Numerical Solutions of the Nonlinear Fractional-Order Brusselator System by Bernstein Polynomials

PubMed Central

Khan, Rahmat Ali; Tajadodi, Haleh; Johnston, Sarah Jane

2014-01-01

In this paper we propose the Bernstein polynomials to achieve the numerical solutions of nonlinear fractional-order chaotic system known by fractional-order Brusselator system. We use operational matrices of fractional integration and multiplication of Bernstein polynomials, which turns the nonlinear fractional-order Brusselator system to a system of algebraic equations. Two illustrative examples are given in order to demonstrate the accuracy and simplicity of the proposed techniques. PMID:25485293

Image compression-encryption algorithms by combining hyper-chaotic system with discrete fractional random transform

NASA Astrophysics Data System (ADS)

Gong, Lihua; Deng, Chengzhi; Pan, Shumin; Zhou, Nanrun

2018-07-01

Based on hyper-chaotic system and discrete fractional random transform, an image compression-encryption algorithm is designed. The original image is first transformed into a spectrum by the discrete cosine transform and the resulting spectrum is compressed according to the method of spectrum cutting. The random matrix of the discrete fractional random transform is controlled by a chaotic sequence originated from the high dimensional hyper-chaotic system. Then the compressed spectrum is encrypted by the discrete fractional random transform. The order of DFrRT and the parameters of the hyper-chaotic system are the main keys of this image compression and encryption algorithm. The proposed algorithm can compress and encrypt image signal, especially can encrypt multiple images once. To achieve the compression of multiple images, the images are transformed into spectra by the discrete cosine transform, and then the spectra are incised and spliced into a composite spectrum by Zigzag scanning. Simulation results demonstrate that the proposed image compression and encryption algorithm is of high security and good compression performance.

Sliding Mode Control of Fractional-Order Delayed Memristive Chaotic System with Uncertainty and Disturbance

NASA Astrophysics Data System (ADS)

Ding, Da-Wei; Liu, Fang-Fang; Chen, Hui; Wang, Nian; Liang, Dong

2017-12-01

In this paper, a simplest fractional-order delayed memristive chaotic system is proposed in order to control the chaos behaviors via sliding mode control strategy. Firstly, we design a sliding mode control strategy for the fractional-order system with time delay to make the states of the system asymptotically stable. Then, we obtain theoretical analysis results of the control method using Lyapunov stability theorem which guarantees the asymptotic stability of the non-commensurate order and commensurate order system with and without uncertainty and an external disturbance. Finally, numerical simulations are given to verify that the proposed sliding mode control method can eliminate chaos and stabilize the fractional-order delayed memristive system in a finite time. Supported by the National Nature Science Foundation of China under Grant No. 61201227, Funding of China Scholarship Council, the Natural Science Foundation of Anhui Province under Grant No. 1208085M F93, 211 Innovation Team of Anhui University under Grant Nos. KJTD007A and KJTD001B

Chaos synchronization of uncertain chaotic systems using composite nonlinear feedback based integral sliding mode control.

PubMed

Mobayen, Saleh

2018-06-01

This paper proposes a combination of composite nonlinear feedback and integral sliding mode techniques for fast and accurate chaos synchronization of uncertain chaotic systems with Lipschitz nonlinear functions, time-varying delays and disturbances. The composite nonlinear feedback method allows accurate following of the master chaotic system and the integral sliding mode control provides invariance property which rejects the perturbations and preserves the stability of the closed-loop system. Based on the Lyapunov- Krasovskii stability theory and linear matrix inequalities, a novel sufficient condition is offered for the chaos synchronization of uncertain chaotic systems. This method not only guarantees the robustness against perturbations and time-delays, but also eliminates reaching phase and avoids chattering problem. Simulation results demonstrate that the suggested procedure leads to a great control performance. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Model-free adaptive sliding mode controller design for generalized projective synchronization of the fractional-order chaotic system via radial basis function neural networks

NASA Astrophysics Data System (ADS)

Wang, L. M.

2017-09-01

A novel model-free adaptive sliding mode strategy is proposed for a generalized projective synchronization (GPS) between two entirely unknown fractional-order chaotic systems subject to the external disturbances. To solve the difficulties from the little knowledge about the master-slave system and to overcome the bad effects of the external disturbances on the generalized projective synchronization, the radial basis function neural networks are used to approach the packaged unknown master system and the packaged unknown slave system (including the external disturbances). Consequently, based on the slide mode technology and the neural network theory, a model-free adaptive sliding mode controller is designed to guarantee asymptotic stability of the generalized projective synchronization error. The main contribution of this paper is that a control strategy is provided for the generalized projective synchronization between two entirely unknown fractional-order chaotic systems subject to the unknown external disturbances, and the proposed control strategy only requires that the master system has the same fractional orders as the slave system. Moreover, the proposed method allows us to achieve all kinds of generalized projective chaos synchronizations by turning the user-defined parameters onto the desired values. Simulation results show the effectiveness of the proposed method and the robustness of the controlled system.

Synchronization between uncertain nonidentical networks with quantum chaotic behavior

NASA Astrophysics Data System (ADS)

Li, Wenlin; Li, Chong; Song, Heshan

2016-11-01

Synchronization between uncertain nonidentical networks with quantum chaotic behavior is researched. The identification laws of unknown parameters in state equations of network nodes, the adaptive laws of configuration matrix elements and outer coupling strengths are determined based on Lyapunov theorem. The conditions of realizing synchronization between uncertain nonidentical networks are discussed and obtained. Further, Jaynes-Cummings model in physics are taken as the nodes of two networks and simulation results show that the synchronization performance between networks is very stable.

Sufficient conditions for asymptotic stability and stabilization of autonomous fractional order systems

NASA Astrophysics Data System (ADS)

Lenka, Bichitra Kumar; Banerjee, Soumitro

2018-03-01

We discuss the asymptotic stability of autonomous linear and nonlinear fractional order systems where the state equations contain same or different fractional orders which lie between 0 and 2. First, we use the Laplace transform method to derive some sufficient conditions which ensure asymptotic stability of linear fractional order systems. Then by using the obtained results and linearization technique, a stability theorem is presented for autonomous nonlinear fractional order system. Finally, we design a control strategy for stabilization of autonomous nonlinear fractional order systems, and apply the results to the chaotic fractional order Lorenz system in order to verify its effectiveness.

Bifurcation and chaos of a new discrete fractional-order logistic map

NASA Astrophysics Data System (ADS)

Ji, YuanDong; Lai, Li; Zhong, SuChuan; Zhang, Lu

2018-04-01

The fractional-order discrete maps with chaotic behaviors based on the theory of ;fractional difference; are proposed in recent years. In this paper, instead of using fractional difference, a new fractionalized logistic map is proposed based on the numerical algorithm of fractional differentiation definition. The bifurcation diagrams of this map with various differential orders are given by numerical simulation. The simulation results show that the fractional-order logistic map derived in this manner holds rich dynamical behaviors because of its memory effect. In addition, new types of behaviors of bifurcation and chaos are found, which are different from those of the integer-order and the previous fractional-order logistic maps.

Order or chaos in Boolean gene networks depends on the mean fraction of canalizing functions

NASA Astrophysics Data System (ADS)

Karlsson, Fredrik; Hörnquist, Michael

2007-10-01

We explore the connection between order/chaos in Boolean networks and the naturally occurring fraction of canalizing functions in such systems. This fraction turns out to give a very clear indication of whether the system possesses ordered or chaotic dynamics, as measured by Derrida plots, and also the degree of order when we compare different networks with the same number of vertices and edges. By studying also a wide distribution of indegrees in a network, we show that the mean probability of canalizing functions is a more reliable indicator of the type of dynamics for a finite network than the classical result on stability relating the bias to the mean indegree. Finally, we compare by direct simulations two biologically derived networks with networks of similar sizes but with power-law and Poisson distributions of indegrees, respectively. The biologically motivated networks are not more ordered than the latter, and in one case the biological network is even chaotic while the others are not.

Chaos in a Fractional Order Chua System

NASA Technical Reports Server (NTRS)

Lorenzo, Carl F.; Hartley, Tom T.; Qammar, Helen Killory

1996-01-01

This report studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. Varying the total system order incrementally from 2.6 to 3.7 demonstrates that systems of 'order' less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition of order which can no longer be considered only by the total number of differentiations or by the highest power of the Laplace variable.

Image encryption technique based on new two-dimensional fractional-order discrete chaotic map and Menezes–Vanstone elliptic curve cryptosystem

NASA Astrophysics Data System (ADS)

Liu, Zeyu; Xia, Tiecheng; Wang, Jinbo

2018-03-01

We propose a new fractional two-dimensional triangle function combination discrete chaotic map (2D-TFCDM) with the discrete fractional difference. Moreover, the chaos behaviors of the proposed map are observed and the bifurcation diagrams, the largest Lyapunov exponent plot, and the phase portraits are derived, respectively. Finally, with the secret keys generated by Menezes–Vanstone elliptic curve cryptosystem, we apply the discrete fractional map into color image encryption. After that, the image encryption algorithm is analyzed in four aspects and the result indicates that the proposed algorithm is more superior than the other algorithms. Project supported by the National Natural Science Foundation of China (Grant Nos. 61072147 and 11271008).

A semi-analytical method for the computation of the Lyapunov exponents of fractional-order systems

NASA Astrophysics Data System (ADS)

Caponetto, Riccardo; Fazzino, Stefano

2013-01-01

Fractional-order differential equations are interesting for their applications in the construction of mathematical models in finance, materials science or diffusion. In this paper, an application of a well known transformation technique, Differential Transform Method (DTM), to the area of fractional differential equation is employed for calculating Lyapunov exponents of fractional order systems. It is known that the Lyapunov exponents, first introduced by Oseledec, play a crucial role in characterizing the behaviour of dynamical systems. They can be used to analyze the sensitive dependence on initial conditions and the presence of chaotic attractors. The results reveal that the proposed method is very effective and simple and leads to accurate, approximately convergent solutions.

Performance and robustness of optimal fractional fuzzy PID controllers for pitch control of a wind turbine using chaotic optimization algorithms.

