-staged VSTF compressed representation, we develop a robust and efficient algorithm of nonlinear system identification (optical performance monitoring) estimating the VSTF by transmission of an extended training sequence over the OFDM link, performing just a matrix-vector multiplication at the receiver by a pseudo-inverse matrix which is pre-evaluated offline. For 512 (1024) frequency samples per channel, the VSTF measurement takes less than 1 (10) msec to complete with computational complexity of one real-valued multiply-add operation per time sample. Relative to a naïve exhaustive three-tone-test, our algorithm is far more tolerant of ASE additive noise and its acquisition time is orders of magnitude faster.

A holistic approach to movement education in sport and fitness: a systems based model.

PubMed

Polsgrove, Myles Jay

2012-01-01

The typical model used by movement professionals to enhance performance relies on the notion that a linear increase in load results in steady and progressive gains, whereby, the greater the effort, the greater the gains in performance. Traditional approaches to movement progression typically rely on the proper sequencing of extrinsically based activities to facilitate the individual in reaching performance objectives. However, physical rehabilitation or physical performance rarely progresses in such a linear fashion; instead they tend to evolve non-linearly and rather unpredictably. A dynamic system can be described as an entity that self-organizes into increasingly complex forms. Applying this view to the human body, practitioners could facilitate non-linear performance gains through a systems based programming approach. Utilizing a dynamic systems view, the Holistic Approach to Movement Education (HADME) is a model designed to optimize performance by accounting for non-linear and self-organizing traits associated with human movement. In this model, gains in performance occur through advancing individual perspectives and through optimizing sub-system performance. This inward shift of the focus of performance creates a sharper self-awareness and may lead to more optimal movements. Copyright © 2011 Elsevier Ltd. All rights reserved.

Rogue waves and W-shaped solitons in the multiple self-induced transparency system.

PubMed

Wang, Xin; Liu, Chong; Wang, Lei

2017-09-01

We study localized nonlinear waves on a plane wave background in the multiple self-induced transparency (SIT) system, which describes an important enhancement of the amplification and control of optical waves compared to the single SIT system. A hierarchy of exact multiparametric rational solutions in a compact determinant representation is presented. We demonstrate that this family of solutions contain known rogue wave solutions and unusual W-shaped soliton solutions. State transitions between the fundamental rogue waves and W-shaped solitons as well as higher-order nonlinear superposition modes are revealed in the zero-frequency perturbation region by the suitable choice for the background wavenumber of the electric field component. Particularly, it is found that the multiple SIT system can admit both stationary and nonstationary W-shaped solitons in contrast to the stationary results in the single SIT system. Moreover, the W-shaped soliton complex which is formed by a certain number of fundamental W-shaped solitons with zero phase parameters and its decomposition mechanism in the case of the nonzero phase parameters are shown. Meanwhile, some important characteristics of the nonlinear waves including trajectories and spectrum are discussed through the numerical and analytical methods.

New preconditioning strategy for Jacobian-free solvers for variably saturated flows with Richards’ equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lipnikov, Konstantin; Moulton, David; Svyatskiy, Daniil

2016-04-29

We develop a new approach for solving the nonlinear Richards’ equation arising in variably saturated flow modeling. The growing complexity of geometric models for simulation of subsurface flows leads to the necessity of using unstructured meshes and advanced discretization methods. Typically, a numerical solution is obtained by first discretizing PDEs and then solving the resulting system of nonlinear discrete equations with a Newton-Raphson-type method. Efficiency and robustness of the existing solvers rely on many factors, including an empiric quality control of intermediate iterates, complexity of the employed discretization method and a customized preconditioner. We propose and analyze a new preconditioningmore » strategy that is based on a stable discretization of the continuum Jacobian. We will show with numerical experiments for challenging problems in subsurface hydrology that this new preconditioner improves convergence of the existing Jacobian-free solvers 3-20 times. Furthermore, we show that the Picard method with this preconditioner becomes a more efficient nonlinear solver than a few widely used Jacobian-free solvers.« less

Parametric system identification of resonant micro/nanosystems operating in a nonlinear response regime

NASA Astrophysics Data System (ADS)

Sabater, A. B.; Rhoads, J. F.

2017-02-01

The parametric system identification of macroscale resonators operating in a nonlinear response regime can be a challenging research problem, but at the micro- and nanoscales, experimental constraints add additional complexities. For example, due to the small and noisy signals micro/nanoresonators produce, a lock-in amplifier is commonly used to characterize the amplitude and phase responses of the systems. While the lock-in enables detection, it also prohibits the use of established time-domain, multi-harmonic, and frequency-domain methods, which rely upon time-domain measurements. As such, the only methods that can be used for parametric system identification are those based on fitting experimental data to an approximate solution, typically derived via perturbation methods and/or Galerkin methods, of a reduced-order model. Thus, one could view the parametric system identification of micro/nanosystems operating in a nonlinear response regime as the amalgamation of four coupled sub-problems: nonparametric system identification, or proper experimental design and data acquisition; the generation of physically consistent reduced-order models; the calculation of accurate approximate responses; and the application of nonlinear least-squares parameter estimation. This work is focused on the theoretical foundations that underpin each of these sub-problems, as the methods used to address one sub-problem can strongly influence the results of another. To provide context, an electromagnetically transduced microresonator is used as an example. This example provides a concrete reference for the presented findings and conclusions.

Instantaneous nonlinear assessment of complex cardiovascular dynamics by Laguerre-Volterra point process models.

PubMed

Valenza, Gaetano; Citi, Luca; Barbieri, Riccardo

2013-01-01

We report an exemplary study of instantaneous assessment of cardiovascular dynamics performed using point-process nonlinear models based on Laguerre expansion of the linear and nonlinear Wiener-Volterra kernels. As quantifiers, instantaneous measures such as high order spectral features and Lyapunov exponents can be estimated from a quadratic and cubic autoregressive formulation of the model first order moment, respectively. Here, these measures are evaluated on heartbeat series coming from 16 healthy subjects and 14 patients with Congestive Hearth Failure (CHF). Data were gathered from the on-line repository PhysioBank, which has been taken as landmark for testing nonlinear indices. Results show that the proposed nonlinear Laguerre-Volterra point-process methods are able to track the nonlinear and complex cardiovascular dynamics, distinguishing significantly between CHF and healthy heartbeat series.

Nonlinear responses of coastal salt marshes to nutrient additions and sea level rise

EPA Science Inventory

Increasing nutrients and accelerated sea level rise (SLR) can cause marsh loss in some coastal systems. Responses to nutrients and SLR are complex and vary with soil matrix, marsh elevation, sediment inputs, and hydroperiod. We describe field and greenhouse studies examining sing...

Dynamic Identification for Control of Large Space Structures

NASA Technical Reports Server (NTRS)

Ibrahim, S. R.

1985-01-01

This is a compilation of reports by the one author on one subject. It consists of the following five journal articles: (1) A Parametric Study of the Ibrahim Time Domain Modal Identification Algorithm; (2) Large Modal Survey Testing Using the Ibrahim Time Domain Identification Technique; (3) Computation of Normal Modes from Identified Complex Modes; (4) Dynamic Modeling of Structural from Measured Complex Modes; and (5) Time Domain Quasi-Linear Identification of Nonlinear Dynamic Systems.

Direct heuristic dynamic programming for damping oscillations in a large power system.

PubMed

Lu, Chao; Si, Jennie; Xie, Xiaorong

2008-08-01

This paper applies a neural-network-based approximate dynamic programming method, namely, the direct heuristic dynamic programming (direct HDP), to a large power system stability control problem. The direct HDP is a learning- and approximation-based approach to addressing nonlinear coordinated control under uncertainty. One of the major design parameters, the controller learning objective function, is formulated to directly account for network-wide low-frequency oscillation with the presence of nonlinearity, uncertainty, and coupling effect among system components. Results include a novel learning control structure based on the direct HDP with applications to two power system problems. The first case involves static var compensator supplementary damping control, which is used to provide a comprehensive evaluation of the learning control performance. The second case aims at addressing a difficult complex system challenge by providing a new solution to a large interconnected power network oscillation damping control problem that frequently occurs in the China Southern Power Grid.

The 1992 annual report on scientific programs: A broad research program on the sciences of complexity

NASA Astrophysics Data System (ADS)

In 1992 the Santa Fe Institute hosted more than 100 short- and long-term research visitors who conducted a total of 212 person-months of residential research in complex systems. To date this 1992 work has resulted in more than 50 SFI Working Papers and nearly 150 publications in the scientific literature. The Institute's book series in the sciences of complexity continues to grow, now numbering more than 20 volumes. The fifth annual complex systems summer school brought nearly 60 graduate students and postdoctoral fellows to Santa Fe for an intensive introduction to the field. Research on complex systems - the focus of work at SFI - involves an extraordinary range of topics normally studied in seemingly disparate fields. Natural systems displaying complex adaptive behavior range upwards from DNA through cells and evolutionary systems to human societies. Research models exhibiting complex behavior include spin glasses, cellular automata, and genetic algorithms. Some of the major questions facing complex systems researchers are: (1) explaining how complexity arises from the nonlinear interaction of simple components; (2) describing the mechanisms underlying high-level aggregate behavior of complex systems (such as the overt behavior of an organism, the flow of energy in an ecology, and the Gross National Product (GNP) of an economy); and (3) creating a theoretical framework to enable predictions about the likely behavior of such systems in various conditions.

1992 annual report on scientific programs: A broad research program on the sciences of complexity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Not Available

1992-12-31

In 1992 the Santa Fe Institute hosted more than 100 short- and long-term research visitors who conducted a total of 212 person-months of residential research in complex systems. To date this 1992 work has resulted in more than 50 SFI Working Papers and nearly 150 publications in the scientific literature. The Institute`s book series in the sciences of complexity continues to grow, now numbering more than 20 volumes. The fifth annual complex systems summer school brought nearly 60 graduate students and postdoctoral fellows to Santa Fe for an intensive introduction to the field. Research on complex systems-the focus of workmore » at SFI-involves an extraordinary range of topics normally studied in seemingly disparate fields. Natural systems displaying complex adaptive behavior range upwards from DNA through cells and evolutionary systems to human societies. Research models exhibiting complex behavior include spin glasses, cellular automata, and genetic algorithms. Some of the major questions facing complex systems researchers are: (1) explaining how complexity arises from the nonlinear interaction of simple components; (2) describing the mechanisms underlying high-level aggregate behavior of complex systems (such as the overt behavior of an organism, the flow of energy in an ecology, the GNP of an economy); and (3) creating a theoretical framework to enable predictions about the likely behavior of such systems in various conditions.« less

Dynamical Signatures of Living Systems

NASA Technical Reports Server (NTRS)

Zak, M.

1999-01-01

One of the main challenges in modeling living systems is to distinguish a random walk of physical origin (for instance, Brownian motions) from those of biological origin and that will constitute the starting point of the proposed approach. As conjectured, the biological random walk must be nonlinear. Indeed, any stochastic Markov process can be described by linear Fokker-Planck equation (or its discretized version), only that type of process has been observed in the inanimate world. However, all such processes always converge to a stable (ergodic or periodic) state, i.e., to the states of a lower complexity and high entropy. At the same time, the evolution of living systems directed toward a higher level of complexity if complexity is associated with a number of structural variations. The simplest way to mimic such a tendency is to incorporate a nonlinearity into the random walk; then the probability evolution will attain the features of diffusion equation: the formation and dissipation of shock waves initiated by small shallow wave disturbances. As a result, the evolution never "dies:" it produces new different configurations which are accompanied by an increase or decrease of entropy (the decrease takes place during formation of shock waves, the increase-during their dissipation). In other words, the evolution can be directed "against the second law of thermodynamics" by forming patterns outside of equilibrium in the probability space. Due to that, a specie is not locked up in a certain pattern of behavior: it still can perform a variety of motions, and only the statistics of these motions is constrained by this pattern. It should be emphasized that such a "twist" is based upon the concept of reflection, i.e., the existence of the self-image (adopted from psychology). The model consists of a generator of stochastic processes which represents the motor dynamics in the form of nonlinear random walks, and a simulator of the nonlinear version of the diffusion equation which represents the mental dynamics. It has been demonstrated that coupled mental-motor dynamics can simulate emerging self-organization, prey-predator games, collaboration and competition, "collective brain," etc.

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

NASA Astrophysics Data System (ADS)

Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha

2017-06-01

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

A controlled experiment in ground water flow model calibration

USGS Publications Warehouse

Hill, M.C.; Cooley, R.L.; Pollock, D.W.

1998-01-01

Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.Nonlinear regression was introduced to ground water modeling in the 1970s, but has been used very little to calibrate numerical models of complicated ground water systems. Apparently, nonlinear regression is thought by many to be incapable of addressing such complex problems. With what we believe to be the most complicated synthetic test case used for such a study, this work investigates using nonlinear regression in ground water model calibration. Results of the study fall into two categories. First, the study demonstrates how systematic use of a well designed nonlinear regression method can indicate the importance of different types of data and can lead to successive improvement of models and their parameterizations. Our method differs from previous methods presented in the ground water literature in that (1) weighting is more closely related to expected data errors than is usually the case; (2) defined diagnostic statistics allow for more effective evaluation of the available data, the model, and their interaction; and (3) prior information is used more cautiously. Second, our results challenge some commonly held beliefs about model calibration. For the test case considered, we show that (1) field measured values of hydraulic conductivity are not as directly applicable to models as their use in some geostatistical methods imply; (2) a unique model does not necessarily need to be identified to obtain accurate predictions; and (3) in the absence of obvious model bias, model error was normally distributed. The complexity of the test case involved implies that the methods used and conclusions drawn are likely to be powerful in practice.

Magnetic localization and orientation of the capsule endoscope based on a random complex algorithm.

PubMed

He, Xiaoqi; Zheng, Zizhao; Hu, Chao

2015-01-01

The development of the capsule endoscope has made possible the examination of the whole gastrointestinal tract without much pain. However, there are still some important problems to be solved, among which, one important problem is the localization of the capsule. Currently, magnetic positioning technology is a suitable method for capsule localization, and this depends on a reliable system and algorithm. In this paper, based on the magnetic dipole model as well as magnetic sensor array, we propose nonlinear optimization algorithms using a random complex algorithm, applied to the optimization calculation for the nonlinear function of the dipole, to determine the three-dimensional position parameters and two-dimensional direction parameters. The stability and the antinoise ability of the algorithm is compared with the Levenberg-Marquart algorithm. The simulation and experiment results show that in terms of the error level of the initial guess of magnet location, the random complex algorithm is more accurate, more stable, and has a higher "denoise" capacity, with a larger range for initial guess values.

A robust in-situ warp-correction algorithm for VISAR streak camera data at the National Ignition Facility

NASA Astrophysics Data System (ADS)

Labaria, George R.; Warrick, Abbie L.; Celliers, Peter M.; Kalantar, Daniel H.

2015-02-01

The National Ignition Facility (NIF) at the Lawrence Livermore National Laboratory is a 192-beam pulsed laser system for high energy density physics experiments. Sophisticated diagnostics have been designed around key performance metrics to achieve ignition. The Velocity Interferometer System for Any Reflector (VISAR) is the primary diagnostic for measuring the timing of shocks induced into an ignition capsule. The VISAR system utilizes three streak cameras; these streak cameras are inherently nonlinear and require warp corrections to remove these nonlinear effects. A detailed calibration procedure has been developed with National Security Technologies (NSTec) and applied to the camera correction analysis in production. However, the camera nonlinearities drift over time affecting the performance of this method. An in-situ fiber array is used to inject a comb of pulses to generate a calibration correction in order to meet the timing accuracy requirements of VISAR. We develop a robust algorithm for the analysis of the comb calibration images to generate the warp correction that is then applied to the data images. Our algorithm utilizes the method of thin-plate splines (TPS) to model the complex nonlinear distortions in the streak camera data. In this paper, we focus on the theory and implementation of the TPS warp-correction algorithm for the use in a production environment.

All-fibre optical gating system for measuring a complex-shaped periodic broadband signal with picosecond resolution in a nanosecond time window

NASA Astrophysics Data System (ADS)

Andrianov, A. V.

2018-04-01

We have developed an optical gating system for continuously monitoring a complex-shaped periodic optical signal with picosecond resolution in a nanosecond time window using an all-fibre optical gate in the form of a nonlinear loop mirror and a passively mode-locked femtosecond laser. The distinctive features of the system are the possibility of characterizing signals with a very large spectral bandwidth, the possibility of using a gating pulse source with a wavelength falling in the band of the signal under study and its all-fibre design with the use of standard fibres and telecom components.

Algorithms for sum-of-squares-based stability analysis and control design of uncertain nonlinear systems

NASA Astrophysics Data System (ADS)

Ataei-Esfahani, Armin

In this dissertation, we present algorithmic procedures for sum-of-squares based stability analysis and control design for uncertain nonlinear systems. In particular, we consider the case of robust aircraft control design for a hypersonic aircraft model subject to parametric uncertainties in its aerodynamic coefficients. In recent years, Sum-of-Squares (SOS) method has attracted increasing interest as a new approach for stability analysis and controller design of nonlinear dynamic systems. Through the application of SOS method, one can describe a stability analysis or control design problem as a convex optimization problem, which can efficiently be solved using Semidefinite Programming (SDP) solvers. For nominal systems, the SOS method can provide a reliable and fast approach for stability analysis and control design for low-order systems defined over the space of relatively low-degree polynomials. However, The SOS method is not well-suited for control problems relating to uncertain systems, specially those with relatively high number of uncertainties or those with non-affine uncertainty structure. In order to avoid issues relating to the increased complexity of the SOS problems for uncertain system, we present an algorithm that can be used to transform an SOS problem with uncertainties into a LMI problem with uncertainties. A new Probabilistic Ellipsoid Algorithm (PEA) is given to solve the robust LMI problem, which can guarantee the feasibility of a given solution candidate with an a-priori fixed probability of violation and with a fixed confidence level. We also introduce two approaches to approximate the robust region of attraction (RROA) for uncertain nonlinear systems with non-affine dependence on uncertainties. The first approach is based on a combination of PEA and SOS method and searches for a common Lyapunov function, while the second approach is based on the generalized Polynomial Chaos (gPC) expansion theorem combined with the SOS method and searches for parameter-dependent Lyapunov functions. The control design problem is investigated through a case study of a hypersonic aircraft model with parametric uncertainties. Through time-scale decomposition and a series of function approximations, the complexity of the aircraft model is reduced to fall within the capability of SDP solvers. The control design problem is then formulated as a convex problem using the dual of the Lyapunov theorem. A nonlinear robust controller is searched using the combined PEA/SOS method. The response of the uncertain aircraft model is evaluated for two sets of pilot commands. As the simulation results show, the aircraft remains stable under up to 50% uncertainty in aerodynamic coefficients and can follow the pilot commands.

Dynamical principles in neuroscience

NASA Astrophysics Data System (ADS)

Rabinovich, Mikhail I.; Varona, Pablo; Selverston, Allen I.; Abarbanel, Henry D. I.

2006-10-01

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?

Dynamical principles in neuroscience

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rabinovich, Mikhail I.; Varona, Pablo; Selverston, Allen I.

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only amore » few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?.« less

Synchronization stability of memristor-based complex-valued neural networks with time delays.

PubMed

Liu, Dan; Zhu, Song; Ye, Er

2017-12-01

This paper focuses on the dynamical property of a class of memristor-based complex-valued neural networks (MCVNNs) with time delays. By constructing the appropriate Lyapunov functional and utilizing the inequality technique, sufficient conditions are proposed to guarantee exponential synchronization of the coupled systems based on drive-response concept. The proposed results are very easy to verify, and they also extend some previous related works on memristor-based real-valued neural networks. Meanwhile, the obtained sufficient conditions of this paper may be conducive to qualitative analysis of some complex-valued nonlinear delayed systems. A numerical example is given to demonstrate the effectiveness of our theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Menstruation, perimenopause, and chaos theory.

PubMed

Derry, Paula S; Derry, Gregory N

2012-01-01

This article argues that menstruation, including the transition to menopause, results from a specific kind of complex system, namely, one that is nonlinear, dynamical, and chaotic. A complexity-based perspective changes how we think about and research menstruation-related health problems and positive health. Chaotic systems are deterministic but not predictable, characterized by sensitivity to initial conditions and strange attractors. Chaos theory provides a coherent framework that qualitatively accounts for puzzling results from perimenopause research. It directs attention to variability within and between women, adaptation, lifespan development, and the need for complex explanations of disease. Whether the menstrual cycle is chaotic can be empirically tested, and a summary of our research on 20- to 40-year-old women is provided.

Non-linear analysis of wave progagation using transform methods and plates and shells using integral equations

NASA Astrophysics Data System (ADS)

Pipkins, Daniel Scott

Two diverse topics of relevance in modern computational mechanics are treated. The first involves the modeling of linear and non-linear wave propagation in flexible, lattice structures. The technique used combines the Laplace Transform with the Finite Element Method (FEM). The procedure is to transform the governing differential equations and boundary conditions into the transform domain where the FEM formulation is carried out. For linear problems, the transformed differential equations can be solved exactly, hence the method is exact. As a result, each member of the lattice structure is modeled using only one element. In the non-linear problem, the method is no longer exact. The approximation introduced is a spatial discretization of the transformed non-linear terms. The non-linear terms are represented in the transform domain by making use of the complex convolution theorem. A weak formulation of the resulting transformed non-linear equations yields a set of element level matrix equations. The trial and test functions used in the weak formulation correspond to the exact solution of the linear part of the transformed governing differential equation. Numerical results are presented for both linear and non-linear systems. The linear systems modeled are longitudinal and torsional rods and Bernoulli-Euler and Timoshenko beams. For non-linear systems, a viscoelastic rod and Von Karman type beam are modeled. The second topic is the analysis of plates and shallow shells under-going finite deflections by the Field/Boundary Element Method. Numerical results are presented for two plate problems. The first is the bifurcation problem associated with a square plate having free boundaries which is loaded by four, self equilibrating corner forces. The results are compared to two existing numerical solutions of the problem which differ substantially.

Chaos in World Politics: A Reflection

NASA Astrophysics Data System (ADS)

Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.

Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.

Thermodynamics of random reaction networks.

PubMed

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa -1.5 for linear and -1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks.

Thermodynamics of Random Reaction Networks

PubMed Central

Fischer, Jakob; Kleidon, Axel; Dittrich, Peter

2015-01-01

Reaction networks are useful for analyzing reaction systems occurring in chemistry, systems biology, or Earth system science. Despite the importance of thermodynamic disequilibrium for many of those systems, the general thermodynamic properties of reaction networks are poorly understood. To circumvent the problem of sparse thermodynamic data, we generate artificial reaction networks and investigate their non-equilibrium steady state for various boundary fluxes. We generate linear and nonlinear networks using four different complex network models (Erdős-Rényi, Barabási-Albert, Watts-Strogatz, Pan-Sinha) and compare their topological properties with real reaction networks. For similar boundary conditions the steady state flow through the linear networks is about one order of magnitude higher than the flow through comparable nonlinear networks. In all networks, the flow decreases with the distance between the inflow and outflow boundary species, with Watts-Strogatz networks showing a significantly smaller slope compared to the three other network types. The distribution of entropy production of the individual reactions inside the network follows a power law in the intermediate region with an exponent of circa −1.5 for linear and −1.66 for nonlinear networks. An elevated entropy production rate is found in reactions associated with weakly connected species. This effect is stronger in nonlinear networks than in the linear ones. Increasing the flow through the nonlinear networks also increases the number of cycles and leads to a narrower distribution of chemical potentials. We conclude that the relation between distribution of dissipation, network topology and strength of disequilibrium is nontrivial and can be studied systematically by artificial reaction networks. PMID:25723751

Linear and non-linear contributions to oxygen transport and utilization during moderate random exercise in humans.

PubMed

Beltrame, T; Hughson, R L

2017-05-01

What is the central question of this study? The pulmonary oxygen uptake (pV̇O2) data used to study the muscle aerobic system dynamics during moderate-exercise transitions is classically described as a mono-exponential function controlled by a complex interaction of the oxygen delivery-utilization balance. This elevated complexity complicates the acquisition of relevant information regarding aerobic system dynamics based on pV̇O2 data during a varying exercise stimulus. What is the main finding and its importance? The elevated complexity of pV̇O2 dynamics is a consequence of a multiple-order interaction between muscle oxygen uptake and circulatory distortion. Our findings challenge the use of a first-order function to study the influences of the oxygen delivery-utilization balance over the pV̇O2 dynamics. The assumption of aerobic system linearity implies that the pulmonary oxygen uptake (pV̇O2) dynamics during exercise transitions present a first-order characteristic. The main objective of this study was to test the linearity of the oxygen delivery-utilization balance during random moderate exercise. The cardiac output (Q̇) and deoxygenated haemoglobin concentration ([HHb]) were measured to infer the central and local O 2 availability, respectively. Thirteen healthy men performed two consecutive pseudorandom binary sequence cycling exercises followed by an incremental protocol. The system input and the outputs pV̇O2, [HHb] and Q̇ were submitted to frequency-domain analysis. The linearity of the variables was tested by computing the ability of the response at a specific frequency to predict the response at another frequency. The predictability levels were assessed by the coefficient of determination. In a first-order system, a participant who presents faster dynamics at a specific frequency should also present faster dynamics at any other frequency. All experimentally obtained variables (pV̇O2, [HHb] and Q̇) presented a certainly degree of non-linearity. The local O 2 availability, evaluated by the ratio pV̇O2/[HHb], presented the most irregular behaviour. The overall [HHb] kinetics were faster than pV̇O2 and Q̇ kinetics. In conclusion, the oxygen delivery-utilization balance behaved as a non-linear phenomenon. Therefore, the elevated complexity of the pulmonary oxygen uptake dynamics is governed by a complex multiple-order interaction between the oxygen delivery and utilization systems. © 2017 The Authors. Experimental Physiology © 2017 The Physiological Society.

a Statistical Dynamic Approach to Structural Evolution of Complex Capital Market Systems

NASA Astrophysics Data System (ADS)

Shao, Xiao; Chai, Li H.

As an important part of modern financial systems, capital market has played a crucial role on diverse social resource allocations and economical exchanges. Beyond traditional models and/or theories based on neoclassical economics, considering capital markets as typical complex open systems, this paper attempts to develop a new approach to overcome some shortcomings of the available researches. By defining the generalized entropy of capital market systems, a theoretical model and nonlinear dynamic equation on the operations of capital market are proposed from statistical dynamic perspectives. The US security market from 1995 to 2001 is then simulated and analyzed as a typical case. Some instructive results are discussed and summarized.

Modal interactions due to friction in the nonlinear vibration response of the "Harmony" test structure: Experiments and simulations

NASA Astrophysics Data System (ADS)

Claeys, M.; Sinou, J.-J.; Lambelin, J.-P.; Todeschini, R.

2016-08-01

The nonlinear vibration response of an assembly with friction joints - named "Harmony" - is studied both experimentally and numerically. The experimental results exhibit a softening effect and an increase of dissipation with excitation level. Modal interactions due to friction are also evidenced. The numerical methodology proposed groups together well-known structural dynamic methods, including finite elements, substructuring, Harmonic Balance and continuation methods. On the one hand, the application of this methodology proves its capacity to treat a complex system where several friction movements occur at the same time. On the other hand, the main contribution of this paper is the experimental and numerical study of evidence of modal interactions due to friction. The simulation methodology succeeds in reproducing complex form of dynamic behavior such as these modal interactions.

Dust acoustic cnoidal waves in a polytropic complex plasma

NASA Astrophysics Data System (ADS)

El-Labany, S. K.; El-Taibany, W. F.; Abdelghany, A. M.