PubMed

Asgharnia, Amirhossein; Shahnazi, Reza; Jamali, Ali

2018-05-11

The most studied controller for pitch control of wind turbines is proportional-integral-derivative (PID) controller. However, due to uncertainties in wind turbine modeling and wind speed profiles, the need for more effective controllers is inevitable. On the other hand, the parameters of PID controller usually are unknown and should be selected by the designer which is neither a straightforward task nor optimal. To cope with these drawbacks, in this paper, two advanced controllers called fuzzy PID (FPID) and fractional-order fuzzy PID (FOFPID) are proposed to improve the pitch control performance. Meanwhile, to find the parameters of the controllers the chaotic evolutionary optimization methods are used. Using evolutionary optimization methods not only gives us the unknown parameters of the controllers but also guarantees the optimality based on the chosen objective function. To improve the performance of the evolutionary algorithms chaotic maps are used. All the optimization procedures are applied to the 2-mass model of 5-MW wind turbine model. The proposed optimal controllers are validated using simulator FAST developed by NREL. Simulation results demonstrate that the FOFPID controller can reach to better performance and robustness while guaranteeing fewer fatigue damages in different wind speeds in comparison to FPID, fractional-order PID (FOPID) and gain-scheduling PID (GSPID) controllers. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

The synchronisation of fractional-order hyperchaos compound system

NASA Astrophysics Data System (ADS)

Noghredani, Naeimadeen; Riahi, Aminreza; Pariz, Naser; Karimpour, Ali

2018-02-01

This paper presents a new compound synchronisation scheme among four hyperchaotic memristor system with incommensurate fractional-order derivatives. First a new controller was designed based on adaptive technique to minimise the errors and guarantee compound synchronisation of four fractional-order memristor chaotic systems. According to the suitability of compound synchronisation as a reliable solution for secure communication, we then examined the application of the proposed adaptive compound synchronisation scheme in the presence of noise for secure communication. In addition, the unpredictability and complexity of the drive systems enhance the security of secure communication. The corresponding theoretical analysis and results of simulation validated the effectiveness of the proposed synchronisation scheme using MATLAB.

Chaotic Motions in the Real Fuzzy Electronic Circuits (Preprint)

DTIC Science & Technology

2012-12-01

the research field of secure communications, the original source should be blended with other complex signals. Chaotic signals are one of the good... blending of the linear system models. Consider a continuous-time nonlinear dynamic system as follows: Rule i: IF )(1 tx is ...1iM and )(txn is...Chaos Solitons Fractals, vol. 21, no. 4, pp. 957–965, 2004. 29. L. M. Tam and W. M. SiTou, “Parametric study of the fractional order Chen–Lee

A New Color Image Encryption Scheme Using CML and a Fractional-Order Chaotic System

PubMed Central

Wu, Xiangjun; Li, Yang; Kurths, Jürgen

2015-01-01

The chaos-based image cryptosystems have been widely investigated in recent years to provide real-time encryption and transmission. In this paper, a novel color image encryption algorithm by using coupled-map lattices (CML) and a fractional-order chaotic system is proposed to enhance the security and robustness of the encryption algorithms with a permutation-diffusion structure. To make the encryption procedure more confusing and complex, an image division-shuffling process is put forward, where the plain-image is first divided into four sub-images, and then the position of the pixels in the whole image is shuffled. In order to generate initial conditions and parameters of two chaotic systems, a 280-bit long external secret key is employed. The key space analysis, various statistical analysis, information entropy analysis, differential analysis and key sensitivity analysis are introduced to test the security of the new image encryption algorithm. The cryptosystem speed is analyzed and tested as well. Experimental results confirm that, in comparison to other image encryption schemes, the new algorithm has higher security and is fast for practical image encryption. Moreover, an extensive tolerance analysis of some common image processing operations such as noise adding, cropping, JPEG compression, rotation, brightening and darkening, has been performed on the proposed image encryption technique. Corresponding results reveal that the proposed image encryption method has good robustness against some image processing operations and geometric attacks. PMID:25826602

A fractional approach to the Fermi-Pasta-Ulam problem

NASA Astrophysics Data System (ADS)

Machado, J. A. T.

2013-09-01

This paper studies the Fermi-Pasta-Ulam problem having in mind the generalization provided by Fractional Calculus (FC). The study starts by addressing the classical formulation, based on the standard integer order differential calculus and evaluates the time and frequency responses. A first generalization to be investigated consists in the direct replacement of the springs by fractional elements of the dissipative type. It is observed that the responses settle rapidly and no relevant phenomena occur. A second approach consists of replacing the springs by a blend of energy extracting and energy inserting elements of symmetrical fractional order with amplitude modulated by quadratic terms. The numerical results reveal a response close to chaotic behaviour.

A numerical solution for a variable-order reaction-diffusion model by using fractional derivatives with non-local and non-singular kernel

NASA Astrophysics Data System (ADS)

Coronel-Escamilla, A.; Gómez-Aguilar, J. F.; Torres, L.; Escobar-Jiménez, R. F.

2018-02-01

A reaction-diffusion system can be represented by the Gray-Scott model. The reaction-diffusion dynamic is described by a pair of time and space dependent Partial Differential Equations (PDEs). In this paper, a generalization of the Gray-Scott model by using variable-order fractional differential equations is proposed. The variable-orders were set as smooth functions bounded in (0 , 1 ] and, specifically, the Liouville-Caputo and the Atangana-Baleanu-Caputo fractional derivatives were used to express the time differentiation. In order to find a numerical solution of the proposed model, the finite difference method together with the Adams method were applied. The simulations results showed the chaotic behavior of the proposed model when different variable-orders are applied.

A New Chaotic Flow with Hidden Attractor: The First Hyperjerk System with No Equilibrium

NASA Astrophysics Data System (ADS)

Ren, Shuili; Panahi, Shirin; Rajagopal, Karthikeyan; Akgul, Akif; Pham, Viet-Thanh; Jafari, Sajad

2018-02-01

Discovering unknown aspects of non-equilibrium systems with hidden strange attractors is an attractive research topic. A novel quadratic hyperjerk system is introduced in this paper. It is noteworthy that this non-equilibrium system can generate hidden chaotic attractors. The essential properties of such systems are investigated by means of equilibrium points, phase portrait, bifurcation diagram, and Lyapunov exponents. In addition, a fractional-order differential equation of this new system is presented. Moreover, an electronic circuit is also designed and implemented to verify the feasibility of the theoretical model.

Fractional order fuzzy control of hybrid power system with renewable generation using chaotic PSO.

PubMed

Pan, Indranil; Das, Saptarshi

2016-05-01

This paper investigates the operation of a hybrid power system through a novel fuzzy control scheme. The hybrid power system employs various autonomous generation systems like wind turbine, solar photovoltaic, diesel engine, fuel-cell, aqua electrolyzer etc. Other energy storage devices like the battery, flywheel and ultra-capacitor are also present in the network. A novel fractional order (FO) fuzzy control scheme is employed and its parameters are tuned with a particle swarm optimization (PSO) algorithm augmented with two chaotic maps for achieving an improved performance. This FO fuzzy controller shows better performance over the classical PID, and the integer order fuzzy PID controller in both linear and nonlinear operating regimes. The FO fuzzy controller also shows stronger robustness properties against system parameter variation and rate constraint nonlinearity, than that with the other controller structures. The robustness is a highly desirable property in such a scenario since many components of the hybrid power system may be switched on/off or may run at lower/higher power output, at different time instants. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Anti-windup adaptive PID control design for a class of uncertain chaotic systems with input saturation.

PubMed

Tahoun, A H

2017-01-01

In this paper, the stabilization problem of actuators saturation in uncertain chaotic systems is investigated via an adaptive PID control method. The PID control parameters are auto-tuned adaptively via adaptive control laws. A multi-level augmented error is designed to account for the extra terms appearing due to the use of PID and saturation. The proposed control technique uses both the state-feedback and the output-feedback methodologies. Based on Lyapunov׳s stability theory, new anti-windup adaptive controllers are proposed. Demonstrative examples with MATLAB simulations are studied. The simulation results show the efficiency of the proposed adaptive PID controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Adaptive Fractional-order Control for Synchronization of Two Coupled Neurons in the External Electrical Stimulation

PubMed Central

Mehdiabadi, M. R. Rahmani; Rouhani, E.; Mashhadi, S. K. Mousavi; Jalali, A. A.

2014-01-01

This paper addresses synchronizing two coupled chaotic FitzHugh–Nagumo (FHN) neurons with weakly gap junction under external electrical stimulation (EES). To transmit information among coupled neurons, by generalization of the integer-order FHN equations of the coupled system into the fractional-order in frequency domain using Crone approach, the behavior of each coupled neuron relies on its past behavior and the memorized system can be a better fit for the neuron response. An adaptive fractional-order controller based on the Lyaponuv stability theory was designed to synchronize two neurons electrically coupled with gap junction in EES. The proposed controller is also robust to the inevitable random noise such as disturbances of ionic channels. The simulation results demonstrate the effectiveness of the control scheme. PMID:25337373

Spatiotemporal chaos of fractional order logistic equation in nonlinear coupled lattices

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; Wang, Xing-Yuan; Liu, Li-Yan; He, Yi; Liu, Jia

2017-11-01

We investigate a new spatiotemporal dynamics with fractional order differential logistic map and spatial nonlinear coupling. The spatial nonlinear coupling features such as the higher percentage of lattices in chaotic behaviors for most of parameters and none periodic windows in bifurcation diagrams are held, which are more suitable for encryptions than the former adjacent coupled map lattices. Besides, the proposed model has new features such as the wider parameter range and wider range of state amplitude for ergodicity, which contributes a wider range of key space when applied in encryptions. The simulations and theoretical analyses are developed in this paper.

On Complete Control and Synchronization of Zhang Chaotic System with Uncertain Parameters using Adaptive Control Method

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed

2018-03-01

Chaos control and synchronization of chaotic systems is seemingly a challenging problem and has got a lot of attention in recent years due to its numerous applications in science and industry. This paper concentrates on the control and synchronization problem of the three-dimensional (3D) Zhang chaotic system. At first, an adaptive control law and a parameter estimation law are achieved for controlling the behavior of the Zhang chaotic system. Then, non-identical synchronization of Zhang chaotic system is provided with considering the Lü chaotic system as the follower system. The synchronization problem and parameters identification are achieved by introducing an adaptive control law and a parameters estimation law. Stability analysis of the proposed method is proved by the Lyapanov stability theorem. In addition, the convergence of the estimated parameters to their truly unknown values are evaluated. Finally, some numerical simulations are carried out to illustrate and to validate the effectiveness of the suggested method.