2018-01-01

The nonlinear characteristics of dust acoustic (DA) waves in an unmagnetized collisionless complex plasma containing adiabatic electrons and ions and negatively charged dust grains (including the effects of modified polarization force) are investigated. Employing the reductive perturbation technique, a Korteweg-de Vries-Burgers (KdVB) equation is derived. The analytical solution for the KdVB equation is discussed. Also, the bifurcation and phase portrait analyses are presented to recognize different types of possible solutions. The dependence of the properties of nonlinear DA waves on the system parameters is investigated. It has been shown that an increase in the value of the modified polarization parameter leads to a fast decay and diminishes the oscillation amplitude of the DA damped cnoidal wave. The relevance of our findings and their possible applications to laboratory and space plasma situations is discussed.

Incorporation of nonlinear thermorheological complexity into the phenomenologies of structural relaxation.

PubMed

Hodge, Ian M

2005-09-22

A distribution of activation energies is introduced into the nonlinear Adam-Gibbs ("Hodge-Scherer") phenomenology for structural relaxation. The resulting dependencies of the stretched exponential beta parameter on thermodynamic temperature and fictive temperature (nonlinear thermorheological complexity) are derived. No additional adjustable parameters are introduced, and contact is made with the predictions of the random first-order transition theory of aging of Lubchenko and Wolynes [J. Chem. Physics121, 2852 (2004)].

Characterization of local complex structures in a recurrence plot to improve nonlinear dynamic discriminant analysis.

PubMed

Ding, Hang

2014-01-01

Structures in recurrence plots (RPs), preserving the rich information of nonlinear invariants and trajectory characteristics, have been increasingly analyzed in dynamic discrimination studies. The conventional analysis of RPs is mainly focused on quantifying the overall diagonal and vertical line structures through a method, called recurrence quantification analysis (RQA). This study extensively explores the information in RPs by quantifying local complex RP structures. To do this, an approach was developed to analyze the combination of three major RQA variables: determinism, laminarity, and recurrence rate (DLR) in a metawindow moving over a RP. It was then evaluated in two experiments discriminating (1) ideal nonlinear dynamic series emulated from the Lorenz system with different control parameters and (2) data sets of human heart rate regulations with normal sinus rhythms (n = 18) and congestive heart failure (n = 29). Finally, the DLR was compared with seven major RQA variables in terms of discriminatory power, measured by standardized mean difference (DSMD). In the two experiments, DLR resulted in the highest discriminatory power with DSMD = 2.53 and 0.98, respectively, which were 7.41 and 2.09 times the best performance from RQA. The study also revealed that the optimal RP structures for the discriminations were neither typical diagonal structures nor vertical structures. These findings indicate that local complex RP structures contain some rich information unexploited by RQA. Therefore, future research to extensively analyze complex RP structures would potentially improve the effectiveness of the RP analysis in dynamic discrimination studies.

Adaptive neural network decentralized backstepping output-feedback control for nonlinear large-scale systems with time delays.

PubMed

Tong, Shao Cheng; Li, Yong Ming; Zhang, Hua-Guang

2011-07-01

In this paper, two adaptive neural network (NN) decentralized output feedback control approaches are proposed for a class of uncertain nonlinear large-scale systems with immeasurable states and unknown time delays. Using NNs to approximate the unknown nonlinear functions, an NN state observer is designed to estimate the immeasurable states. By combining the adaptive backstepping technique with decentralized control design principle, an adaptive NN decentralized output feedback control approach is developed. In order to overcome the problem of "explosion of complexity" inherent in the proposed control approach, the dynamic surface control (DSC) technique is introduced into the first adaptive NN decentralized control scheme, and a simplified adaptive NN decentralized output feedback DSC approach is developed. It is proved that the two proposed control approaches can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded, and the observer errors and the tracking errors converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approaches.

Identification and compensation of friction for a novel two-axis differential micro-feed system

NASA Astrophysics Data System (ADS)

Du, Fuxin; Zhang, Mingyang; Wang, Zhaoguo; Yu, Chen; Feng, Xianying; Li, Peigang

2018-06-01

Non-linear friction in a conventional drive feed system (CDFS) feeding at low speed is one of the main factors that lead to the complexity of the feed drive. The CDFS will inevitably enter or approach a non-linear creeping work area at extremely low speed. A novel two-axis differential micro-feed system (TDMS) is developed in this paper to overcome the accuracy limitation of CDFS. A dynamic model of TDMS is first established. Then, a novel all-component friction parameter identification method (ACFPIM) using a genetic algorithm (GA) to identify the friction parameters of a TDMS is introduced. The friction parameters of the ball screw and linear motion guides are identified independently using the method, assuring the accurate modelling of friction force at all components. A proportional-derivate feed drive position controller with an observer-based friction compensator is implemented to achieve an accurate trajectory tracking performance. Finally, comparative experiments demonstrate the effectiveness of the TDMS in inhibiting the disadvantageous influence of non-linear friction and the validity of the proposed identification method for TDMS.

Chaotic behavior in the locomotion of Amoeba proteus.

PubMed

Miyoshi, H; Kagawa, Y; Tsuchiya, Y

2001-01-01

The locomotion of Amoeba proteus has been investigated by algorithms evaluating correlation dimension and Lyapunov spectrum developed in the field of nonlinear science. It is presumed by these parameters whether the random behavior of the system is stochastic or deterministic. For the analysis of the nonlinear parameters, n-dimensional time-delayed vectors have been reconstructed from a time series of periphery and area of A. proteus images captured with a charge-coupled-device camera, which characterize its random motion. The correlation dimension analyzed has shown the random motion of A. proteus is subjected only to 3-4 macrovariables, though the system is a complex system composed of many degrees of freedom. Furthermore, the analysis of the Lyapunov spectrum has shown its largest exponent takes positive values. These results indicate the random behavior of A. proteus is chaotic and deterministic motion on an attractor with low dimension. It may be important for the elucidation of the cell locomotion to take account of nonlinear interactions among a small number of dynamics such as the sol-gel transformation, the cytoplasmic streaming, and the relating chemical reaction occurring in the cell.

Scaling and characterisation of a 2-DoF velocity amplified electromagnetic vibration energy harvester

NASA Astrophysics Data System (ADS)

O’Donoghue, D.; Frizzell, R.; Punch, J.

2018-07-01

Vibration energy harvesters (VEHs) offer an alternative to batteries for the autonomous operation of low-power electronics. Understanding the influence of scaling on VEHs is of great importance in the design of reduced scale harvesters. The nonlinear harvesters investigated here employ velocity amplification, a technique used to increase velocity through impacts, to improve the power output of multiple-degree-of-freedom VEHs, compared to linear resonators. Such harvesters, employing electromagnetic induction, are referred to as velocity amplified electromagnetic generators (VAEGs), with gains in power achieved by increasing the relative velocity between the magnet and coil in the transducer. The influence of scaling on a nonlinear 2-DoF VAEG is presented. Due to the increased complexity of VAEGs, compared to linear systems, linear scaling theory cannot be directly applied to VAEGs. Therefore, a detailed nonlinear scaling method is utilised. Experimental and numerical methods are employed. This nonlinear scaling method can be used for analysing the scaling behaviour of all nonlinear electromagnetic VEHs. It is demonstrated that the electromagnetic coupling coefficient degrades more rapidly with scale for systems with larger displacement amplitudes, meaning that systems operating at low frequencies will scale poorly compared to those operating at higher frequencies. The load power of the 2-DoF VAEG is predicted to scale as {P}L\\propto {s}5.51 (s = volume1/3), suggesting that achieving high power densities in a VAEG with low device volume is extremely challenging.

Sequential double second-order nonlinear optical switch by an acido-triggered photochromic cyclometallated platinum(II) complex.

PubMed

Boixel, Julien; Guerchais, Véronique; Le Bozec, Hubert; Chantzis, Agisilaos; Jacquemin, Denis; Colombo, Alessia; Dragonetti, Claudia; Marinotto, Daniele; Roberto, Dominique

2015-05-07

An unprecedented DTE-based Pt(II) complex, 2(o), which stands as the first example of a sequential double nonlinear optical switch, induced first by protonation and next upon irradiation with UV light is presented.

Neural network applications in telecommunications

NASA Technical Reports Server (NTRS)

Alspector, Joshua

1994-01-01

Neural network capabilities include automatic and organized handling of complex information, quick adaptation to continuously changing environments, nonlinear modeling, and parallel implementation. This viewgraph presentation presents Bellcore work on applications, learning chip computational function, learning system block diagram, neural network equalization, broadband access control, calling-card fraud detection, software reliability prediction, and conclusions.

Evaluation: Boundary Identification in the Non-Linear Special Education System.

ERIC Educational Resources Information Center

Yacobacci, Patricia M.

The evaluation process within special education, as in general education, most often becomes one of data collection consisting of formal and informal tests given by the school psychologist and the classroom instructor. Influences of the complex environment on the educational process are often ignored. Evaluation factors include mainstreaming,…

Synthesis and Characterization of Electroresponsive Materials with Applications In: Part I. Second Harmonic Generation. Part II. Organic-Lanthanide Ion Complexes for Electroluminescence and Optical Amplifiers.

NASA Astrophysics Data System (ADS)

Claude, Charles

1995-01-01

Materials for optical waveguides were developed from two different approaches, inorganic-organic composites and soft gel polymers. Inorganic-organic composites were developed from alkoxysilane and organically modified silanes based on nonlinear optical chromophores. Organically modified silanes based on N-((3^' -trialkoxysilyl)propyl)-4-nitroaniline were synthesized and sol-gelled with trimethoxysilane. After a densification process at 190^circC with a corona discharge, the second harmonic of the film was measured with a Nd:YAG laser with a fundamental wavelength of 1064nm, d_{33} = 13pm/V. The decay of the second harmonic was expressed by a stretched bi-exponential equation. The decay time (tau _2) was equal to 3374 hours, and was comparable to nonlinear optical systems based on epoxy/Disperse Orange 1. The processing temperature of the organically modified silane was limited to 200^circC due to the decomposition of the organic chromophore. Soft gel polymers were synthesized and characterized for the development of optical waveguides with dc-electrical field assisted phase-matching. Polymers based on 4-nitroaniline terminated poly(ethylene oxide-co-propylene oxide) were shown to exhibit second harmonic generation that were optically phase-matched in an electrical field. The optical signals were stable and reproducible. Siloxane polymers modified with 1-mercapto-4-nitrobenzene and 1-mercapto-4-methylsulfonylstilbene nonlinear optical chromophores were synthesized. The physical and the linear and nonlinear optical properties of the polymers were characterized. Waveguides were developed from the polymers which were optically phase -matched and had an efficiency of 8.1%. The siloxane polymers exhibited optical phase-matching in an applied electrical field and can be used with a semiconductor laser. Organic lanthanide ion complexes for electroluminescence and optical amplifiers were synthesized and characterized. The complexes were characterized for their thermal and oxidative stability and for their optical properties. Organic-europium ion complexes based on derivatives of 2-benzoyl benzoate are stable to a temperature 70^circ C higher than the europium beta -diketonate complexes. The optical and fluorescence properties of the organic-europium ion complexes were characterized. The methoxy and the t-butyl derivatives of the europium 2-benzoylbenzoate complexes exhibited fluorescence quantum efficiencies that were comparable to europium tris(thenoyl trifluoroacetonate) in methylene chloride but the extinction coefficient was two-thirds of the europium thenoyltrifluoroacetonate complexes. The last complex characterized was the europium bis(diphenylphosphino)imine complex. The complex exhibited thermal stability to 550 ^circC under nitrogen.

Coexistence of Multiple Nonlinear States in a Tristable Passive Kerr Resonator

NASA Astrophysics Data System (ADS)

Anderson, Miles; Wang, Yadong; Leo, François; Coen, Stéphane; Erkintalo, Miro; Murdoch, Stuart G.

2017-07-01

Passive Kerr cavities driven by coherent laser fields display a rich landscape of nonlinear physics, including bistability, pattern formation, and localized dissipative structures (solitons). Their conceptual simplicity has for several decades offered an unprecedented window into nonlinear cavity dynamics, providing insights into numerous systems and applications ranging from all-optical memory devices to microresonator frequency combs. Yet despite the decades of study, a recent theoretical work has surprisingly alluded to an entirely new and unexplored paradigm in the regime where nonlinearly tilted cavity resonances overlap with one another [T. Hansson and S. Wabnitz, J. Opt. Soc. Am. B 32, 1259 (2015), 10.1364/JOSAB.32.001259]. We use synchronously driven fiber ring resonators to experimentally access this regime and observe the rise of new nonlinear dissipative states. Specifically, we observe, for the first time to the best of our knowledge, the stable coexistence of temporal Kerr cavity solitons and extended modulation instability (Turing) patterns, and perform real-time measurements that unveil the dynamics of the ensuing nonlinear structure. When operating in the regime of continuous wave tristability, we further observe the coexistence of two distinct cavity soliton states, one of which can be identified as a "super" cavity soliton, as predicted by Hansson and Wabnitz. Our experimental findings are in excellent agreement with theoretical analyses and numerical simulations of the infinite-dimensional Ikeda map that governs the cavity dynamics. The results from our work reveal that experimental systems can support complex combinations of distinct nonlinear states, and they could have practical implications to future microresonator-based frequency comb sources.

Nonlinear dynamics of the magnetosphere and space weather

NASA Technical Reports Server (NTRS)

Sharma, A. Surjalal

1996-01-01

The solar wind-magnetosphere system exhibits coherence on the global scale and such behavior can arise from nonlinearity on the dynamics. The observational time series data were used together with phase space reconstruction techniques to analyze the magnetospheric dynamics. Analysis of the solar wind, auroral electrojet and Dst indices showed low dimensionality of the dynamics and accurate prediction can be made with an input/output model. The predictability of the magnetosphere in spite of the apparent complexity arises from its dynamical synchronism with the solar wind. The electrodynamic coupling between different regions of the magnetosphere yields its coherent, low dimensional behavior. The data from multiple satellites and ground stations can be used to develop a spatio-temporal model that identifies the coupling between different regions. These nonlinear dynamical models provide space weather forecasting capabilities.

Numerical Simulation of the ``Fluid Mechanical Sewing Machine''

NASA Astrophysics Data System (ADS)

Brun, Pierre-Thomas; Audoly, Basile; Ribe, Neil

2011-11-01

A thin thread of viscous fluid falling onto a moving conveyor belt generates a wealth of complex ``stitch'' patterns depending on the belt speed and the fall height. To understand the rich nonlinear dynamics of this system, we have developed a new numerical code for simulating unsteady viscous threads, based on a discrete description of the geometry and a variational formulation for the viscous stresses. The code successfully reproduces all major features of the experimental state diagram of Morris et al. (Phys. Rev. E 2008). Fourier analysis of the motion of the thread's contact point with the belt suggests a new classification of the observed patterns, and reveals that the system behaves as a nonlinear oscillator coupling the pendulum modes of the thread.

Data-Driven Modeling of Complex Systems by means of a Dynamical ANN

NASA Astrophysics Data System (ADS)

Seleznev, A.; Mukhin, D.; Gavrilov, A.; Loskutov, E.; Feigin, A.

2017-12-01

The data-driven methods for modeling and prognosis of complex dynamical systems become more and more popular in various fields due to growth of high-resolution data. We distinguish the two basic steps in such an approach: (i) determining the phase subspace of the system, or embedding, from available time series and (ii) constructing an evolution operator acting in this reduced subspace. In this work we suggest a novel approach combining these two steps by means of construction of an artificial neural network (ANN) with special topology. The proposed ANN-based model, on the one hand, projects the data onto a low-dimensional manifold, and, on the other hand, models a dynamical system on this manifold. Actually, this is a recurrent multilayer ANN which has internal dynamics and capable of generating time series. Very important point of the proposed methodology is the optimization of the model allowing us to avoid overfitting: we use Bayesian criterion to optimize the ANN structure and estimate both the degree of evolution operator nonlinearity and the complexity of nonlinear manifold which the data are projected on. The proposed modeling technique will be applied to the analysis of high-dimensional dynamical systems: Lorenz'96 model of atmospheric turbulence, producing high-dimensional space-time chaos, and quasi-geostrophic three-layer model of the Earth's atmosphere with the natural orography, describing the dynamics of synoptical vortexes as well as mesoscale blocking systems. The possibility of application of the proposed methodology to analyze real measured data is also discussed. The study was supported by the Russian Science Foundation (grant #16-12-10198).

Characterization of Combustion Dynamics, Detection, and Prevention of an Unstable Combustion State Based on a Complex-Network Theory

NASA Astrophysics Data System (ADS)

Gotoda, Hiroshi; Kinugawa, Hikaru; Tsujimoto, Ryosuke; Domen, Shohei; Okuno, Yuta

2017-04-01

Complex-network theory has attracted considerable attention for nearly a decade, and it enables us to encompass our understanding of nonlinear dynamics in complex systems in a wide range of fields, including applied physics and mechanical, chemical, and electrical engineering. We conduct an experimental study using a pragmatic online detection methodology based on complex-network theory to prevent a limiting unstable state such as blowout in a confined turbulent combustion system. This study introduces a modified version of the natural visibility algorithm based on the idea of a visibility limit to serve as a pragmatic online detector. The average degree of the modified version of the natural visibility graph allows us to detect the onset of blowout, resulting in online prevention.

Investigation of advanced pre- and post-equalization schemes in high-order CAP modulation based high-speed indoor VLC transmission system

NASA Astrophysics Data System (ADS)

Wang, Yiguang; Chi, Nan

2016-10-01

Light emitting diodes (LEDs) based visible light communication (VLC) has been considered as a promising technology for indoor high-speed wireless access, due to its unique advantages, such as low cost, license free and high security. To achieve high-speed VLC transmission, carrierless amplitude and phase (CAP) modulation has been utilized for its lower complexity and high spectral efficiency. Moreover, to compensate the linear and nonlinear distortions such as frequency attenuation, sampling time offset, LED nonlinearity etc., series of pre- and post-equalization schemes should be employed in high-speed VLC systems. In this paper, we make an investigation on several advanced pre- and postequalization schemes for high-order CAP modulation based VLC systems. We propose to use a weighted preequalization technique to compensate the LED frequency attenuation. In post-equalization, a hybrid post equalizer is proposed, which consists of a linear equalizer, a Volterra series based nonlinear equalizer, and a decision-directed least mean square (DD-LMS) equalizer. Modified cascaded multi-modulus algorithm (M-CMMA) is employed to update the weights of the linear and the nonlinear equalizer, while DD-LMS can further improve the performance after the preconvergence. Based on high-order CAP modulation and these equalization schemes, we have experimentally demonstrated a 1.35-Gb/s, a 4.5-Gb/s and a 8-Gb/s high-speed indoor VLC transmission systems. The results show the benefit and feasibility of the proposed equalization schemes for high-speed VLC systems.

Toy models and stylized realities

NASA Astrophysics Data System (ADS)

Marsili, M.

2007-01-01

I discuss the role of toy models as theoretical tools for understanding complex systems of interacting agents. I review some concrete examples, in order to illustrate how this approach is able to capture, though in an admittedly stylized way, the interactions and non-linearities which are responsible for the rich phenomenology observed in reality. This allows one to interpret the system's behavior in terms of phase transitions and critical phenomena.

Identification of cascade water tanks using a PWARX model

NASA Astrophysics Data System (ADS)

Mattsson, Per; Zachariah, Dave; Stoica, Petre

2018-06-01

In this paper we consider the identification of a discrete-time nonlinear dynamical model for a cascade water tank process. The proposed method starts with a nominal linear dynamical model of the system, and proceeds to model its prediction errors using a model that is piecewise affine in the data. As data is observed, the nominal model is refined into a piecewise ARX model which can capture a wide range of nonlinearities, such as the saturation in the cascade tanks. The proposed method uses a likelihood-based methodology which adaptively penalizes model complexity and directly leads to a computationally efficient implementation.

The Dynamics and Evolution of Poles and Rogue Waves for Nonlinear Schrödinger Equations*

NASA Astrophysics Data System (ADS)

Chiu, Tin Lok; Liu, Tian Yang; Chan, Hiu Ning; Wing Chow, Kwok

2017-09-01

Rogue waves are unexpectedly large deviations from equilibrium or otherwise calm positions in physical systems, e.g. hydrodynamic waves and optical beam intensities. The profiles and points of maximum displacements of these rogue waves are correlated with the movement of poles of the exact solutions extended to the complex plane through analytic continuation. Such links are shown to be surprisingly precise for the first order rogue wave of the nonlinear Schrödinger (NLS) and the derivative NLS equations. A computational study on the second order rogue waves of the NLS equation also displays remarkable agreements.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

PubMed

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

NASA Astrophysics Data System (ADS)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Empirical modeling for intelligent, real-time manufacture control

NASA Technical Reports Server (NTRS)

Xu, Xiaoshu

1994-01-01

Artificial neural systems (ANS), also known as neural networks, are an attempt to develop computer systems that emulate the neural reasoning behavior of biological neural systems (e.g. the human brain). As such, they are loosely based on biological neural networks. The ANS consists of a series of nodes (neurons) and weighted connections (axons) that, when presented with a specific input pattern, can associate specific output patterns. It is essentially a highly complex, nonlinear, mathematical relationship or transform. These constructs have two significant properties that have proven useful to the authors in signal processing and process modeling: noise tolerance and complex pattern recognition. Specifically, the authors have developed a new network learning algorithm that has resulted in the successful application of ANS's to high speed signal processing and to developing models of highly complex processes. Two of the applications, the Weld Bead Geometry Control System and the Welding Penetration Monitoring System, are discussed in the body of this paper.

Rich complex behaviour of self-assembled nanoparticles far from equilibrium

PubMed Central

Ilday, Serim; Makey, Ghaith; Akguc, Gursoy B.; Yavuz, Özgün; Tokel, Onur; Pavlov, Ihor; Gülseren, Oguz; Ilday, F. Ömer

2017-01-01

A profoundly fundamental question at the interface between physics and biology remains open: what are the minimum requirements for emergence of complex behaviour from nonliving systems? Here, we address this question and report complex behaviour of tens to thousands of colloidal nanoparticles in a system designed to be as plain as possible: the system is driven far from equilibrium by ultrafast laser pulses that create spatiotemporal temperature gradients, inducing Marangoni flow that drags particles towards aggregation; strong Brownian motion, used as source of fluctuations, opposes aggregation. Nonlinear feedback mechanisms naturally arise between flow, aggregate and Brownian motion, allowing fast external control with minimal intervention. Consequently, complex behaviour, analogous to those seen in living organisms, emerges, whereby aggregates can self-sustain, self-regulate, self-replicate, self-heal and can be transferred from one location to another, all within seconds. Aggregates can comprise only one pattern or bifurcated patterns can coexist, compete, endure or perish. PMID:28443636

Rich complex behaviour of self-assembled nanoparticles far from equilibrium

NASA Astrophysics Data System (ADS)

Ilday, Serim; Makey, Ghaith; Akguc, Gursoy B.; Yavuz, Özgün; Tokel, Onur; Pavlov, Ihor; Gülseren, Oguz; Ilday, F. Ömer

2017-04-01

A profoundly fundamental question at the interface between physics and biology remains open: what are the minimum requirements for emergence of complex behaviour from nonliving systems? Here, we address this question and report complex behaviour of tens to thousands of colloidal nanoparticles in a system designed to be as plain as possible: the system is driven far from equilibrium by ultrafast laser pulses that create spatiotemporal temperature gradients, inducing Marangoni flow that drags particles towards aggregation; strong Brownian motion, used as source of fluctuations, opposes aggregation. Nonlinear feedback mechanisms naturally arise between flow, aggregate and Brownian motion, allowing fast external control with minimal intervention. Consequently, complex behaviour, analogous to those seen in living organisms, emerges, whereby aggregates can self-sustain, self-regulate, self-replicate, self-heal and can be transferred from one location to another, all within seconds. Aggregates can comprise only one pattern or bifurcated patterns can coexist, compete, endure or perish.

Modulational instability in a PT-symmetric vector nonlinear Schrödinger system

NASA Astrophysics Data System (ADS)

Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.

2016-12-01

A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.

Distributed robust adaptive control of high order nonlinear multi agent systems.

PubMed

Hashemi, Mahnaz; Shahgholian, Ghazanfar

2018-03-01

In this paper, a robust adaptive neural network based controller is presented for multi agent high order nonlinear systems with unknown nonlinear functions, unknown control gains and unknown actuator failures. At first, Neural Network (NN) is used to approximate the nonlinear uncertainty terms derived from the controller design procedure for the followers. Then, a novel distributed robust adaptive controller is developed by combining the backstepping method and the Dynamic Surface Control (DSC) approach. The proposed controllers are distributed in the sense that the designed controller for each follower agent only requires relative state information between itself and its neighbors. By using the Young's inequality, only few parameters need to be tuned regardless of NN nodes number. Accordingly, the problems of dimensionality curse and explosion of complexity are counteracted, simultaneously. New adaptive laws are designed by choosing the appropriate Lyapunov-Krasovskii functionals. The proposed approach proves the boundedness of all the closed-loop signals in addition to the convergence of the distributed tracking errors to a small neighborhood of the origin. Simulation results indicate that the proposed controller is effective and robust. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Differential flatness properties and multivariable adaptive control of ovarian system dynamics

NASA Astrophysics Data System (ADS)

Rigatos, Gerasimos

2016-12-01

The ovarian system exhibits nonlinear dynamics which is modeled by a set of coupled nonlinear differential equations. The paper proposes adaptive fuzzy control based on differential flatness theory for the complex dynamics of the ovarian system. It is proven that the dynamic model of the ovarian system, having as state variables the LH and the FSH hormones and their derivatives, is a differentially flat one. This means that all its state variables and its control inputs can be described as differential functions of the flat output. By exploiting differential flatness properties the system's dynamic model is written in the multivariable linear canonical (Brunovsky) form, for which the design of a state feedback controller becomes possible. After this transformation, the new control inputs of the system contain unknown nonlinear parts, which are identified with the use of neurofuzzy approximators. The learning procedure for these estimators is determined by the requirement the first derivative of the closed-loop's Lyapunov function to be a negative one. Moreover, Lyapunov stability analysis shows that H-infinity tracking performance is succeeded for the feedback control loop and this assures improved robustness to the aforementioned model uncertainty as well as to external perturbations. The efficiency of the proposed adaptive fuzzy control scheme is confirmed through simulation experiments.

Maximum Correntropy Unscented Kalman Filter for Ballistic Missile Navigation System based on SINS/CNS Deeply Integrated Mode.

PubMed

Hou, Bowen; He, Zhangming; Li, Dong; Zhou, Haiyin; Wang, Jiongqi

2018-05-27

Strap-down inertial navigation system/celestial navigation system ( SINS/CNS) integrated navigation is a high precision navigation technique for ballistic missiles. The traditional navigation method has a divergence in the position error. A deeply integrated mode for SINS/CNS navigation system is proposed to improve the navigation accuracy of ballistic missile. The deeply integrated navigation principle is described and the observability of the navigation system is analyzed. The nonlinearity, as well as the large outliers and the Gaussian mixture noises, often exists during the actual navigation process, leading to the divergence phenomenon of the navigation filter. The new nonlinear Kalman filter on the basis of the maximum correntropy theory and unscented transformation, named the maximum correntropy unscented Kalman filter, is deduced, and the computational complexity is analyzed. The unscented transformation is used for restricting the nonlinearity of the system equation, and the maximum correntropy theory is used to deal with the non-Gaussian noises. Finally, numerical simulation illustrates the superiority of the proposed filter compared with the traditional unscented Kalman filter. The comparison results show that the large outliers and the influence of non-Gaussian noises for SINS/CNS deeply integrated navigation is significantly reduced through the proposed filter.