Adaptive neural output-feedback control for nonstrict-feedback time-delay fractional-order systems with output constraints and actuator nonlinearities.

PubMed

Zouari, Farouk; Ibeas, Asier; Boulkroune, Abdesselem; Cao, Jinde; Mehdi Arefi, Mohammad

2018-06-01

This study addresses the issue of the adaptive output tracking control for a category of uncertain nonstrict-feedback delayed incommensurate fractional-order systems in the presence of nonaffine structures, unmeasured pseudo-states, unknown control directions, unknown actuator nonlinearities and output constraints. Firstly, the mean value theorem and the Gaussian error function are introduced to eliminate the difficulties that arise from the nonaffine structures and the unknown actuator nonlinearities, respectively. Secondly, the immeasurable tracking error variables are suitably estimated by constructing a fractional-order linear observer. Thirdly, the neural network, the Razumikhin Lemma, the variable separation approach, and the smooth Nussbaum-type function are used to deal with the uncertain nonlinear dynamics, the unknown time-varying delays, the nonstrict feedback and the unknown control directions, respectively. Fourthly, asymmetric barrier Lyapunov functions are employed to overcome the violation of the output constraints and to tune online the parameters of the adaptive neural controller. Through rigorous analysis, it is proved that the boundedness of all variables in the closed-loop system and the semi global asymptotic tracking are ensured without transgression of the constraints. The principal contributions of this study can be summarized as follows: (1) based on Caputo's definitions and new lemmas, methods concerning the controllability, observability and stability analysis of integer-order systems are extended to fractional-order ones, (2) the output tracking objective for a relatively large class of uncertain systems is achieved with a simple controller and less tuning parameters. Finally, computer-simulation studies from the robotic field are given to demonstrate the effectiveness of the proposed controller. Copyright © 2018 Elsevier Ltd. All rights reserved.

On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system

NASA Astrophysics Data System (ADS)

Hajipour, Ahamad; Hajipour, Mojtaba; Baleanu, Dumitru

2018-05-01

This manuscript mainly focuses on the construction, dynamic analysis and control of a new fractional-order financial system. The basic dynamical behaviors of the proposed system are studied such as the equilibrium points and their stability, Lyapunov exponents, bifurcation diagrams, phase portraits of state variables and the intervals of system parameters. It is shown that the system exhibits hyperchaotic behavior for a number of system parameters and fractional-order values. To stabilize the proposed hyperchaotic fractional system with uncertain dynamics and disturbances, an efficient adaptive sliding mode controller technique is developed. Using the proposed technique, two hyperchaotic fractional-order financial systems are also synchronized. Numerical simulations are presented to verify the successful performance of the designed controllers.

Topological horseshoe analysis and field-programmable gate array implementation of a fractional-order four-wing chaotic attractor

NASA Astrophysics Data System (ADS)

Dong, En-Zeng; Wang, Zhen; Yu, Xiao; Chen, Zeng-Qiang; Wang, Zeng-Hui

2018-01-01

Not Available Project supported by the National Natural Science Foundation of China (Grant Nos. 61502340 and 61374169), the Application Base and Frontier Technology Research Project of Tianjin, China (Grant No. 15JCYBJC51800), and the South African National Research Foundation Incentive Grants (Grant No. 81705).

New numerical approximation of fractional derivative with non-local and non-singular kernel: Application to chaotic models

NASA Astrophysics Data System (ADS)

Toufik, Mekkaoui; Atangana, Abdon

2017-10-01

Recently a new concept of fractional differentiation with non-local and non-singular kernel was introduced in order to extend the limitations of the conventional Riemann-Liouville and Caputo fractional derivatives. A new numerical scheme has been developed, in this paper, for the newly established fractional differentiation. We present in general the error analysis. The new numerical scheme was applied to solve linear and non-linear fractional differential equations. We do not need a predictor-corrector to have an efficient algorithm, in this method. The comparison of approximate and exact solutions leaves no doubt believing that, the new numerical scheme is very efficient and converges toward exact solution very rapidly.

Time-delayed chameleon: Analysis, synchronization and FPGA implementation

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Jafari, Sajad; Laarem, Guessas

2017-12-01

In this paper we report a time-delayed chameleon-like chaotic system which can belong to different families of chaotic attractors depending on the choices of parameters. Such a characteristic of self-excited and hidden chaotic flows in a simple 3D system with time delay has not been reported earlier. Dynamic analysis of the proposed time-delayed systems are analysed in time-delay space and parameter space. A novel adaptive modified functional projective lag synchronization algorithm is derived for synchronizing identical time-delayed chameleon systems with uncertain parameters. The proposed time-delayed systems and the synchronization algorithm with controllers and parameter estimates are then implemented in FPGA using hardware-software co-simulation and the results are presented.

On Chaotic Behavior of Temperature Distribution in a Heat Exchanger

NASA Astrophysics Data System (ADS)

Bagyalakshmi, Morachan; Gangadharan, Saisundarakrishnan; Ganesh, Madhu

The objective of this paper is to introduce the notion of fractional derivatives in the energy equations and to study the chaotic nature of the temperature distribution in a heat exchanger with variation of temperature dependent transport properties. The governing fractional partial differential equations are transformed to a set of recurrence relations using fractional differential transform method and solved using inverse transform. The approximate analytical solution obtained by the proposed method has good agreement with the existing results.

Closed form solutions of two time fractional nonlinear wave equations

NASA Astrophysics Data System (ADS)

Akbar, M. Ali; Ali, Norhashidah Hj. Mohd.; Roy, Ripan

2018-06-01

In this article, we investigate the exact traveling wave solutions of two nonlinear time fractional wave equations. The fractional derivatives are described in the sense of conformable fractional derivatives. In addition, the traveling wave solutions are accomplished in the form of hyperbolic, trigonometric, and rational functions involving free parameters. To investigate such types of solutions, we implement the new generalized (G‧ / G) -expansion method. The extracted solutions are reliable, useful and suitable to comprehend the optimal control problems, chaotic vibrations, global and local bifurcations and resonances, furthermore, fission and fusion phenomena occur in solitons, the relativistic energy-momentum relation, scalar electrodynamics, quantum relativistic one-particle theory, electromagnetic interactions etc. The results reveal that the method is very fruitful and convenient for exploring nonlinear differential equations of fractional order treated in theoretical physics.

The structure of motion in a 4-component galaxy mass model

NASA Astrophysics Data System (ADS)

Caranicolas, N. D.

1996-03-01

We use a composite galaxy model consisting of a disk-halo, bulge, nucleus and dark-halo components in order to investigate the motion of stars in ther-z plane. It is observed that high angular momentum stars move in regular orbits. The majority of orbits are box orbits. There are also banana-like orbits. For a given value of energy, only a fraction of the low angular momentum stars — those going near the nucleus — show chaotic motion while the rest move in regular orbits. Again one observes the above two kinds of orbits. In addition to the above one can also see orbits with the characteristics of the 2/3 and 3/4 resonance. It is also shown that, in the absence of the bulge component, the area of chaotic motion in the surface of section increases, significantly. This suggests that a larger number of low angular momentum stars are in chaotic orbits in galaxies with massive nuclei and no bulge components.

Theory of chaotic orbital variations confirmed by Cretaceous geological evidence

NASA Astrophysics Data System (ADS)

Ma, Chao; Meyers, Stephen R.; Sageman, Bradley B.

2017-02-01

Variations in the Earth’s orbit and spin vector are a primary control on insolation and climate; their recognition in the geological record has revolutionized our understanding of palaeoclimate dynamics, and has catalysed improvements in the accuracy and precision of the geological timescale. Yet the secular evolution of the planetary orbits beyond 50 million years ago remains highly uncertain, and the chaotic dynamical nature of the Solar System predicted by theoretical models has yet to be rigorously confirmed by well constrained (radioisotopically calibrated and anchored) geological data. Here we present geological evidence for a chaotic resonance transition associated with interactions between the orbits of Mars and the Earth, using an integrated radioisotopic and astronomical timescale from the Cretaceous Western Interior Basin of what is now North America. This analysis confirms the predicted chaotic dynamical behaviour of the Solar System, and provides a constraint for refining numerical solutions for insolation, which will enable a more precise and accurate geological timescale to be produced.

Theory of chaotic orbital variations confirmed by Cretaceous geological evidence.

PubMed

Ma, Chao; Meyers, Stephen R; Sageman, Bradley B

2017-02-22

Variations in the Earth's orbit and spin vector are a primary control on insolation and climate; their recognition in the geological record has revolutionized our understanding of palaeoclimate dynamics, and has catalysed improvements in the accuracy and precision of the geological timescale. Yet the secular evolution of the planetary orbits beyond 50 million years ago remains highly uncertain, and the chaotic dynamical nature of the Solar System predicted by theoretical models has yet to be rigorously confirmed by well constrained (radioisotopically calibrated and anchored) geological data. Here we present geological evidence for a chaotic resonance transition associated with interactions between the orbits of Mars and the Earth, using an integrated radioisotopic and astronomical timescale from the Cretaceous Western Interior Basin of what is now North America. This analysis confirms the predicted chaotic dynamical behaviour of the Solar System, and provides a constraint for refining numerical solutions for insolation, which will enable a more precise and accurate geological timescale to be produced.

Finite-time robust control of uncertain fractional-order Hopfield neural networks via sliding mode control

NASA Astrophysics Data System (ADS)

Xi, Yangui; Yu, Yongguang; Zhang, Shuo; Hai, Xudong

2018-01-01

Not Available Project supported by the National Natural Science Foundation of China (Grant Nos. 11371049 and 61772063) and the Fundamental Research Funds for the Central Universities, China (Grant No. 2016JBM070).

Preparing to be Unprepared: Ground Force Commander Decision Making in a Volatile, Uncertain, Complex, and Ambiguous World

DTIC Science & Technology

2016-06-01

44 IV. CONCLUSION, RECOMMENDATIONS, AND FURTHER RESEARCH ...development and mental preparation. .......................................50 C. FURTHER RESEARCH ...unforgiving, chaotic environment. With that purpose in mind, my research questions are: what are the characteristics of effective GFC decision making? What

A new class of galactic discrete gamma ray sources: Chaotic winds of massive stars

NASA Technical Reports Server (NTRS)

Chen, Wan; White, Richard L.