Piecewise compensation for the nonlinear error of fiber-optic gyroscope scale factor

NASA Astrophysics Data System (ADS)

Zhang, Yonggang; Wu, Xunfeng; Yuan, Shun; Wu, Lei

2013-08-01

Fiber-Optic Gyroscope (FOG) scale factor nonlinear error will result in errors in Strapdown Inertial Navigation System (SINS). In order to reduce nonlinear error of FOG scale factor in SINS, a compensation method is proposed in this paper based on curve piecewise fitting of FOG output. Firstly, reasons which can result in FOG scale factor error are introduced and the definition of nonlinear degree is provided. Then we introduce the method to divide the output range of FOG into several small pieces, and curve fitting is performed in each output range of FOG to obtain scale factor parameter. Different scale factor parameters of FOG are used in different pieces to improve FOG output precision. These parameters are identified by using three-axis turntable, and nonlinear error of FOG scale factor can be reduced. Finally, three-axis swing experiment of SINS verifies that the proposed method can reduce attitude output errors of SINS by compensating the nonlinear error of FOG scale factor and improve the precision of navigation. The results of experiments also demonstrate that the compensation scheme is easy to implement. It can effectively compensate the nonlinear error of FOG scale factor with slightly increased computation complexity. This method can be used in inertial technology based on FOG to improve precision.

A coupled "AB" system: Rogue waves and modulation instabilities.

PubMed

Wu, C F; Grimshaw, R H J; Chow, K W; Chan, H N

2015-10-01

Rogue waves are unexpectedly large and localized displacements from an equilibrium position or an otherwise calm background. For the nonlinear Schrödinger (NLS) model widely used in fluid mechanics and optics, these waves can occur only when dispersion and nonlinearity are of the same sign, a regime of modulation instability. For coupled NLS equations, rogue waves will arise even if dispersion and nonlinearity are of opposite signs in each component as new regimes of modulation instability will appear in the coupled system. The same phenomenon will be demonstrated here for a coupled "AB" system, a wave-current interaction model describing baroclinic instability processes in geophysical flows. Indeed, the onset of modulation instability correlates precisely with the existence criterion for rogue waves for this system. Transitions from "elevation" rogue waves to "depression" rogue waves are elucidated analytically. The dispersion relation as a polynomial of the fourth order may possess double pairs of complex roots, leading to multiple configurations of rogue waves for a given set of input parameters. For special parameter regimes, the dispersion relation reduces to a cubic polynomial, allowing the existence criterion for rogue waves to be computed explicitly. Numerical tests correlating modulation instability and evolution of rogue waves were conducted.

About the Effect of Control on Flutter and Post-Flutter of a Supersonic/Hypersonic Cross-Sectional Wing

NASA Technical Reports Server (NTRS)

Silva, Walter A.; Librescu, Liviu; Marzocca, Piergiovanni

2001-01-01

The control of the flutter instability and the conversion of the dangerous character of the flutter instability boundary into the undangerous one of a cross-sectional wing in a supersonic/hypersonic flow field is presented. The objective of this paper is twofold: i) to analyze the implications of nonlinear unsteady aerodynamics and physical nonlinearities on the character of the instability boundary in the presence of a control capability, and ii) to outline the effects played in the same respect by some important parameters of the aeroelastic system. As a by-product of this analysis, the implications of the active control on the linearized flutter behavior of the system are captured and emphasized. The bifurcation behavior of the open/closed loop aeroelastic system in the vicinity of the flutter boundary is studied via the use of a new methodology based on the Liapunov First Quantity. The expected outcome of this study is: a) to greatly enhance the scope and reliability of the aeroelastic analysis and design criteria of advanced supersonic/hypersonic flight vehicles and, b) provide a theoretical basis for the analysis of more complex nonlinear aeroelastic systems.

About the Effect of Control on Flutter and Post-Flutter of a Supersonic/Hypersonic Cross-Sectional Wing

NASA Technical Reports Server (NTRS)

Marzocca, Piergiovanni; Librescu, Liviu; Silva, Walter A.

2000-01-01

The control of the flutter instability and the conversion of the dangerous character of the flutter instability boundary into the undangerous one of a cross-sectional wing in a supersonic/hypersonic flow field is presented. The objective of this paper is twofold: i) to analyze the implications of nonlinear unsteady aerodynamics and physical nonlinearities on the character of the instability boundary in the presence of a control capability, and ii) to outline the effects played in the same respect by some important parameters of the aeroelastic system. As a by-product of this analysis, the implications of the active control on the linearized flutter behavior of the system are captured and emphasized. The bifurcation behavior of the open/closed loop aeroelastic system in the vicinity of the flutter boundary is studied via the use of a new methodology based on the Liapunov First Quantity. The expected outcome of this study is: a) to greatly enhance the scope and reliability of the aeroelastic analysis and design criteria of advanced supersonic/hypersonic flight vehicles and, b) provide a theoretical basis for the analysis of more complex nonlinear aeroelastic systems.

Parameter identification for nonlinear aerodynamic systems

NASA Technical Reports Server (NTRS)

Pearson, Allan E.

1990-01-01

Parameter identification for nonlinear aerodynamic systems is examined. It is presumed that the underlying model can be arranged into an input/output (I/O) differential operator equation of a generic form. The algorithm estimation is especially efficient since the equation error can be integrated exactly given any I/O pair to obtain an algebraic function of the parameters. The algorithm for parameter identification was extended to the order determination problem for linear differential system. The degeneracy in a least squares estimate caused by feedback was addressed. A method of frequency analysis for determining the transfer function G(j omega) from transient I/O data was formulated using complex valued Fourier based modulating functions in contrast with the trigonometric modulating functions for the parameter estimation problem. A simulation result of applying the algorithm is given under noise-free conditions for a system with a low pass transfer function.

Thinking about complexity in health: A systematic review of the key systems thinking and complexity ideas in health.

PubMed

Rusoja, Evan; Haynie, Deson; Sievers, Jessica; Mustafee, Navonil; Nelson, Fred; Reynolds, Martin; Sarriot, Eric; Swanson, Robert Chad; Williams, Bob

2018-01-30

As the Sustainable Development Goals are rolled out worldwide, development leaders will be looking to the experiences of the past to improve implementation in the future. Systems thinking and complexity science (ST/CS) propose that health and the health system are composed of dynamic actors constantly evolving in response to each other and their context. While offering practical guidance for steering the next development agenda, there is no consensus as to how these important ideas are discussed in relation to health. This systematic review sought to identify and describe some of the key terms, concepts, and methods in recent ST/CS literature. Using the search terms "systems thinkin * AND health OR complexity theor* AND health OR complex adaptive system* AND health," we identified 516 relevant full texts out of 3982 titles across the search period (2002-2015). The peak number of articles were published in 2014 (83) with journals specifically focused on medicine/healthcare (265) and particularly the Journal of Evaluation in Clinical Practice (37) representing the largest number by volume. Dynamic/dynamical systems (n = 332), emergence (n = 294), complex adaptive system(s) (n = 270), and interdependent/interconnected (n = 263) were the most common terms with systems dynamic modelling (58) and agent-based modelling (43) as the most common methods. The review offered several important conclusions. First, while there was no core ST/CS "canon," certain terms appeared frequently across the reviewed texts. Second, even as these ideas are gaining traction in academic and practitioner communities, most are concentrated in a few journals. Finally, articles on ST/CS remain largely theoretical illustrating the need for further study and practical application. Given the challenge posed by the next phase of development, gaining a better understanding of ST/CS ideas and their use may lead to improvements in the implementation and practice of the Sustainable Development Goals. Key messages Systems thinking and complexity science, theories that acknowledge the dynamic, connected, and context-dependent nature of health, are highly relevant to the post-millennium development goal era yet lack consensus on their use in relation to health Although heterogeneous, terms, and concepts like emergence, dynamic/dynamical Systems, nonlinear(ity), and interdependent/interconnected as well as methods like systems dynamic modelling and agent-based modelling that comprise systems thinking and complexity science in the health literature are shared across an increasing number of publications within medical/healthcare disciplines Planners, practitioners, and theorists that can better understand these key systems thinking and complexity science concepts will be better equipped to tackle the challenges of the upcoming development goals. © 2018 John Wiley & Sons, Ltd.

Autonomous control systems: applications to remote sensing and image processing

NASA Astrophysics Data System (ADS)

Jamshidi, Mohammad

2001-11-01

One of the main challenges of any control (or image processing) paradigm is being able to handle complex systems under unforeseen uncertainties. A system may be called complex here if its dimension (order) is too high and its model (if available) is nonlinear, interconnected, and information on the system is uncertain such that classical techniques cannot easily handle the problem. Examples of complex systems are power networks, space robotic colonies, national air traffic control system, and integrated manufacturing plant, the Hubble Telescope, the International Space Station, etc. Soft computing, a consortia of methodologies such as fuzzy logic, neuro-computing, genetic algorithms and genetic programming, has proven to be powerful tools for adding autonomy and semi-autonomy to many complex systems. For such systems the size of soft computing control architecture will be nearly infinite. In this paper new paradigms using soft computing approaches are utilized to design autonomous controllers and image enhancers for a number of application areas. These applications are satellite array formations for synthetic aperture radar interferometry (InSAR) and enhancement of analog and digital images.

Fractal and multifractal models for extreme bursts in space plasmas.

NASA Astrophysics Data System (ADS)

Watkins, Nicholas; Chapman, Sandra; Credgington, Dan; Rosenberg, Sam; Sanchez, Raul

2010-05-01

Space plasmas may be said to show at least two types of "universality". One type arises from the fact that plasma physics underpins all astrophysical systems, while another arises from the generic properties of coupled nonlinear physical systems, a branch of the emerging science of complexity. Much work in complexity science is contributing to the physical understanding of the ways by which complex interactions in such systems cause driven or random perturbations to be nonlinearly amplified in amplitude and/or spread out over a wide range of frequencies. These mechanisms lead to non-Gaussian fluctuations and long-ranged temporal memory (referred to by Mandelbrot as the "Noah" and "Joseph" effects, respectively). This poster discusses a standard toy model (linear fractional stable motion, LFSM) which combines the Noah and Joseph effects in a controllable way. I will describe how LFSM is being used to explore the interplay of the above two effects in the distribution of bursts above thresholds, with applications to extreme events in space time series. I will describe ongoing work to improve the accuracy of maximum likelihood-based estimation of burst size and waiting time distributions for LFSM first reported in Watkins et al [Space Science Review, 2005; PRE, 2009]. The relevance of turbulent cascades to space plasmas necessitates comparison between this model and multifractal models, and early results will be described [Watkins et al, PRL comment, 2009].

Ranking Support Vector Machine with Kernel Approximation

PubMed Central

Dou, Yong

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms. PMID:28293256

Ranking Support Vector Machine with Kernel Approximation.

PubMed

Chen, Kai; Li, Rongchun; Dou, Yong; Liang, Zhengfa; Lv, Qi

2017-01-01

Learning to rank algorithm has become important in recent years due to its successful application in information retrieval, recommender system, and computational biology, and so forth. Ranking support vector machine (RankSVM) is one of the state-of-art ranking models and has been favorably used. Nonlinear RankSVM (RankSVM with nonlinear kernels) can give higher accuracy than linear RankSVM (RankSVM with a linear kernel) for complex nonlinear ranking problem. However, the learning methods for nonlinear RankSVM are still time-consuming because of the calculation of kernel matrix. In this paper, we propose a fast ranking algorithm based on kernel approximation to avoid computing the kernel matrix. We explore two types of kernel approximation methods, namely, the Nyström method and random Fourier features. Primal truncated Newton method is used to optimize the pairwise L2-loss (squared Hinge-loss) objective function of the ranking model after the nonlinear kernel approximation. Experimental results demonstrate that our proposed method gets a much faster training speed than kernel RankSVM and achieves comparable or better performance over state-of-the-art ranking algorithms.

Vagal-dependent nonlinear variability in the respiratory pattern of anesthetized, spontaneously breathing rats

PubMed Central

Dhingra, R. R.; Jacono, F. J.; Fishman, M.; Loparo, K. A.; Rybak, I. A.

2011-01-01

Physiological rhythms, including respiration, exhibit endogenous variability associated with health, and deviations from this are associated with disease. Specific changes in the linear and nonlinear sources of breathing variability have not been investigated. In this study, we used information theory-based techniques, combined with surrogate data testing, to quantify and characterize the vagal-dependent nonlinear pattern variability in urethane-anesthetized, spontaneously breathing adult rats. Surrogate data sets preserved the amplitude distribution and linear correlations of the original data set, but nonlinear correlation structure in the data was removed. Differences in mutual information and sample entropy between original and surrogate data sets indicated the presence of deterministic nonlinear or stochastic non-Gaussian variability. With vagi intact (n = 11), the respiratory cycle exhibited significant nonlinear behavior in templates of points separated by time delays ranging from one sample to one cycle length. After vagotomy (n = 6), even though nonlinear variability was reduced significantly, nonlinear properties were still evident at various time delays. Nonlinear deterministic variability did not change further after subsequent bilateral microinjection of MK-801, an N-methyl-d-aspartate receptor antagonist, in the Kölliker-Fuse nuclei. Reversing the sequence (n = 5), blocking N-methyl-d-aspartate receptors bilaterally in the dorsolateral pons significantly decreased nonlinear variability in the respiratory pattern, even with the vagi intact, and subsequent vagotomy did not change nonlinear variability. Thus both vagal and dorsolateral pontine influences contribute to nonlinear respiratory pattern variability. Furthermore, breathing dynamics of the intact system are mutually dependent on vagal and pontine sources of nonlinear complexity. Understanding the structure and modulation of variability provides insight into disease effects on respiratory patterning. PMID:21527661

Dynamics and Control of a Quadrotor with Active Geometric Morphing

NASA Astrophysics Data System (ADS)

Wallace, Dustin A.

Quadrotors are manufactured in a wide variety of shapes, sizes, and performance levels to fulfill a multitude of roles. Robodub Inc. has patented a morphing quadrotor which will allow active reconfiguration between various shapes for performance optimization across a wider spectrum of roles. The dynamics of the system are studied and modeled using Newtonian Mechanics. Controls are developed and simulated using both Linear Quadratic and Numerical Nonlinear Optimal control for a symmetric simplificiation of the system dynamics. Various unique vehicle capabilities are investigated, including novel single-throttle flight control using symmetric geometric morphing, as well as recovery from motor loss by reconfiguring into a trirotor configuration. The system dynamics were found to be complex and highly nonlinear. All attempted control strategies resulted in controllability, suggesting further research into each may lead to multiple viable control strategies for a physical prototype.

Structure-based control of complex networks with nonlinear dynamics.