1992-01-01

We propose a new class of galactic discrete gamma-ray sources, the chaotic, high mass-loss-rate winds from luminous early-type stars. Early-type stellar winds are highly unstable due to intrinsic line-driven instabilities, and so are permeated by numerous strong shocks. These shocks can accelerate a small fraction of thermal electrons and ions to relativistic energies via the first-order Fermi mechanism. A power-law-like photon spectrum extending from keV to above 10 MeV energies is produced by inverse Compton scattering of the extremely abundant stellar UV photons by the relativistic electrons. In addition, a typical pi(sup 0)-decay gamma-ray spectrum is generated by proton-ion interactions in the densest part of the winds.

Complete synchronization of uncertain chaotic systems via a single proportional adaptive controller: A comparative study

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

Ahmad, Israr, E-mail: iak-2000plus@yahoo.com; Saaban, Azizan Bin, E-mail: azizan.s@uum.edu.my; Ibrahim, Adyda Binti, E-mail: adyda@uum.edu.my

This paper addresses a comparative computational study on the synchronization quality, cost and converging speed for two pairs of identical chaotic and hyperchaotic systems with unknown time-varying parameters. It is assumed that the unknown time-varying parameters are bounded. Based on the Lyapunov stability theory and using the adaptive control method, a single proportional controller is proposed to achieve the goal of complete synchronizations. Accordingly, appropriate adaptive laws are designed to identify the unknown time-varying parameters. The designed control strategy is easy to implement in practice. Numerical simulations results are provided to verify the effectiveness of the proposed synchronization scheme.

Dynamic analysis with a fractional-order chaotic system for estimation of peripheral arterial disease in diabetic foot

NASA Astrophysics Data System (ADS)

Li, Chien-Ming; Du, Yi-Chun; Wu, Jian-Xing; Lin, Chia-Hung; Ho, Yueh-Ren; Chen, Tainsong

2013-08-01

Lower-extremity peripheral arterial disease (PAD) is caused by narrowing or occlusion of vessels in patients like type 2 diabetes mellitus, the elderly and smokers. Patients with PAD are mostly asymptomatic; typical early symptoms of this limb-threatening disorder are intermittent claudication and leg pain, suggesting the necessity for accurate diagnosis by invasive angiography and ankle-brachial pressure index. This index acts as a gold standard reference for PAD diagnosis and categorizes its severity into normal, low-grade and high-grade, with respective cut-off points of ≥0.9, 0.9-0.5 and <0.5. PAD can be assessed using photoplethysmography as a diagnostic screening tool, displaying changes in pulse transit time and shape, and dissimilarities of these changes between lower limbs. The present report proposed photoplethysmogram with fractional-order chaotic system to assess PAD in 14 diabetics and 11 healthy adults, with analysis of dynamic errors based on various butterfly motion patterns, and color relational analysis as classifier for pattern recognition. The results show that the classification of PAD severity among these testees was achieved with high accuracy and efficiency. This noninvasive methodology potentially provides timing and accessible feedback to patients with asymptomatic PAD and their physicians for further invasive diagnosis or strict management of risk factors to intervene in the disease progression.

Uncertain viscoelastic models with fractional order: A new spectral tau method to study the numerical simulations of the solution

NASA Astrophysics Data System (ADS)

Ahmadian, A.; Ismail, F.; Salahshour, S.; Baleanu, D.; Ghaemi, F.

2017-12-01

The analysis of the behaviors of physical phenomena is important to discover significant features of the character and the structure of mathematical models. Frequently the unknown parameters involve in the models are assumed to be unvarying over time. In reality, some of them are uncertain and implicitly depend on several factors. In this study, to consider such uncertainty in variables of the models, they are characterized based on the fuzzy notion. We propose here a new model based on fractional calculus to deal with the Kelvin-Voigt (KV) equation and non-Newtonian fluid behavior model with fuzzy parameters. A new and accurate numerical algorithm using a spectral tau technique based on the generalized fractional Legendre polynomials (GFLPs) is developed to solve those problems under uncertainty. Numerical simulations are carried out and the analysis of the results highlights the significant features of the new technique in comparison with the previous findings. A detailed error analysis is also carried out and discussed.

Using Chaotic System in Encryption

NASA Astrophysics Data System (ADS)

Findik, Oğuz; Kahramanli, Şirzat

In this paper chaotic systems and RSA encryption algorithm are combined in order to develop an encryption algorithm which accomplishes the modern standards. E.Lorenz's weather forecast' equations which are used to simulate non-linear systems are utilized to create chaotic map. This equation can be used to generate random numbers. In order to achieve up-to-date standards and use online and offline status, a new encryption technique that combines chaotic systems and RSA encryption algorithm has been developed. The combination of RSA algorithm and chaotic systems makes encryption system.

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.

Synchronization of coupled different chaotic FitzHugh-Nagumo neurons with unknown parameters under communication-direction-dependent coupling.

PubMed

Iqbal, Muhammad; Rehan, Muhammad; Khaliq, Abdul; Saeed-ur-Rehman; Hong, Keum-Shik

2014-01-01

This paper investigates the chaotic behavior and synchronization of two different coupled chaotic FitzHugh-Nagumo (FHN) neurons with unknown parameters under external electrical stimulation (EES). The coupled FHN neurons of different parameters admit unidirectional and bidirectional gap junctions in the medium between them. Dynamical properties, such as the increase in synchronization error as a consequence of the deviation of neuronal parameters for unlike neurons, the effect of difference in coupling strengths caused by the unidirectional gap junctions, and the impact of large time-delay due to separation of neurons, are studied in exploring the behavior of the coupled system. A novel integral-based nonlinear adaptive control scheme, to cope with the infeasibility of the recovery variable, for synchronization of two coupled delayed chaotic FHN neurons of different and unknown parameters under uncertain EES is derived. Further, to guarantee robust synchronization of different neurons against disturbances, the proposed control methodology is modified to achieve the uniformly ultimately bounded synchronization. The parametric estimation errors can be reduced by selecting suitable control parameters. The effectiveness of the proposed control scheme is illustrated via numerical simulations.

Chaotic electrical activity of living β-cells in the mouse pancreatic islet

NASA Astrophysics Data System (ADS)

Kanno, Takahiro; Miyano, Takaya; Tokuda, Isao; Galvanovskis, Juris; Wakui, Makoto

2007-02-01

To test for chaotic dynamics of the insulin producing β-cell and explore its biological role, we observed the action potentials with the perforated patch clamp technique, for isolated cells as well as for intact cells of the mouse pancreatic islet. The time series obtained were analyzed using nonlinear diagnostic algorithms associated with the surrogate method. The isolated cells exhibited short-term predictability and visible determinism, in the steady state response to 10 mM glucose, while the intact cells did not. In the latter case, determinism became visible after the application of a gap junction inhibitor. This tendency was enhanced by the stimulation with tolbutamide. Our observations suggest that, thanks to the integration of individual chaotic dynamics via gap junction coupling, the β-cells will lose memory of fluctuations occurring at any instant in their electrical activity more rapidly with time. This is likely to contribute to the functional stability of the islet against uncertain perturbations.

Chaotic Signal Denoising Based on Hierarchical Threshold Synchrosqueezed Wavelet Transform

NASA Astrophysics Data System (ADS)

Wang, Wen-Bo; Jing, Yun-yu; Zhao, Yan-chao; Zhang, Lian-Hua; Wang, Xiang-Li

2017-12-01

In order to overcoming the shortcoming of single threshold synchrosqueezed wavelet transform(SWT) denoising method, an adaptive hierarchical threshold SWT chaotic signal denoising method is proposed. Firstly, a new SWT threshold function is constructed based on Stein unbiased risk estimation, which is two order continuous derivable. Then, by using of the new threshold function, a threshold process based on the minimum mean square error was implemented, and the optimal estimation value of each layer threshold in SWT chaotic denoising is obtained. The experimental results of the simulating chaotic signal and measured sunspot signals show that, the proposed method can filter the noise of chaotic signal well, and the intrinsic chaotic characteristic of the original signal can be recovered very well. Compared with the EEMD denoising method and the single threshold SWT denoising method, the proposed method can obtain better denoising result for the chaotic signal.

Chaos-based partial image encryption scheme based on linear fractional and lifting wavelet transforms

NASA Astrophysics Data System (ADS)

Belazi, Akram; Abd El-Latif, Ahmed A.; Diaconu, Adrian-Viorel; Rhouma, Rhouma; Belghith, Safya

2017-01-01

In this paper, a new chaos-based partial image encryption scheme based on Substitution-boxes (S-box) constructed by chaotic system and Linear Fractional Transform (LFT) is proposed. It encrypts only the requisite parts of the sensitive information in Lifting-Wavelet Transform (LWT) frequency domain based on hybrid of chaotic maps and a new S-box. In the proposed encryption scheme, the characteristics of confusion and diffusion are accomplished in three phases: block permutation, substitution, and diffusion. Then, we used dynamic keys instead of fixed keys used in other approaches, to control the encryption process and make any attack impossible. The new S-box was constructed by mixing of chaotic map and LFT to insure the high confidentiality in the inner encryption of the proposed approach. In addition, the hybrid compound of S-box and chaotic systems strengthened the whole encryption performance and enlarged the key space required to resist the brute force attacks. Extensive experiments were conducted to evaluate the security and efficiency of the proposed approach. In comparison with previous schemes, the proposed cryptosystem scheme showed high performances and great potential for prominent prevalence in cryptographic applications.

Transition between order and chaos in a composite disk galaxy model with a massive nucleus and a dark matter halo

NASA Astrophysics Data System (ADS)

Caranicolas, Nicolaos D.; Zotos, Euaggelos E.

2013-02-01

We investigate the transition from regular to chaotic motion in a composite galaxy model with a disk-halo, a massive dense nucleus and a dark halo component. We obtain relationships connecting the critical value of the mass of the nucleus or the critical value of the angular momentum Lzc, with the mass Mh of the dark halo, where the transition from regular motion to chaos occurs. We also present 3D diagrams connecting the mass of nucleus the energy and the percentage of stars that can show chaotic motion. The fraction of the chaotic orbits observed in the (r,pr) phase plane, as a function of the mass of the dark halo is also computed. We use a semi-numerical method, that is a combination of theoretical and numerical procedure. The theoretical results obtained using the version 8.0 of the Mathematica package, while all the numerical calculations were made using a Bulirsch-Stöer FORTRAN routine in double precision. The results can be obtained in semi-numerical or numerical form and give good description for the connection of the physical quantities entering the model and the transition between regular and chaotic motion. We observe that the mass of the dark halo, the mass of the dense nucleus and the Lz component of the angular momentum, are important physical quantities, as they are linked to the regular or chaotic character of orbits in disk galaxies described by the model. Our numerical experiments suggest, that the amount of the dark matter plays an important role in disk galaxies represented by the model, as the mass of the halo affects, not only the regular or chaotic nature of motion but it is also connected with the existence of the different families of regular orbits. Comparison of the present results with earlier work is also presented.

Analytically solvable chaotic oscillator based on a first-order filter.

PubMed

Corron, Ned J; Cooper, Roy M; Blakely, Jonathan N

2016-02-01

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform for any stable infinite-impulse response filter is chaotic.

Analytically solvable chaotic oscillator based on a first-order filter

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

Corron, Ned J.; Cooper, Roy M.; Blakely, Jonathan N.

2016-02-15

A chaotic hybrid dynamical system is introduced and its analytic solution is derived. The system is described as an unstable first order filter subject to occasional switching of a set point according to a feedback rule. The system qualitatively differs from other recently studied solvable chaotic hybrid systems in that the timing of the switching is regulated by an external clock. The chaotic analytic solution is an optimal waveform for communications in noise when a resistor-capacitor-integrate-and-dump filter is used as a receiver. As such, these results provide evidence in support of a recent conjecture that the optimal communication waveform formore » any stable infinite-impulse response filter is chaotic.« less

Modeling Nucleation and Grain Growth in the Solar Nebula: Initial Progress Report

NASA Technical Reports Server (NTRS)

Nuth, Joseph A.; Paquette, J. A.; Ferguson, F. T.

2010-01-01

The primitive solar nebula was a violent and chaotic environment where high energy collisions, lightning, shocks and magnetic re-connection events rapidly vaporized some fraction of nebular dust, melted larger particles while leaving the largest grains virtually undisturbed. At the same time, some tiny grains containing very easily disturbed noble gas signatures (e.g., small, pre-solar graphite or SiC particles) never experienced this violence, yet can be found directly adjacent to much larger meteoritic components (chondrules or CAIs) that did. Additional components in the matrix of the most primitive carbonaceous chondrites and in some chondritic porous interplanetary dust particles include tiny nebular condensates, aggregates of condensates and partially annealed aggregates. Grains formed in violent transient events in the solar nebula did not come to equilibrium with their surroundings. To understand the formation and textures of these materials as well as their nebular abundances we must rely on Nucleation Theory and kinetic models of grain growth, coagulation and annealing. Such models have been very uncertain in the past: we will discuss the steps we are taking to increase their reliability.

Controller Synthesis for Periodically Forced Chaotic Systems

NASA Astrophysics Data System (ADS)

Basso, Michele; Genesio, Roberto; Giovanardi, Lorenzo

Delayed feedback controllers are an appealing tool for stabilization of periodic orbits in chaotic systems. Despite their conceptual simplicity, specific and reliable design procedures are difficult to obtain, partly also because of their inherent infinite-dimensional structure. This chapter considers the use of finite dimensional linear time invariant controllers for stabilization of periodic solutions in a general class of sinusoidally forced nonlinear systems. For such controllers — which can be interpreted as rational approximations of the delayed ones — we provide a computationally attractive synthesis technique based on Linear Matrix Inequalities (LMIs), by mixing results concerning absolute stability of nonlinear systems and robustness of uncertain linear systems. The resulting controllers prove to be effective for chaos suppression in electronic circuits and systems, as shown by two different application examples.

Improvement and empirical research on chaos control by theory of "chaos + chaos = order".

PubMed

Fulai, Wang

2012-12-01

This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos = order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ≥ 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos = order" also exist in the dynamics generated by non-Mandelbrot maps.

Chaos and crises in a model for cooperative hunting: a symbolic dynamics approach.

PubMed

Duarte, Jorge; Januário, Cristina; Martins, Nuno; Sardanyés, Josep

2009-12-01

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K,C(0)) and (K,sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K(c) decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

On the relevance of chaos for halo stars in the solar neighbourhood II

NASA Astrophysics Data System (ADS)

Maffione, Nicolas P.; Gómez, Facundo A.; Cincotta, Pablo M.; Giordano, Claudia M.; Grand, Robert J. J.; Marinacci, Federico; Pakmor, Rüdiger; Simpson, Christine M.; Springel, Volker; Frenk, Carlos S.

2018-05-01

In a previous paper based on dark matter only simulations we show that, in the approximation of an analytic and static potential describing the strongly triaxial and cuspy shape of Milky Way-sized haloes, diffusion due to chaotic mixing in the neighbourhood of the Sun does not efficiently erase phase space signatures of past accretion events. In this second paper we further explore the effect of chaotic mixing using multicomponent Galactic potential models and solar neighbourhood-like volumes extracted from fully cosmological hydrodynamic simulations, thus naturally accounting for the gravitational potential associated with baryonic components, such as the bulge and disc. Despite the strong change in the global Galactic potentials with respect to those obtained in dark matter only simulations, our results confirm that a large fraction of halo particles evolving on chaotic orbits exhibit their chaotic behaviour after periods of time significantly larger than a Hubble time. In addition, significant diffusion in phase space is not observed on those particles that do exhibit chaotic behaviour within a Hubble time.

Randomly chosen chaotic maps can give rise to nearly ordered behavior

NASA Astrophysics Data System (ADS)

Boyarsky, Abraham; Góra, Paweł; Islam, Md. Shafiqul

2005-10-01

Parrondo’s paradox [J.M.R. Parrondo, G.P. Harmer, D. Abbott, New paradoxical games based on Brownian ratchets, Phys. Rev. Lett. 85 (2000), 5226-5229] (see also [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68-72]) states that two losing gambling games when combined one after the other (either deterministically or randomly) can result in a winning game: that is, a losing game followed by a losing game = a winning game. Inspired by this paradox, a recent study [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124-132] asked an analogous question in discrete time dynamical system: can two chaotic systems give rise to order, namely can they be combined into another dynamical system which does not behave chaotically? Numerical evidence is provided in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124-132] that two chaotic quadratic maps, when composed with each other, create a new dynamical system which has a stable period orbit. The question of what happens in the case of random composition of maps is posed in [J. Almeida, D. Peralta-Salas, M. Romera, Can two chaotic systems give rise to order? Physica D 200 (2005) 124-132] but left unanswered. In this note we present an example of a dynamical system where, at each iteration, a map is chosen in a probabilistic manner from a collection of chaotic maps. The resulting random map is proved to have an infinite absolutely continuous invariant measure (acim) with spikes at two points. From this we show that the dynamics behaves in a nearly ordered manner. When the foregoing maps are applied one after the other, deterministically as in [O.E. Percus, J.K. Percus, Can two wrongs make a right? Coin-tossing games and Parrondo’s paradox, Math. Intelligencer 24 (3) (2002) 68-72], the resulting composed map has a periodic orbit which is stable.

Design of an image encryption scheme based on a multiple chaotic map

NASA Astrophysics Data System (ADS)

Tong, Xiao-Jun

2013-07-01

In order to solve the problem that chaos is degenerated in limited computer precision and Cat map is the small key space, this paper presents a chaotic map based on topological conjugacy and the chaotic characteristics are proved by Devaney definition. In order to produce a large key space, a Cat map named block Cat map is also designed for permutation process based on multiple-dimensional chaotic maps. The image encryption algorithm is based on permutation-substitution, and each key is controlled by different chaotic maps. The entropy analysis, differential analysis, weak-keys analysis, statistical analysis, cipher random analysis, and cipher sensibility analysis depending on key and plaintext are introduced to test the security of the new image encryption scheme. Through the comparison to the proposed scheme with AES, DES and Logistic encryption methods, we come to the conclusion that the image encryption method solves the problem of low precision of one dimensional chaotic function and has higher speed and higher security.

Chaotic CDMA watermarking algorithm for digital image in FRFT domain

NASA Astrophysics Data System (ADS)

Liu, Weizhong; Yang, Wentao; Feng, Zhuoming; Zou, Xuecheng

2007-11-01

A digital image-watermarking algorithm based on fractional Fourier transform (FRFT) domain is presented by utilizing chaotic CDMA technique in this paper. As a popular and typical transmission technique, CDMA has many advantages such as privacy, anti-jamming and low power spectral density, which can provide robustness against image distortions and malicious attempts to remove or tamper with the watermark. A super-hybrid chaotic map, with good auto-correlation and cross-correlation characteristics, is adopted to produce many quasi-orthogonal codes (QOC) that can replace the periodic PN-code used in traditional CDAM system. The watermarking data is divided into a lot of segments that correspond to different chaotic QOC respectively and are modulated into the CDMA watermarking data embedded into low-frequency amplitude coefficients of FRFT domain of the cover image. During watermark detection, each chaotic QOC extracts its corresponding watermarking segment by calculating correlation coefficients between chaotic QOC and watermarked data of the detected image. The CDMA technique not only can enhance the robustness of watermark but also can compress the data of the modulated watermark. Experimental results show that the watermarking algorithm has good performances in three aspects: better imperceptibility, anti-attack robustness and security.

Chimeras and clusters in networks of hyperbolic chaotic oscillators

NASA Astrophysics Data System (ADS)

Cano, A. V.; Cosenza, M. G.

2017-03-01

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables. Chimera states, clusters, complete synchronization, and incoherence are thus characterized on the space of parameters of the system. We find that chimera states are related to the formation of clusters in the system. In addition, we show that chimera states arise for a sufficiently long range of interactions in nonlocally coupled networks of these maps. Our results reveal that, under some circumstances, hyperbolicity does not impede the formation of chimera states in networks of coupled chaotic systems, as it had been previously hypothesized.