PubMed

Zañudo, Jorge Gomez Tejeda; Yang, Gang; Albert, Réka

2017-07-11

What can we learn about controlling a system solely from its underlying network structure? Here we adapt a recently developed framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This feedback-based framework provides realizable node overrides that steer a system toward any of its natural long-term dynamic behaviors, regardless of the specific functional forms and system parameters. We use this framework on several real networks, identify the topological characteristics that underlie the predicted node overrides, and compare its predictions to those of structural controllability in control theory. Finally, we demonstrate this framework's applicability in dynamic models of gene regulatory networks and identify nodes whose override is necessary for control in the general case but not in specific model instances.

Self-sustained vibrations in volcanic areas extracted by Independent Component Analysis: a review and new results

NASA Astrophysics Data System (ADS)

de Lauro, E.; de Martino, S.; Falanga, M.; Palo, M.

2011-12-01

We investigate the physical processes associated with volcanic tremor and explosions. A volcano is a complex system where a fluid source interacts with the solid edifice so generating seismic waves in a regime of low turbulence. Although the complex behavior escapes a simple universal description, the phases of activity generate stable (self-sustained) oscillations that can be described as a non-linear dynamical system of low dimensionality. So, the system requires to be investigated with non-linear methods able to individuate, decompose, and extract the main characteristics of the phenomenon. Independent Component Analysis (ICA), an entropy-based technique is a good candidate for this purpose. Here, we review the results of ICA applied to seismic signals acquired in some volcanic areas. We emphasize analogies and differences among the self-oscillations individuated in three cases: Stromboli (Italy), Erebus (Antarctica) and Volcán de Colima (Mexico). The waveforms of the extracted independent components are specific for each volcano, whereas the similarity can be ascribed to a very general common source mechanism involving the interaction between gas/magma flow and solid structures (the volcanic edifice). Indeed, chocking phenomena or inhomogeneities in the volcanic cavity can play the same role in generating self-oscillations as the languid and the reed do in musical instruments. The understanding of these background oscillations is relevant not only for explaining the volcanic source process and to make a forecast into the future, but sheds light on the physics of complex systems developing low turbulence.

Nonlinear spectral singularities for confined nonlinearities.

PubMed

Mostafazadeh, Ali

2013-06-28

We introduce a notion of spectral singularity that applies for a general class of nonlinear Schrödinger operators involving a confined nonlinearity. The presence of the nonlinearity does not break the parity-reflection symmetry of spectral singularities but makes them amplitude dependent. Nonlinear spectral singularities are, therefore, associated with a resonance effect that produces amplified waves with a specific amplitude-wavelength profile. We explore the consequences of this phenomenon for a complex δ-function potential that is subject to a general confined nonlinearity.

Systems thinking and complexity: considerations for health promoting schools.

PubMed

Rosas, Scott R

2017-04-01

The health promoting schools concept reflects a comprehensive and integrated philosophy to improving student and personnel health and well-being. Conceptualized as a configuration of interacting, interdependent parts connected through a web of relationships that form a whole greater than the sum of its parts, school health promotion initiatives often target several levels (e.g. individual, professional, procedural and policy) simultaneously. Health promoting initiatives, such as those operationalized under the whole school approach, include several interconnected components that are coordinated to improve health outcomes in complex settings. These complex systems interventions are embedded in intricate arrangements of physical, biological, ecological, social, political and organizational relationships. Systems thinking and characteristics of complex adaptive systems are introduced in this article to provide a perspective that emphasizes the patterns of inter-relationships associated with the nonlinear, dynamic and adaptive nature of complex hierarchical systems. Four systems thinking areas: knowledge, networks, models and organizing are explored as a means to further manage the complex nature of the development and sustainability of health promoting schools. Applying systems thinking and insights about complex adaptive systems can illuminate how to address challenges found in settings with both complicated (i.e. multi-level and multisite) and complex aspects (i.e. synergistic processes and emergent outcomes). © The Author 2015. Published by Oxford University Press. All rights reserved. For Permissions, please email: journals.permissions@oup.com.

Complexity analyses show two distinct types of nonlinear dynamics in short heart period variability recordings

PubMed Central

Porta, Alberto; Bari, Vlasta; Marchi, Andrea; De Maria, Beatrice; Cysarz, Dirk; Van Leeuwen, Peter; Takahashi, Anielle C. M.; Catai, Aparecida M.; Gnecchi-Ruscone, Tomaso

2015-01-01

Two diverse complexity metrics quantifying time irreversibility and local prediction, in connection with a surrogate data approach, were utilized to detect nonlinear dynamics in short heart period (HP) variability series recorded in fetuses, as a function of the gestational period, and in healthy humans, as a function of the magnitude of the orthostatic challenge. The metrics indicated the presence of two distinct types of nonlinear HP dynamics characterized by diverse ranges of time scales. These findings stress the need to render more specific the analysis of nonlinear components of HP dynamics by accounting for different temporal scales. PMID:25806002

Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lebedev, M. E., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Alfimov, G. L., E-mail: gloriouslair@gmail.com, E-mail: galfimov@yahoo.com; Malomed, Boris A., E-mail: malomed@post.tau.ac.il

We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate thatmore » one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.« less

Cx-02 Program, workshop on modeling complex systems

USGS Publications Warehouse

Mossotti, Victor G.; Barragan, Jo Ann; Westergard, Todd D.

2003-01-01

This publication contains the abstracts and program for the workshop on complex systems that was held on November 19-21, 2002, in Reno, Nevada. Complex systems are ubiquitous within the realm of the earth sciences. Geological systems consist of a multiplicity of linked components with nested feedback loops; the dynamics of these systems are non-linear, iterative, multi-scale, and operate far from equilibrium. That notwithstanding, It appears that, with the exception of papers on seismic studies, geology and geophysics work has been disproportionally underrepresented at regional and national meetings on complex systems relative to papers in the life sciences. This is somewhat puzzling because geologists and geophysicists are, in many ways, preadapted to thinking of complex system mechanisms. Geologists and geophysicists think about processes involving large volumes of rock below the sunlit surface of Earth, the accumulated consequence of processes extending hundreds of millions of years in the past. Not only do geologists think in the abstract by virtue of the vast time spans, most of the evidence is out-of-sight. A primary goal of this workshop is to begin to bridge the gap between the Earth sciences and life sciences through demonstration of the universality of complex systems science, both philosophically and in model structures.

Continuous-wave to pulse regimes for a family of passively mode-locked lasers with saturable nonlinearity

NASA Astrophysics Data System (ADS)

Dikandé, Alain M.; Voma Titafan, J.; Essimbi, B. Z.

2017-10-01

The transition dynamics from continuous-wave to pulse regimes of operation for a generic model of passively mode-locked lasers with saturable absorbers, characterized by an active medium with non-Kerr nonlinearity, are investigated analytically and numerically. The system is described by a complex Ginzburg-Landau equation with a general m:n saturable nonlinearity (i.e {I}m/{(1+{{Γ }}I)}n, where I is the field intensity and m and n are two positive numbers), coupled to a two-level gain equation. An analysis of stability of continuous waves, following the modulational instability approach, provides a global picture of the self-starting dynamics in the system. The analysis reveals two distinct routes depending on values of the couple (m, n), and on the dispersion regime: in the normal dispersion regime, when m = 2 and n is arbitrary, the self-starting requires positive values of the fast saturable absorber and nonlinearity coefficients, but negative values of these two parameters for the family with m = 0. However, when the spectral filter is negative, the laser can self-start for certain values of the input field and the nonlinearity saturation coefficient Γ. The present work provides a general map for the self-starting mechanisms of rare-earth doped figure-eight fiber lasers, as well as Kerr-lens mode-locked solid-state lasers.

Discovering governing equations from data by sparse identification of nonlinear dynamical systems

PubMed Central

Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan

2016-01-01

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing. PMID:27035946

Discovering governing equations from data by sparse identification of nonlinear dynamical systems.

PubMed

Brunton, Steven L; Proctor, Joshua L; Kutz, J Nathan

2016-04-12

Extracting governing equations from data is a central challenge in many diverse areas of science and engineering. Data are abundant whereas models often remain elusive, as in climate science, neuroscience, ecology, finance, and epidemiology, to name only a few examples. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing equations from noisy measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems in an appropriate basis. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. This results in parsimonious models that balance accuracy with model complexity to avoid overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized systems and systems that are time-varying or have external forcing.

Efficient quantum computing using coherent photon conversion.

PubMed

Langford, N K; Ramelow, S; Prevedel, R; Munro, W J; Milburn, G J; Zeilinger, A

2011-10-12

Single photons are excellent quantum information carriers: they were used in the earliest demonstrations of entanglement and in the production of the highest-quality entanglement reported so far. However, current schemes for preparing, processing and measuring them are inefficient. For example, down-conversion provides heralded, but randomly timed, single photons, and linear optics gates are inherently probabilistic. Here we introduce a deterministic process--coherent photon conversion (CPC)--that provides a new way to generate and process complex, multiquanta states for photonic quantum information applications. The technique uses classically pumped nonlinearities to induce coherent oscillations between orthogonal states of multiple quantum excitations. One example of CPC, based on a pumped four-wave-mixing interaction, is shown to yield a single, versatile process that provides a full set of photonic quantum processing tools. This set satisfies the DiVincenzo criteria for a scalable quantum computing architecture, including deterministic multiqubit entanglement gates (based on a novel form of photon-photon interaction), high-quality heralded single- and multiphoton states free from higher-order imperfections, and robust, high-efficiency detection. It can also be used to produce heralded multiphoton entanglement, create optically switchable quantum circuits and implement an improved form of down-conversion with reduced higher-order effects. Such tools are valuable building blocks for many quantum-enabled technologies. Finally, using photonic crystal fibres we experimentally demonstrate quantum correlations arising from a four-colour nonlinear process suitable for CPC and use these measurements to study the feasibility of reaching the deterministic regime with current technology. Our scheme, which is based on interacting bosonic fields, is not restricted to optical systems but could also be implemented in optomechanical, electromechanical and superconducting systems with extremely strong intrinsic nonlinearities. Furthermore, exploiting higher-order nonlinearities with multiple pump fields yields a mechanism for multiparty mediation of the complex, coherent dynamics.

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks

PubMed Central

Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the “information networks” different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed. PMID:28796797

Chaotic itinerancy within the coupled dynamics between a physical body and neural oscillator networks.

PubMed

Park, Jihoon; Mori, Hiroki; Okuyama, Yuji; Asada, Minoru

2017-01-01

Chaotic itinerancy is a phenomenon in which the state of a nonlinear dynamical system spontaneously explores and attracts certain states in a state space. From this perspective, the diverse behavior of animals and its spontaneous transitions lead to a complex coupled dynamical system, including a physical body and a brain. Herein, a series of simulations using different types of non-linear oscillator networks (i.e., regular, small-world, scale-free, random) with a musculoskeletal model (i.e., a snake-like robot) as a physical body are conducted to understand how the chaotic itinerancy of bodily behavior emerges from the coupled dynamics between the body and the brain. A behavior analysis (behavior clustering) and network analysis for the classified behavior are then applied. The former consists of feature vector extraction from the motions and classification of the movement patterns that emerged from the coupled dynamics. The network structures behind the classified movement patterns are revealed by estimating the "information networks" different from the given non-linear oscillator networks based on the transfer entropy which finds the information flow among neurons. The experimental results show that: (1) the number of movement patterns and their duration depend on the sensor ratio to control the balance of strength between the body and the brain dynamics and on the type of the given non-linear oscillator networks; and (2) two kinds of information networks are found behind two kinds movement patterns with different durations by utilizing the complex network measures, clustering coefficient and the shortest path length with a negative and a positive relationship with the duration periods of movement patterns. The current results seem promising for a future extension of the method to a more complicated body and environment. Several requirements are also discussed.

Non-linear regime shifts in Holocene Asian monsoon variability: potential impacts on cultural change and migratory patterns

NASA Astrophysics Data System (ADS)

Donges, J. F.; Donner, R. V.; Marwan, N.; Breitenbach, S. F. M.; Rehfeld, K.; Kurths, J.

2015-05-01

The Asian monsoon system is an important tipping element in Earth's climate with a large impact on human societies in the past and present. In light of the potentially severe impacts of present and future anthropogenic climate change on Asian hydrology, it is vital to understand the forcing mechanisms of past climatic regime shifts in the Asian monsoon domain. Here we use novel recurrence network analysis techniques for detecting episodes with pronounced non-linear changes in Holocene Asian monsoon dynamics recorded in speleothems from caves distributed throughout the major branches of the Asian monsoon system. A newly developed multi-proxy methodology explicitly considers dating uncertainties with the COPRA (COnstructing Proxy Records from Age models) approach and allows for detection of continental-scale regime shifts in the complexity of monsoon dynamics. Several epochs are characterised by non-linear regime shifts in Asian monsoon variability, including the periods around 8.5-7.9, 5.7-5.0, 4.1-3.7, and 3.0-2.4 ka BP. The timing of these regime shifts is consistent with known episodes of Holocene rapid climate change (RCC) and high-latitude Bond events. Additionally, we observe a previously rarely reported non-linear regime shift around 7.3 ka BP, a timing that matches the typical 1.0-1.5 ky return intervals of Bond events. A detailed review of previously suggested links between Holocene climatic changes in the Asian monsoon domain and the archaeological record indicates that, in addition to previously considered longer-term changes in mean monsoon intensity and other climatic parameters, regime shifts in monsoon complexity might have played an important role as drivers of migration, pronounced cultural changes, and the collapse of ancient human societies.

Complex nonlinear autonomic nervous system modulation link cardiac autonomic neuropathy and peripheral vascular disease.