The weaker effects of First-order mean motion resonances in intermediate inclinations

NASA Astrophysics Data System (ADS)

Chen, YuanYuan; Quillen, Alice C.; Ma, Yuehua; Chinese Scholar Council, the National Natural Science Foundation of China, the Natural Science Foundation of Jiangsu Province, the Minor Planet Foundation of the Purple Mountain Observatory

2017-10-01

During planetary migration, a planet or planetesimal can be captured into a low-order mean motion resonance with another planet. Using a second-order expansion of the disturbing function in eccentricity and inclination, we explore the sensitivity of the capture probability of first-order mean motion resonances to orbital inclination. We find that second-order inclination contributions affect the resonance strengths, reducing them at intermediate inclinations of around 10-40° for major first-order resonances. We also integrated the Hamilton's equations with arbitrary initial arguments, and provided the varying tendencies of resonance capture probabilities versus orbital inclinations for different resonances and different particle or planetary eccentricities. Resonance-weaker ranges in inclinations generally appear at the places where resonance strengths are low, around 10-40° in general. The weaker ranges disappear with a higher particle eccentricity (≳0.05) or planetary eccentricity (≳0.05). These resonance-weaker ranges in inclinations implies that intermediate-inclination objects are less likely to be disturbed or captured into the first-order resonances, which would make them entering into the chaotic area around Neptune with a larger fraction than those with low inclinations, during the epoch of Neptune's outward migration. The privilege of high-inclination particles leave them to be more likely captured into Neptune Trojans, which might be responsible for the unexpected high fraction of high-inclination Neptune Trojans.

Chaotic Motifs in Gene Regulatory Networks

PubMed Central

Zhang, Zhaoyang; Ye, Weiming; Qian, Yu; Zheng, Zhigang; Huang, Xuhui; Hu, Gang

2012-01-01

Chaos should occur often in gene regulatory networks (GRNs) which have been widely described by nonlinear coupled ordinary differential equations, if their dimensions are no less than 3. It is therefore puzzling that chaos has never been reported in GRNs in nature and is also extremely rare in models of GRNs. On the other hand, the topic of motifs has attracted great attention in studying biological networks, and network motifs are suggested to be elementary building blocks that carry out some key functions in the network. In this paper, chaotic motifs (subnetworks with chaos) in GRNs are systematically investigated. The conclusion is that: (i) chaos can only appear through competitions between different oscillatory modes with rivaling intensities. Conditions required for chaotic GRNs are found to be very strict, which make chaotic GRNs extremely rare. (ii) Chaotic motifs are explored as the simplest few-node structures capable of producing chaos, and serve as the intrinsic source of chaos of random few-node GRNs. Several optimal motifs causing chaos with atypically high probability are figured out. (iii) Moreover, we discovered that a number of special oscillators can never produce chaos. These structures bring some advantages on rhythmic functions and may help us understand the robustness of diverse biological rhythms. (iv) The methods of dominant phase-advanced driving (DPAD) and DPAD time fraction are proposed to quantitatively identify chaotic motifs and to explain the origin of chaotic behaviors in GRNs. PMID:22792171

The spatial dynamics of ecosystem engineers.

PubMed

Franco, Caroline; Fontanari, José F

2017-10-01

The changes on abiotic features of ecosystems have rarely been taken into account by population dynamics models, which typically focus on trophic and competitive interactions between species. However, understanding the population dynamics of organisms that must modify their habitats in order to survive, the so-called ecosystem engineers, requires the explicit incorporation of abiotic interactions in the models. Here we study a model of ecosystem engineers that is discrete both in space and time, and where the engineers and their habitats are arranged in patches fixed to the sites of regular lattices. The growth of the engineer population is modeled by Ricker equation with a density-dependent carrying capacity that is given by the number of modified habitats. A diffusive dispersal stage ensures that a fraction of the engineers move from their birth patches to neighboring patches. We find that dispersal influences the metapopulation dynamics only in the case that the local or single-patch dynamics exhibit chaotic behavior. In that case, it can suppress the chaotic behavior and avoid extinctions in the regime of large intrinsic growth rate of the population. Copyright © 2017 Elsevier Inc. All rights reserved.

Design and Hardware Implementation of a New Chaotic Secure Communication Technique

PubMed Central

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness. PMID:27548385

Design and Hardware Implementation of a New Chaotic Secure Communication Technique.

PubMed

Xiong, Li; Lu, Yan-Jun; Zhang, Yong-Fang; Zhang, Xin-Guo; Gupta, Parag

2016-01-01

In this paper, a scheme for chaotic modulation secure communication is proposed based on chaotic synchronization of an improved Lorenz system. For the first time, the intensity limit and stability of the transmitted signal, the characteristics of broadband and the requirements for accuracy of electronic components are presented by Multisim simulation. In addition, some improvements are made on the measurement method and the proposed experimental circuit in order to facilitate the experiments of chaotic synchronization, chaotic non-synchronization, experiment without signal and experiment with signal. To illustrate the effectiveness of the proposed scheme, some numerical simulations are presented. Then, the proposed chaotic secure communication circuit is implemented through analog electronic circuit, which is characterized by its high accuracy and good robustness.

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.

Some new surprises in chaos.

PubMed

Bunimovich, Leonid A; Vela-Arevalo, Luz V

2015-09-01

"Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.

Chaotic Oscillations of Second Order Linear Hyperbolic Equations with Nonlinear Boundary Conditions: A Factorizable but Noncommutative Case

NASA Astrophysics Data System (ADS)

Li, Liangliang; Huang, Yu; Chen, Goong; Huang, Tingwen

If a second order linear hyperbolic partial differential equation in one-space dimension can be factorized as a product of two first order operators and if the two first order operators commute, with one boundary condition being the van der Pol type and the other being linear, one can establish the occurrence of chaos when the parameters enter a certain regime [Chen et al., 2014]. However, if the commutativity of the two first order operators fails to hold, then the treatment in [Chen et al., 2014] no longer works and significant new challenges arise in determining nonlinear boundary conditions that engenders chaos. In this paper, we show that by incorporating a linear memory effect, a nonlinear van der Pol boundary condition can cause chaotic oscillations when the parameter enters a certain regime. Numerical simulations illustrating chaotic oscillations are also presented.

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

NASA Astrophysics Data System (ADS)

Li, Fei; Li, Wenwu; Xu, Lan

2018-06-01

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system's chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.

Chaotic Dynamics of a Josephson Junction with a Ratchet Potential and Current-Modulating Damping

NASA Astrophysics Data System (ADS)

Li, Fei; Li, Wenwu; Xu, Lan

2018-04-01

The chaotic dynamics of a Josephson junction with a ratchet potential and current-modulating damping are studied. Under the first-order approximation, we construct the general solution of the first-order equation whose boundedness condition contains the famous Melnikov chaotic criterion. Based on the general solution, the incomputability and unpredictability of the system's chaotic behavior are discussed. For the case beyond perturbation conditions, the evolution of stroboscopic Poincaré sections shows that the system undergoes a quasi-periodic transition to chaos with an increasing intensity of the rf-current. Through a suitable feedback controlling strategy, the chaos can be effectively suppressed and the intensity of the controller can vary in a large range. It is also found that the current between the two separated superconductors increases monotonously in some specific parameter spaces.

Simple Chaotic Flow with Circle and Square Equilibrium

NASA Astrophysics Data System (ADS)

Gotthans, Tomas; Sprott, Julien Clinton; Petrzela, Jiri

Simple systems of third-order autonomous nonlinear differential equations can exhibit chaotic behavior. In this paper, we present a new class of chaotic flow with a square-shaped equilibrium. This unique property has apparently not yet been described. Such a system belongs to a newly introduced category of chaotic systems with hidden attractors that are interesting and important in engineering applications. The mathematical model is accompanied by an electrical circuit implementation, demonstrating structural stability of the strange attractor. The circuit is simulated with PSpice, constructed, and analyzed (measured).

Chaos analysis of viscoelastic chaotic flows of polymeric fluids in a micro-channel

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

Lim, C. P.; Lam, Y. C., E-mail: myclam@ntu.edu.sg; BioSystems and Micromechanics

2015-07-15

Many fluids, including biological fluids such as mucus and blood, are viscoelastic. Through the introduction of chaotic flows in a micro-channel and the construction of maps of characteristic chaos parameters, differences in viscoelastic properties of these fluids can be measured. This is demonstrated by creating viscoelastic chaotic flows induced in an H-shaped micro-channel through the steady infusion of a polymeric fluid of polyethylene oxide (PEO) and another immiscible fluid (silicone oil). A protocol for chaos analysis was established and demonstrated for the analysis of the chaotic flows generated by two polymeric fluids of different molecular weight but with similar relaxationmore » times. The flows were shown to be chaotic through the computation of their correlation dimension (D{sub 2}) and the largest Lyapunov exponent (λ{sub 1}), with D{sub 2} being fractional and λ{sub 1} being positive. Contour maps of D{sub 2} and λ{sub 1} of the respective fluids in the operating space, which is defined by the combination of polymeric fluids and silicone oil flow rates, were constructed to represent the characteristic of the chaotic flows generated. It was observed that, albeit being similar, the fluids have generally distinct characteristic maps with some similar trends. The differences in the D{sub 2} and λ{sub 1} maps are indicative of the difference in the molecular weight of the polymers in the fluids because the driving force of the viscoelastic chaotic flows is of molecular origin. This approach in constructing the characteristic maps of chaos parameters can be employed as a diagnostic tool for biological fluids and, more generally, chaotic signals.« less

A new reduced-order observer for the synchronization of nonlinear chaotic systems: An application to secure communications

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

Castro-Ramírez, Joel, E-mail: ingcastro.7@gmail.com; Martínez-Guerra, Rafael, E-mail: rguerra@ctrl.cinvestav.mx; Cruz-Victoria, Juan Crescenciano, E-mail: juancrescenciano.cruz@uptlax.edu.mx

2015-10-15

This paper deals with the master-slave synchronization scheme for partially known nonlinear chaotic systems, where the unknown dynamics is considered as the master system and we propose the slave system structure which estimates the unknown states. It introduced a new reduced order observer, using the concept of Algebraic Observability; we applied the results to a Sundarapandian chaotic system, and by means of some numerical simulations we show the effectiveness of the suggested approach. Finally, the proposed observer is utilized for encryption, where encryption key is the master system and decryption key is the slave system.

On the Numerical Formulation of Parametric Linear Fractional Transformation (LFT) Uncertainty Models for Multivariate Matrix Polynomial Problems

NASA Technical Reports Server (NTRS)

Belcastro, Christine M.