PubMed

Khalaf, Kinda; Jelinek, Herbert F; Robinson, Caroline; Cornforth, David J; Tarvainen, Mika P; Al-Aubaidy, Hayder

2015-01-01

Physiological interactions are abundant within, and between, body systems. These interactions may evolve into discrete states during pathophysiological processes resulting from common mechanisms. An association between arterial stenosis, identified by low ankle-brachial pressure index (ABPI) and cardiovascular disease (CVD) as been reported. Whether an association between vascular calcification-characterized by high ABPI and a different pathophysiology-is similarly associated with CVD, has not been established. The current study aims to investigate the association between ABPI, and cardiac rhythm, as an indicator of cardiovascular health and functionality, utilizing heart rate variability (HRV). Two hundred and thirty six patients underwent ABPI assessment. Standard time and frequency domain, and non-linear HRV measures were determined from 5-min electrocardiogram. ABPI data were divided into normal (n = 101), low (n = 67) and high (n = 66) and compared to HRV measures.(DFAα1 and SampEn were significantly different between the low ABPI, high ABPI and control groups (p < 0.05). A possible coupling between arterial stenosis and vascular calcification with decreased and increased HRV respectively was observed. Our results suggest a model for interpreting the relationship between vascular pathophysiology and cardiac rhythm. The cardiovascular system may be viewed as a complex system comprising a number of interacting subsystems. These cardiac and vascular subsystems/networks may be coupled and undergo transitions in response to internal or external perturbations. From a clinical perspective, the significantly increased sample entropy compared to the normal ABPI group and the decreased and increased complex correlation properties measured by DFA for the low and high ABPI groups respectively, may be useful indicators that a more holistic treatment approach in line with this more complex clinical picture is required.

Precision pharmacology for Alzheimer's disease.

PubMed

Hampel, Harald; Vergallo, Andrea; Aguilar, Lisi Flores; Benda, Norbert; Broich, Karl; Cuello, A Claudio; Cummings, Jeffrey; Dubois, Bruno; Federoff, Howard J; Fiandaca, Massimo; Genthon, Remy; Haberkamp, Marion; Karran, Eric; Mapstone, Mark; Perry, George; Schneider, Lon S; Welikovitch, Lindsay A; Woodcock, Janet; Baldacci, Filippo; Lista, Simone

2018-04-01

The complex multifactorial nature of polygenic Alzheimer's disease (AD) presents significant challenges for drug development. AD pathophysiology is progressing in a non-linear dynamic fashion across multiple systems levels - from molecules to organ systems - and through adaptation, to compensation, and decompensation to systems failure. Adaptation and compensation maintain homeostasis: a dynamic equilibrium resulting from the dynamic non-linear interaction between genome, epigenome, and environment. An individual vulnerability to stressors exists on the basis of individual triggers, drivers, and thresholds accounting for the initiation and failure of adaptive and compensatory responses. Consequently, the distinct pattern of AD pathophysiology in space and time must be investigated on the basis of the individual biological makeup. This requires the implementation of systems biology and neurophysiology to facilitate Precision Medicine (PM) and Precision Pharmacology (PP). The regulation of several processes at multiple levels of complexity from gene expression to cellular cycle to tissue repair and system-wide network activation has different time delays (temporal scale) according to the affected systems (spatial scale). The initial failure might originate and occur at every level potentially affecting the whole dynamic interrelated systems within an organism. Unraveling the spatial and temporal dynamics of non-linear pathophysiological mechanisms across the continuum of hierarchical self-organized systems levels and from systems homeostasis to systems failure is key to understand AD. Measuring and, possibly, controlling space- and time-scaled adaptive and compensatory responses occurring during AD will represent a crucial step to achieve the capacity to substantially modify the disease course and progression at the best suitable timepoints, thus counteracting disrupting critical pathophysiological inputs. This approach will provide the conceptual basis for effective disease-modifying pathway-based targeted therapies. PP is based on an exploratory and integrative strategy to complex diseases such as brain proteinopathies including AD, aimed at identifying simultaneous aberrant molecular pathways and predicting their temporal impact on the systems levels. The depiction of pathway-based molecular signatures of complex diseases contributes to the accurate and mechanistic stratification of distinct subcohorts of individuals at the earliest compensatory stage when treatment intervention may reverse, stop, or delay the disease. In addition, individualized drug selection may optimize treatment safety by decreasing risk and amplitude of side effects and adverse reactions. From a methodological point of view, comprehensive "omics"-based biomarkers will guide the exploration of spatio-temporal systems-wide morpho-functional shifts along the continuum of AD pathophysiology, from adaptation to irreversible failure. The Alzheimer Precision Medicine Initiative (APMI) and the APMI cohort program (APMI-CP) have commenced to facilitate a paradigm shift towards effective drug discovery and development in AD. Copyright © 2018 Elsevier Ltd. All rights reserved.

One-dimensional optical wave turbulence: Experiment and theory

NASA Astrophysics Data System (ADS)

Laurie, Jason; Bortolozzo, Umberto; Nazarenko, Sergey; Residori, Stefania

2012-05-01

We present a review of the latest developments in one-dimensional (1D) optical wave turbulence (OWT). Based on an original experimental setup that allows for the implementation of 1D OWT, we are able to show that an inverse cascade occurs through the spontaneous evolution of the nonlinear field up to the point when modulational instability leads to soliton formation. After solitons are formed, further interaction of the solitons among themselves and with incoherent waves leads to a final condensate state dominated by a single strong soliton. Motivated by the observations, we develop a theoretical description, showing that the inverse cascade develops through six-wave interaction, and that this is the basic mechanism of nonlinear wave coupling for 1D OWT. We describe theory, numerics and experimental observations while trying to incorporate all the different aspects into a consistent context. The experimental system is described by two coupled nonlinear equations, which we explore within two wave limits allowing for the expression of the evolution of the complex amplitude in a single dynamical equation. The long-wave limit corresponds to waves with wave numbers smaller than the electrical coherence length of the liquid crystal, and the opposite limit, when wave numbers are larger. We show that both of these systems are of a dual cascade type, analogous to two-dimensional (2D) turbulence, which can be described by wave turbulence (WT) theory, and conclude that the cascades are induced by a six-wave resonant interaction process. WT theory predicts several stationary solutions (non-equilibrium and thermodynamic) to both the long- and short-wave systems, and we investigate the necessary conditions required for their realization. Interestingly, the long-wave system is close to the integrable 1D nonlinear Schrödinger equation (NLSE) (which contains exact nonlinear soliton solutions), and as a result during the inverse cascade, nonlinearity of the system at low wave numbers becomes strong. Subsequently, due to the focusing nature of the nonlinearity, this leads to modulational instability (MI) of the condensate and the formation of solitons. Finally, with the aid of the probability density function (PDF) description of WT theory, we explain the coexistence and mutual interactions between solitons and the weakly nonlinear random wave background in the form of a wave turbulence life cycle (WTLC).

Embracing chaos and complexity: a quantum change for public health.

PubMed

Resnicow, Kenneth; Page, Scott E

2008-08-01

Public health research and practice have been guided by a cognitive, rational paradigm where inputs produce linear, predictable changes in outputs. However, the conceptual and statistical assumptions underlying this paradigm may be flawed. In particular, this perspective does not adequately account for nonlinear and quantum influences on human behavior. We propose that health behavior change is better understood through the lens of chaos theory and complex adaptive systems. Key relevant principles include that behavior change (1) is often a quantum event; (2) can resemble a chaotic process that is sensitive to initial conditions, highly variable, and difficult to predict; and (3) occurs within a complex adaptive system with multiple components, where results are often greater than the sum of their parts.

Neural network fusion capabilities for efficient implementation of tracking algorithms

NASA Astrophysics Data System (ADS)

Sundareshan, Malur K.; Amoozegar, Farid

1996-05-01

The ability to efficiently fuse information of different forms for facilitating intelligent decision-making is one of the major capabilities of trained multilayer neural networks that is being recognized int eh recent times. While development of innovative adaptive control algorithms for nonlinear dynamical plants which attempt to exploit these capabilities seems to be more popular, a corresponding development of nonlinear estimation algorithms using these approaches, particularly for application in target surveillance and guidance operations, has not received similar attention. In this paper we describe the capabilities and functionality of neural network algorithms for data fusion and implementation of nonlinear tracking filters. For a discussion of details and for serving as a vehicle for quantitative performance evaluations, the illustrative case of estimating the position and velocity of surveillance targets is considered. Efficient target tracking algorithms that can utilize data from a host of sensing modalities and are capable of reliably tracking even uncooperative targets executing fast and complex maneuvers are of interest in a number of applications. The primary motivation for employing neural networks in these applications comes form the efficiency with which more features extracted from different sensor measurements can be utilized as inputs for estimating target maneuvers. Such an approach results in an overall nonlinear tracking filter which has several advantages over the popular efforts at designing nonlinear estimation algorithms for tracking applications, the principle one being the reduction of mathematical and computational complexities. A system architecture that efficiently integrates the processing capabilities of a trained multilayer neural net with the tracking performance of a Kalman filter is described in this paper.

Development of a Nonlinear Probability of Collision Tool for the Earth Observing System

NASA Technical Reports Server (NTRS)

McKinley, David P.

2006-01-01

The Earth Observing System (EOS) spacecraft Terra, Aqua, and Aura fly in constellation with several other spacecraft in 705-kilometer mean altitude sun-synchronous orbits. All three spacecraft are operated by the Earth Science Mission Operations (ESMO) Project at Goddard Space Flight Center (GSFC). In 2004, the ESMO project began assessing the probability of collision of the EOS spacecraft with other space objects. In addition to conjunctions with high relative velocities, the collision assessment method for the EOS spacecraft must address conjunctions with low relative velocities during potential collisions between constellation members. Probability of Collision algorithms that are based on assumptions of high relative velocities and linear relative trajectories are not suitable for these situations; therefore an algorithm for handling the nonlinear relative trajectories was developed. This paper describes this algorithm and presents results from its validation for operational use. The probability of collision is typically calculated by integrating a Gaussian probability distribution over the volume swept out by a sphere representing the size of the space objects involved in the conjunction. This sphere is defined as the Hard Body Radius. With the assumption of linear relative trajectories, this volume is a cylinder, which translates into simple limits of integration for the probability calculation. For the case of nonlinear relative trajectories, the volume becomes a complex geometry. However, with an appropriate choice of coordinate systems, the new algorithm breaks down the complex geometry into a series of simple cylinders that have simple limits of integration. This nonlinear algorithm will be discussed in detail in the paper. The nonlinear Probability of Collision algorithm was first verified by showing that, when used in high relative velocity cases, it yields similar answers to existing high relative velocity linear relative trajectory algorithms. The comparison with the existing high velocity/linear theory will also be used to determine at what relative velocity the analysis should use the new nonlinear theory in place of the existing linear theory. The nonlinear algorithm was also compared to a known exact solution for the probability of collision between two objects when the relative motion is strictly circular and the error covariance is spherically symmetric. Figure I shows preliminary results from this comparison by plotting the probabilities calculated from the new algorithm and those from the exact solution versus the Hard Body Radius to Covariance ratio. These results show about 5% error when the Hard Body Radius is equal to one half the spherical covariance magnitude. The algorithm was then combined with a high fidelity orbit state and error covariance propagator into a useful tool for analyzing low relative velocity nonlinear relative trajectories. The high fidelity propagator is capable of using atmospheric drag, central body gravitational, solar radiation, and third body forces to provide accurate prediction of the relative trajectories and covariance evolution. The covariance propagator also includes a process noise model to ensure realistic evolutions of the error covariance. This paper will describe the integration of the nonlinear probability algorithm and the propagators into a useful collision assessment tool. Finally, a hypothetical case study involving a low relative velocity conjunction between members of the Earth Observation System constellation will be presented.

Salient features of solitary waves in dusty plasma under the influence of Coriolis force

DOE Office of Scientific and Technical Information (OSTI.GOV)

Das, G. C.; Nag, Apratim; Department of Physics, G. C. College, Silchar-788004

The main interest is to study the nonlinear acoustic wave in rotating dusty plasma augmented through the derivation of a modified Sagdeev potential equation. Small rotation causes the interaction of Coriolis force in the dynamical system, and leads to the complexity in the derivation of the nonlinear wave equation. As a result, the finding of solitary wave propagation in dusty plasma ought to be of merit. However, the nonlinear wave equation has been successfully solved by the use of the hyperbolic method. Main emphasis has been given to the changes on the evolution and propagation of soliton, and the variationmore » caused by the dusty plasma constituents as well as by the Coriolis force have been highlighted. Some interesting nonlinear wave behavior has been found which can be elaborately studied for the interest of laboratory and space plasmas. Further, to support the theoretical investigations, numeric plasma parameters have been taken for finding the inherent features of solitons.« less

Multispectral Image Compression for Improvement of Colorimetric and Spectral Reproducibility by Nonlinear Spectral Transform

NASA Astrophysics Data System (ADS)

Yu, Shanshan; Murakami, Yuri; Obi, Takashi; Yamaguchi, Masahiro; Ohyama, Nagaaki

2006-09-01

The article proposes a multispectral image compression scheme using nonlinear spectral transform for better colorimetric and spectral reproducibility. In the method, we show the reduction of colorimetric error under a defined viewing illuminant and also that spectral accuracy can be improved simultaneously using a nonlinear spectral transform called Labplus, which takes into account the nonlinearity of human color vision. Moreover, we show that the addition of diagonal matrices to Labplus can further preserve the spectral accuracy and has a generalized effect of improving the colorimetric accuracy under other viewing illuminants than the defined one. Finally, we discuss the usage of the first-order Markov model to form the analysis vectors for the higher order channels in Labplus to reduce the computational complexity. We implement a multispectral image compression system that integrates Labplus with JPEG2000 for high colorimetric and spectral reproducibility. Experimental results for a 16-band multispectral image show the effectiveness of the proposed scheme.

Hypersonic entry vehicle state estimation using nonlinearity-based adaptive cubature Kalman filters

NASA Astrophysics Data System (ADS)

Sun, Tao; Xin, Ming

2017-05-01

Guidance, navigation, and control of a hypersonic vehicle landing on the Mars rely on precise state feedback information, which is obtained from state estimation. The high uncertainty and nonlinearity of the entry dynamics make the estimation a very challenging problem. In this paper, a new adaptive cubature Kalman filter is proposed for state trajectory estimation of a hypersonic entry vehicle. This new adaptive estimation strategy is based on the measure of nonlinearity of the stochastic system. According to the severity of nonlinearity along the trajectory, the high degree cubature rule or the conventional third degree cubature rule is adaptively used in the cubature Kalman filter. This strategy has the benefit of attaining higher estimation accuracy only when necessary without causing excessive computation load. The simulation results demonstrate that the proposed adaptive filter exhibits better performance than the conventional third-degree cubature Kalman filter while maintaining the same performance as the uniform high degree cubature Kalman filter but with lower computation complexity.

Inferring nonlinear gene regulatory networks from gene expression data based on distance correlation.

PubMed

Guo, Xiaobo; Zhang, Ye; Hu, Wenhao; Tan, Haizhu; Wang, Xueqin

2014-01-01

Nonlinear dependence is general in regulation mechanism of gene regulatory networks (GRNs). It is vital to properly measure or test nonlinear dependence from real data for reconstructing GRNs and understanding the complex regulatory mechanisms within the cellular system. A recently developed measurement called the distance correlation (DC) has been shown powerful and computationally effective in nonlinear dependence for many situations. In this work, we incorporate the DC into inferring GRNs from the gene expression data without any underling distribution assumptions. We propose three DC-based GRNs inference algorithms: CLR-DC, MRNET-DC and REL-DC, and then compare them with the mutual information (MI)-based algorithms by analyzing two simulated data: benchmark GRNs from the DREAM challenge and GRNs generated by SynTReN network generator, and an experimentally determined SOS DNA repair network in Escherichia coli. According to both the receiver operator characteristic (ROC) curve and the precision-recall (PR) curve, our proposed algorithms significantly outperform the MI-based algorithms in GRNs inference.

Inferring Nonlinear Gene Regulatory Networks from Gene Expression Data Based on Distance Correlation

PubMed Central

Guo, Xiaobo; Zhang, Ye; Hu, Wenhao; Tan, Haizhu; Wang, Xueqin

2014-01-01

Nonlinear dependence is general in regulation mechanism of gene regulatory networks (GRNs). It is vital to properly measure or test nonlinear dependence from real data for reconstructing GRNs and understanding the complex regulatory mechanisms within the cellular system. A recently developed measurement called the distance correlation (DC) has been shown powerful and computationally effective in nonlinear dependence for many situations. In this work, we incorporate the DC into inferring GRNs from the gene expression data without any underling distribution assumptions. We propose three DC-based GRNs inference algorithms: CLR-DC, MRNET-DC and REL-DC, and then compare them with the mutual information (MI)-based algorithms by analyzing two simulated data: benchmark GRNs from the DREAM challenge and GRNs generated by SynTReN network generator, and an experimentally determined SOS DNA repair network in Escherichia coli. According to both the receiver operator characteristic (ROC) curve and the precision-recall (PR) curve, our proposed algorithms significantly outperform the MI-based algorithms in GRNs inference. PMID:24551058

Penalized Nonlinear Least Squares Estimation of Time-Varying Parameters in Ordinary Differential Equations

PubMed Central

Cao, Jiguo; Huang, Jianhua Z.; Wu, Hulin

2012-01-01

Ordinary differential equations (ODEs) are widely used in biomedical research and other scientific areas to model complex dynamic systems. It is an important statistical problem to estimate parameters in ODEs from noisy observations. In this article we propose a method for estimating the time-varying coefficients in an ODE. Our method is a variation of the nonlinear least squares where penalized splines are used to model the functional parameters and the ODE solutions are approximated also using splines. We resort to the implicit function theorem to deal with the nonlinear least squares objective function that is only defined implicitly. The proposed penalized nonlinear least squares method is applied to estimate a HIV dynamic model from a real dataset. Monte Carlo simulations show that the new method can provide much more accurate estimates of functional parameters than the existing two-step local polynomial method which relies on estimation of the derivatives of the state function. Supplemental materials for the article are available online. PMID:23155351

An impulsive receptance technique for the time domain computation of the vibration of a whole aero-engine model with nonlinear bearings

NASA Astrophysics Data System (ADS)

Hai, Pham Minh; Bonello, Philip

2008-12-01

The direct study of the vibration of real engine structures with nonlinear bearings, particularly aero-engines, has been severely limited by the fact that current nonlinear computational techniques are not well-suited for complex large-order systems. This paper introduces a novel implicit "impulsive receptance method" (IRM) for the time domain analysis of such structures. The IRM's computational efficiency is largely immune to the number of modes used and dependent only on the number of nonlinear elements. This means that, apart from retaining numerical accuracy, a much more physically accurate solution is achievable within a short timeframe. Simulation tests on a realistically sized representative twin-spool aero-engine showed that the new method was around 40 times faster than a conventional implicit integration scheme. Preliminary results for a given rotor unbalance distribution revealed the varying degree of journal lift, orbit size and shape at the example engine's squeeze-film damper bearings, and the effect of end-sealing at these bearings.

Supratransmission in a metastable modular metastructure for tunable non-reciprocal wave transmission

NASA Astrophysics Data System (ADS)

Wu, Zhen; Wang, K. W.

2018-03-01

In this research, we numerically and analytically investigate the nonlinear energy transmission phenomenon in a metastable modular metastructure. Numerical studies on a 1D metastable chain provide clear evidence that when driving frequency is within the stopband of the periodic structure, there exists a threshold for the driving amplitude, above which sudden increase in the energy transmission can be observed. This onset of transmission is due to nonlinear instability and is known as supratransmission. We discover that due to spatial asymmetry of strategically configured constituents, such transmission thresholds are considerably different when structure is excited from different ends and this discrepancy creates a region of non-reciprocal energy transmission. We demonstrate that when the loss of stability is due to saddlenode bifurcation, the transmission threshold can be predicted analytically using a localized nonlinear-linear system model, and analyzed via combining harmonic balancing and transfer matrix methods. These investigations elucidate the rich and complex dynamics achievable by nonlinearity and metastabilities, and provide synthesize tools for tunable bandgaps and non-reciprocal wave transmissions.

Method and system for knowledge discovery using non-linear statistical analysis and a 1st and 2nd tier computer program

DOEpatents

Hively, Lee M [Philadelphia, TN

2011-07-12

The invention relates to a method and apparatus for simultaneously processing different sources of test data into informational data and then processing different categories of informational data into knowledge-based data. The knowledge-based data can then be communicated between nodes in a system of multiple computers according to rules for a type of complex, hierarchical computer system modeled on a human brain.

Poverty, Disease, and the Ecology of Complex Systems

PubMed Central

Pluciński, Mateusz M.; Murray, Megan B.; Farmer, Paul E.; Barrett, Christopher B.; Keenan, Donald C.

2014-01-01

Understanding why some human populations remain persistently poor remains a significant challenge for both the social and natural sciences. The extremely poor are generally reliant on their immediate natural resource base for subsistence and suffer high rates of mortality due to parasitic and infectious diseases. Economists have developed a range of models to explain persistent poverty, often characterized as poverty traps, but these rarely account for complex biophysical processes. In this Essay, we argue that by coupling insights from ecology and economics, we can begin to model and understand the complex dynamics that underlie the generation and maintenance of poverty traps, which can then be used to inform analyses and possible intervention policies. To illustrate the utility of this approach, we present a simple coupled model of infectious diseases and economic growth, where poverty traps emerge from nonlinear relationships determined by the number of pathogens in the system. These nonlinearities are comparable to those often incorporated into poverty trap models in the economics literature, but, importantly, here the mechanism is anchored in core ecological principles. Coupled models of this sort could be usefully developed in many economically important biophysical systems—such as agriculture, fisheries, nutrition, and land use change—to serve as foundations for deeper explorations of how fundamental ecological processes influence structural poverty and economic development. PMID:24690902

Multiscale high-order/low-order (HOLO) algorithms and applications

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chacon, Luis; Chen, Guangye; Knoll, Dana Alan

Here, we review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. Themore » HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.« less

Multiscale high-order/low-order (HOLO) algorithms and applications

DOE PAGES

Chacon, Luis; Chen, Guangye; Knoll, Dana Alan; ...

2016-11-11

Here, we review the state of the art in the formulation, implementation, and performance of so-called high-order/low-order (HOLO) algorithms for challenging multiscale problems. HOLO algorithms attempt to couple one or several high-complexity physical models (the high-order model, HO) with low-complexity ones (the low-order model, LO). The primary goal of HOLO algorithms is to achieve nonlinear convergence between HO and LO components while minimizing memory footprint and managing the computational complexity in a practical manner. Key to the HOLO approach is the use of the LO representations to address temporal stiffness, effectively accelerating the convergence of the HO/LO coupled system. Themore » HOLO approach is broadly underpinned by the concept of nonlinear elimination, which enables segregation of the HO and LO components in ways that can effectively use heterogeneous architectures. The accuracy and efficiency benefits of HOLO algorithms are demonstrated with specific applications to radiation transport, gas dynamics, plasmas (both Eulerian and Lagrangian formulations), and ocean modeling. Across this broad application spectrum, HOLO algorithms achieve significant accuracy improvements at a fraction of the cost compared to conventional approaches. It follows that HOLO algorithms hold significant potential for high-fidelity system scale multiscale simulations leveraging exascale computing.« less

Nonlinear dynamics of cardiovascular ageing

PubMed Central

Shiogai, Y.; Stefanovska, A.; McClintock, P.V.E.

2010-01-01

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time–frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing. PMID:20396667

Nonlinear dynamics of cardiovascular ageing

NASA Astrophysics Data System (ADS)

Shiogai, Y.; Stefanovska, A.; McClintock, P. V. E.

2010-03-01

The application of methods drawn from nonlinear and stochastic dynamics to the analysis of cardiovascular time series is reviewed, with particular reference to the identification of changes associated with ageing. The natural variability of the heart rate (HRV) is considered in detail, including the respiratory sinus arrhythmia (RSA) corresponding to modulation of the instantaneous cardiac frequency by the rhythm of respiration. HRV has been intensively studied using traditional spectral analyses, e.g. by Fourier transform or autoregressive methods, and, because of its complexity, has been used as a paradigm for testing several proposed new methods of complexity analysis. These methods are reviewed. The application of time-frequency methods to HRV is considered, including in particular the wavelet transform which can resolve the time-dependent spectral content of HRV. Attention is focused on the cardio-respiratory interaction by introduction of the respiratory frequency variability signal (RFV), which can be acquired simultaneously with HRV by use of a respiratory effort transducer. Current methods for the analysis of interacting oscillators are reviewed and applied to cardio-respiratory data, including those for the quantification of synchronization and direction of coupling. These reveal the effect of ageing on the cardio-respiratory interaction through changes in the mutual modulation of the instantaneous cardiac and respiratory frequencies. Analyses of blood flow signals recorded with laser Doppler flowmetry are reviewed and related to the current understanding of how endothelial-dependent oscillations evolve with age: the inner lining of the vessels (the endothelium) is shown to be of crucial importance to the emerging picture. It is concluded that analyses of the complex and nonlinear dynamics of the cardiovascular system can illuminate the mechanisms of blood circulation, and that the heart, the lungs and the vascular system function as a single entity in dynamical terms. Clear evidence is found for dynamical ageing.

Agent-based modeling of endotoxin-induced acute inflammatory response in human blood leukocytes.

PubMed

Dong, Xu; Foteinou, Panagiota T; Calvano, Steven E; Lowry, Stephen F; Androulakis, Ioannis P

2010-02-18

Inflammation is a highly complex biological response evoked by many stimuli. A persistent challenge in modeling this dynamic process has been the (nonlinear) nature of the response that precludes the single-variable assumption. Systems-based approaches offer a promising possibility for understanding inflammation in its homeostatic context. In order to study the underlying complexity of the acute inflammatory response, an agent-based framework is developed that models the emerging host response as the outcome of orchestrated interactions associated with intricate signaling cascades and intercellular immune system interactions. An agent-based modeling (ABM) framework is proposed to study the nonlinear dynamics of acute human inflammation. The model is implemented using NetLogo software. Interacting agents involve either inflammation-specific molecules or cells essential for the propagation of the inflammatory reaction across the system. Spatial orientation of molecule interactions involved in signaling cascades coupled with the cellular heterogeneity are further taken into account. The proposed in silico model is evaluated through its ability to successfully reproduce a self-limited inflammatory response as well as a series of scenarios indicative of the nonlinear dynamics of the response. Such scenarios involve either a persistent (non)infectious response or innate immune tolerance and potentiation effects followed by perturbations in intracellular signaling molecules and cascades. The ABM framework developed in this study provides insight on the stochastic interactions of the mediators involved in the propagation of endotoxin signaling at the cellular response level. The simulation results are in accordance with our prior research effort associated with the development of deterministic human inflammation models that include transcriptional dynamics, signaling, and physiological components. The hypothetical scenarios explored in this study would potentially improve our understanding of how manipulating the behavior of the molecular species could manifest into emergent behavior of the overall system.

Ecosystems and the Biosphere as Complex Adaptive Systems

NASA Technical Reports Server (NTRS)

Levin, Simon A.

1998-01-01

Ecosystems are prototypical examples of complex adaptive systems, in which patterns at higher levels emerge from localized interactions and selection processes acting at lower levels. An essential aspect of such systems is nonlinearity, leading to historical dependency and multiple possible outcomes of dynamics. Given this, it is essential to determine the degree to which system features are determined by environmental conditions, and the degree to which they are the result of self-organization. Furthermore, given the multiple levels at which dynamics become apparent and at which selection can act, central issues relate to how evolution shapes ecosystems properties, and whether ecosystems become buffered to changes (more resilient) over their ecological and evolutionary development or proceed to critical states and the edge of chaos.

Archetypes for Organisational Safety

NASA Technical Reports Server (NTRS)

Marais, Karen; Leveson, Nancy G.

2003-01-01

We propose a framework using system dynamics to model the dynamic behavior of organizations in accident analysis. Most current accident analysis techniques are event-based and do not adequately capture the dynamic complexity and non-linear interactions that characterize accidents in complex systems. In this paper we propose a set of system safety archetypes that model common safety culture flaws in organizations, i.e., the dynamic behaviour of organizations that often leads to accidents. As accident analysis and investigation tools, the archetypes can be used to develop dynamic models that describe the systemic and organizational factors contributing to the accident. The archetypes help clarify why safety-related decisions do not always result in the desired behavior, and how independent decisions in different parts of the organization can combine to impact safety.