1998-01-01

Robust control system analysis and design is based on an uncertainty description, called a linear fractional transformation (LFT), which separates the uncertain (or varying) part of the system from the nominal system. These models are also useful in the design of gain-scheduled control systems based on Linear Parameter Varying (LPV) methods. Low-order LFT models are difficult to form for problems involving nonlinear parameter variations. This paper presents a numerical computational method for constructing and LFT model for a given LPV model. The method is developed for multivariate polynomial problems, and uses simple matrix computations to obtain an exact low-order LFT representation of the given LPV system without the use of model reduction. Although the method is developed for multivariate polynomial problems, multivariate rational problems can also be solved using this method by reformulating the rational problem into a polynomial form.

On the modeling and nonlinear dynamics of autonomous Silva-Young type chaotic oscillators with flat power spectrum

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

Kengne, Jacques; Kenmogne, Fabien

2014-12-15

The nonlinear dynamics of fourth-order Silva-Young type chaotic oscillators with flat power spectrum recently introduced by Tamaseviciute and collaborators is considered. In this type of oscillators, a pair of semiconductor diodes in an anti-parallel connection acts as the nonlinear component necessary for generating chaotic oscillations. Based on the Shockley diode equation and an appropriate selection of the state variables, a smooth mathematical model (involving hyperbolic sine and cosine functions) is derived for a better description of both the regular and chaotic dynamics of the system. The complex behavior of the oscillator is characterized in terms of its parameters by usingmore » time series, bifurcation diagrams, Lyapunov exponents' plots, Poincaré sections, and frequency spectra. It is shown that the onset of chaos is achieved via the classical period-doubling and symmetry restoring crisis scenarios. Some PSPICE simulations of the nonlinear dynamics of the oscillator are presented in order to confirm the ability of the proposed mathematical model to accurately describe/predict both the regular and chaotic behaviors of the oscillator.« less

Chaotic vibrations of the duffing system with fractional damping

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

Syta, Arkadiusz; Litak, Grzegorz; Lenci, Stefano

2014-03-15

We examined the Duffing system with a fractional damping term. Calculating the basins of attraction, we demonstrate a broad spectrum of non-linear behaviour connected with sensitivity to the initial conditions and chaos. To quantify dynamical response of the system, we propose the statistical 0-1 test as well as the maximal Lyapunov exponent; the application of the latter encounter a few difficulties because of the memory effect due to the fractional derivative. The results are confirmed by bifurcation diagrams, phase portraits, and Poincaré sections.

Crisis and emergency risk communication as an integrative model.

PubMed

Reynolds, Barbara; W Seeger, Matthew

2005-01-01

This article describes a model of communication known as crisis and emergency risk communication (CERC). The model is outlined as a merger of many traditional notions of health and risk communication with work in crisis and disaster communication. The specific kinds of communication activities that should be called for at various stages of disaster or crisis development are outlined. Although crises are by definition uncertain, equivocal, and often chaotic situations, the CERC model is presented as a tool health communicators can use to help manage these complex events.

A mixed analog/digital chaotic neuro-computer system for quadratic assignment problems.

PubMed

Horio, Yoshihiko; Ikeguchi, Tohru; Aihara, Kazuyuki

2005-01-01

We construct a mixed analog/digital chaotic neuro-computer prototype system for quadratic assignment problems (QAPs). The QAP is one of the difficult NP-hard problems, and includes several real-world applications. Chaotic neural networks have been used to solve combinatorial optimization problems through chaotic search dynamics, which efficiently searches optimal or near optimal solutions. However, preliminary experiments have shown that, although it obtained good feasible solutions, the Hopfield-type chaotic neuro-computer hardware system could not obtain the optimal solution of the QAP. Therefore, in the present study, we improve the system performance by adopting a solution construction method, which constructs a feasible solution using the analog internal state values of the chaotic neurons at each iteration. In order to include the construction method into our hardware, we install a multi-channel analog-to-digital conversion system to observe the internal states of the chaotic neurons. We show experimentally that a great improvement in the system performance over the original Hopfield-type chaotic neuro-computer is obtained. That is, we obtain the optimal solution for the size-10 QAP in less than 1000 iterations. In addition, we propose a guideline for parameter tuning of the chaotic neuro-computer system according to the observation of the internal states of several chaotic neurons in the network.

Timing variation in an analytically solvable chaotic system

NASA Astrophysics Data System (ADS)

Blakely, J. N.; Milosavljevic, M. S.; Corron, N. J.

2017-02-01

We present analytic solutions for a chaotic dynamical system that do not have the regular timing characteristic of recently reported solvable chaotic systems. The dynamical system can be viewed as a first order filter with binary feedback. The feedback state may be switched only at instants defined by an external clock signal. Generalizing from a period one clock, we show analytic solutions for period two and higher period clocks. We show that even when the clock 'ticks' randomly the chaotic system has an analytic solution. These solutions can be visualized in a stroboscopic map whose complexity increases with the complexity of the clock. We provide both analytic results as well as experimental data from an electronic circuit implementation of the system. Our findings bridge the gap between the irregular timing of well known chaotic systems such as Lorenz and Rossler and the well regulated oscillations of recently reported solvable chaotic systems.

An information hiding method based on LSB and tent chaotic map

NASA Astrophysics Data System (ADS)

Song, Jianhua; Ding, Qun

2011-06-01

In order to protect information security more effectively, a novel information hiding method based on LSB and Tent chaotic map was proposed, first the secret message is Tent chaotic encrypted, and then LSB steganography is executed for the encrypted message in the cover-image. Compared to the traditional image information hiding method, the simulation results indicate that the method greatly improved in imperceptibility and security, and acquired good results.

Working Towards Führer: A Chaotic View

NASA Astrophysics Data System (ADS)

Cakar, Ulas

Leadership is a concept that has been discussed since the beginning of history. Even though there have been many theories in the field accepting leadership's role in bringing order, chaotic aspects of leadership are generally neglected. This chapter aims to examine the leadership beyond an orderly interpretation of universe. For this purpose, Third Reich period and leadership during this period will be examined. Ian Kershaw's "Working Towards Führer" concept provides a unique understanding of leadership concept. It goes beyond the dualist depiction of Third Reich, it does not state Adolf Hitler as an all powerful dictator, or a weak one. Rather, he expresses that due to the conditions in the Third Reich, Adolf Hitler was both of this. This complex situation can be understood deeper when it is examined through the lens of chaos theory. This study contributes to the field by being the first in using chaos theory for examining "Working Towards Führer" concept and its development. Seemingly orderly nature of synchronization process and its vortex will be shown. Adolf Hitler's storm spot position in the chaotic system and its dynamics are explained. War's entropic power and its effect on the downfall of the system is crucial in understanding this unique chaotic system. The chaotic pattern of "Working Towards Führer" offers an opportunity to analyze the complexities of the leadership concept.

Chaotic He-Ne laser

NASA Astrophysics Data System (ADS)

Kuusela, Tom A.

2017-09-01

A He-Ne laser is an example of a class A laser, which can be described by a single nonlinear differential equation of the complex electric field. This laser system has only one degree of freedom and is thus inherently stable. A He-Ne laser can be driven to the chaotic condition when a large fraction of the output beam is injected back to the laser. In practice, this can be done simply by adding an external mirror. In this situation, the laser system has infinite degrees of freedom and therefore it can have a chaotic attractor. We show the fundamental laser equations and perform elementary stability analysis. In experiments, the laser intensity variations are measured by a simple photodiode circuit. The laser output intensity time series is studied using nonlinear analysis tools which can be found freely on the internet. The results show that the laser system with feedback has an attractor of a reasonably high dimension and that the maximal Lyapunov exponent is positive, which is clear evidence of chaotic behaviour. The experimental setup and analysis steps are so simple that the studies can even be implemented in the undergraduate physics laboratory.

Stability enhancement of high Prandtl number chaotic convection in an anisotropic porous layer with feedback control

NASA Astrophysics Data System (ADS)

Mahmud, M. N.

2018-04-01

The chaotic dynamical behaviour of thermal convection in an anisotropic porous layer subject to gravity, heated from below and cooled from above, is studied based on theory of dynamical system in the presence of feedback control. The extended Darcy model, which includes the time derivative has been employed in the momentum equation to derive a low dimensional Lorenz-like equation by using Galerkin-truncated approximation. The classical fourth-order Runge-Kutta method is used to obtain the numerical solution in order to exemplify the dynamics of the nonlinear autonomous system. The results show that stability enhancement of chaotic convection is feasible via feedback control.

Future missions studies: Combining Schatten's solar activity prediction model with a chaotic prediction model

NASA Technical Reports Server (NTRS)

Ashrafi, S.

1991-01-01

K. Schatten (1991) recently developed a method for combining his prediction model with our chaotic model. The philosophy behind this combined model and his method of combination is explained. Because the Schatten solar prediction model (KS) uses a dynamo to mimic solar dynamics, accurate prediction is limited to long-term solar behavior (10 to 20 years). The Chaotic prediction model (SA) uses the recently developed techniques of nonlinear dynamics to predict solar activity. It can be used to predict activity only up to the horizon. In theory, the chaotic prediction should be several orders of magnitude better than statistical predictions up to that horizon; beyond the horizon, chaotic predictions would theoretically be just as good as statistical predictions. Therefore, chaos theory puts a fundamental limit on predictability.

A new feedback image encryption scheme based on perturbation with dynamical compound chaotic sequence cipher generator

NASA Astrophysics Data System (ADS)

Tong, Xiaojun; Cui, Minggen; Wang, Zhu

2009-07-01

The design of the new compound two-dimensional chaotic function is presented by exploiting two one-dimensional chaotic functions which switch randomly, and the design is used as a chaotic sequence generator which is proved by Devaney's definition proof of chaos. The properties of compound chaotic functions are also proved rigorously. In order to improve the robustness against difference cryptanalysis and produce avalanche effect, a new feedback image encryption scheme is proposed using the new compound chaos by selecting one of the two one-dimensional chaotic functions randomly and a new image pixels method of permutation and substitution is designed in detail by array row and column random controlling based on the compound chaos. The results from entropy analysis, difference analysis, statistical analysis, sequence randomness analysis, cipher sensitivity analysis depending on key and plaintext have proven that the compound chaotic sequence cipher can resist cryptanalytic, statistical and brute-force attacks, and especially it accelerates encryption speed, and achieves higher level of security. By the dynamical compound chaos and perturbation technology, the paper solves the problem of computer low precision of one-dimensional chaotic function.

Volcanic cones in Hydraotes chaos : implications for the chaotic terrains formation

NASA Astrophysics Data System (ADS)

Meresse, S.; Costard, F.; Mangold, N.; Masson, P.; Neukum, G.

2006-12-01

Numerous geologic scenarios have been proposed for the chaotic terrains formation. They include (1) sub-ice volcanism and other magma-ice interactions and (2) catastrophic release of groundwater from confined aquifers. The lack of volcanic morphology in the chaos was an handicap for the hypothesis of magma-ice interactions but the HRSC (High Resolution Stereo Camera) images have recently revealed possible volcanic cones inside the Hydraotes chaos. About thirty cones lie on the lowest parts of the chaos at elevation between -4300 and -5100 meters. They have basal diameters of 500-1900 m and heights exceeding 100 m. They are observed on young surface: the south smooth floor and inside the narrow valleys separating the mesas. The cones are relatively fresh. Similar morphologies of small cone-shaped structures have been previously identified in the northern lowlands of Mars (Chryse, Acidalia, Amazonis, Isidis and Elysuim Planitia) but their origin remains uncertain. A number of volcanic or cold climate landforms were proposed as potential terrestrial analogues : Icelandic pseudocraters (or rootless cones), cinder cones, tuff cones, pingos and spatter cones. The morphologic measurements made on the Hydraotes cones argue rather for a volcanic origin in comparison with terrestrial analogues. These first volcanic cones observed in Hydraotes chaos suggest that volcanic or subvolcanic activity might have played an important part in the chaotic terrains formation and outflow channels genesis.

Diversity of the Lyman continuum escape fractions of high-z galaxies and its origins

NASA Astrophysics Data System (ADS)

Sumida, Takumi; Kashino, Daichi; Hasegawa, Kenji

2018-04-01

The Lyman continuum (LyC) escape fraction is a key quantity to determine the contribution of galaxies to cosmic reionization. It has been known that the escape fractions estimated by observations and numerical simulations show a large diversity. However, the origins of the diversity are still uncertain. In this work, to understand what quantities of galaxies are responsible for controlling the escape fraction, we numerically evaluate the escape fraction by performing ray-tracing calculation with simplified disc galaxy models. With a smooth disc model, we explore the dependence of the escape fraction on the disposition of ionizing sources and find that the escape fraction varies up to ˜3 orders of magnitude. It is also found that the halo mass dependence of disc scale height determines whether the escape fraction increases or decreases with halo mass. With a clumpy disc model, it turns out that the escape fraction increases as the clump mass fraction increases because the density in the inter-clump region decreases. In addition, we find that clumpiness regulates the escape fraction via two ways when the total clump mass dominates the total gas mass; the escape fraction is controlled by the covering factor of clumps if the clumps are dense sufficient to block LyC photons, otherwise the clumpiness works to reduce the escape fraction by increasing the total number of recombination events in a galaxy.

Characterization of chaotic electroconvection near flat electrodes under oscillatory voltages

NASA Astrophysics Data System (ADS)

Kim, Jeonglae; Davidson, Scott; Mani, Ali

2017-11-01

Onset of hydrodynamic instability and chaotic electroconvection in aqueous systems are studied by directly solving the two-dimensional coupled Poisson-Nernst-Planck and Navier-Stokes equations. An aqueous binary electrolyte is bounded by two planar electrodes where time-harmonic voltage is applied at a constant oscillation frequency. The governing equations are solved using a fully-conservative second-order-accurate finite volume discretization and a second-order implicit Euler time advancement. At a sufficiently high amplitude of applied voltage, the system exhibits chaotic behaviors involving strong hydrodynamic mixing and enhanced electroconvection. The system responses are characterized as a function of oscillation frequency, voltage magnitude, and the ratio of diffusivities of two ion species. Our results indicate that electroconvection is most enhanced for frequencies on the order of inverse system RC time scale. We will discuss the dependence of this optimal frequency on the asymmetry of the diffusion coefficients of ionic species. Supported by the Stanford's Precourt Institute.

Random Matrix Theory Approach to Chaotic Coherent Perfect Absorbers

NASA Astrophysics Data System (ADS)

Li, Huanan; Suwunnarat, Suwun; Fleischmann, Ragnar; Schanz, Holger; Kottos, Tsampikos

2017-01-01

We employ random matrix theory in order to investigate coherent perfect absorption (CPA) in lossy systems with complex internal dynamics. The loss strength γCPA and energy ECPA, for which a CPA occurs, are expressed in terms of the eigenmodes of the isolated cavity—thus carrying over the information about the chaotic nature of the target—and their coupling to a finite number of scattering channels. Our results are tested against numerical calculations using complex networks of resonators and chaotic graphs as CPA cavities.

Using chaotic artificial neural networks to model memory in the brain

NASA Astrophysics Data System (ADS)

Aram, Zainab; Jafari, Sajad; Ma, Jun; Sprott, Julien C.; Zendehrouh, Sareh; Pham, Viet-Thanh

2017-03-01

In the current study, a novel model for human memory is proposed based on the chaotic dynamics of artificial neural networks. This new model explains a biological fact about memory which is not yet explained by any other model: There are theories that the brain normally works in a chaotic mode, while during attention it shows ordered behavior. This model uses the periodic windows observed in a previously proposed model for the brain to store and then recollect the information.

Chaotic itinerancy and power-law residence time distribution in stochastic dynamical systems.

PubMed

Namikawa, Jun

2005-08-01

Chaotic itinerant motion among varieties of ordered states is described by a stochastic model based on the mechanism of chaotic itinerancy. The model consists of a random walk on a half-line and a Markov chain with a transition probability matrix. The stability of attractor ruin in the model is investigated by analyzing the residence time distribution of orbits at attractor ruins. It is shown that the residence time distribution averaged over all attractor ruins can be described by the superposition of (truncated) power-law distributions if the basin of attraction for each attractor ruin has a zero measure. This result is confirmed by simulation of models exhibiting chaotic itinerancy. Chaotic itinerancy is also shown to be absent in coupled Milnor attractor systems if the transition probability among attractor ruins can be represented as a Markov chain.

Solving large scale traveling salesman problems by chaotic neurodynamics.

PubMed

Hasegawa, Mikio; Ikeguch, Tohru; Aihara, Kazuyuki

2002-03-01

We propose a novel approach for solving large scale traveling salesman problems (TSPs) by chaotic dynamics. First, we realize the tabu search on a neural network, by utilizing the refractory effects as the tabu effects. Then, we extend it to a chaotic neural network version. We propose two types of chaotic searching methods, which are based on two different tabu searches. While the first one requires neurons of the order of n2 for an n-city TSP, the second one requires only n neurons. Moreover, an automatic parameter tuning method of our chaotic neural network is presented for easy application to various problems. Last, we show that our method with n neurons is applicable to large TSPs such as an 85,900-city problem and exhibits better performance than the conventional stochastic searches and the tabu searches.

The good leader.

PubMed

Bottles, K

2001-01-01

What are the traits of successful leaders and can they be applied to those of us in health care? Leaders must deal with conflict to get a group of people to move in the same direction. Successful leaders learn to have difficult conversations that increase understanding and morale and creatively deal with the inevitable interpersonal conflicts present in every organization made up of people. Another useful trait for a leader during uncertain and chaotic times is the ability to see things as they really are, rather than as we wish or believe them to be. Successful leaders are also usually optimists who level with their co-workers.

On fractality and chaos in Moroccan family business stock returns and volatility

NASA Astrophysics Data System (ADS)

Lahmiri, Salim

2017-05-01

The purpose of this study is to examine existence of fractality and chaos in returns and volatilities of family business companies listed on the Casablanca Stock Exchange (CSE) in Morocco, and also in returns and volatility of the CSE market index. Detrended fluctuation analysis based Hurst exponent and fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model are used to quantify fractality in returns and volatility time series respectively. Besides, the largest Lyapunov exponent is employed to quantify chaos in both time series. The empirical results from sixteen family business companies follow. For return series, fractality analysis show that most of family business returns listed on CSE exhibit anti-persistent dynamics, whilst market returns have persistent dynamics. Besides, chaos tests show that business family stock returns are not chaotic while market returns exhibit evidence of chaotic behaviour. For volatility series, fractality analysis shows that most of family business stocks and market index exhibit long memory in volatility. Furthermore, results from chaos tests show that volatility of family business returns is not chaotic, whilst volatility of market index is chaotic. These results may help understanding irregularities patterns in Moroccan family business stock returns and volatility, and how they are different from market dynamics.

A discrete-time chaos synchronization system for electronic locking devices

NASA Astrophysics Data System (ADS)

Minero-Ramales, G.; López-Mancilla, D.; Castañeda, Carlos E.; Huerta Cuellar, G.; Chiu Z., R.; Hugo García López, J.; Jaimes Reátegui, R.; Villafaña Rauda, E.; Posadas-Castillo, C.

2016-11-01

This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.

Simulation and Visualization of Chaos in a Driven Nonlinear Pendulum -- An Aid to Introducing Chaotic Systems in Physics

NASA Astrophysics Data System (ADS)

Akpojotor, Godfrey; Ehwerhemuepha, Louis; Amromanoh, Ogheneriobororue

2013-03-01

The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions. In order to understand chaotic systems, some sort of simulation and visualization is pertinent. Consequently, in this work, we have simulated and graphically visualized chaos in a driven nonlinear pendulum as a means of introducing chaotic systems. The results obtained which highlight the hypersensitivity of the pendulum are used to discuss the effectiveness of teaching and learning the physics of chaotic system using Python. This study is one of the many studies under the African Computational Science and Engineering Tour Project (PASET) which is using Python to model, simulate and visualize concepts, laws and phenomena in Science and Engineering to compliment the teaching/learning of theory and experiment.

Experimental chaotic quantification in bistable vortex induced vibration systems

NASA Astrophysics Data System (ADS)

Huynh, B. H.; Tjahjowidodo, T.

2017-02-01

The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear out the regularity of periodic responses. For this purpose, a surrogate data test is used in order to check the hypotheses for the presence of chaotic behavior. The analyses from the experimental results support the hypothesis from simulation that chaotic response is likely occur on the real system.

Quantized Synchronization of Chaotic Neural Networks With Scheduled Output Feedback Control.

PubMed

Wan, Ying; Cao, Jinde; Wen, Guanghui

In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.In this paper, the synchronization problem of master-slave chaotic neural networks with remote sensors, quantization process, and communication time delays is investigated. The information communication channel between the master chaotic neural network and slave chaotic neural network consists of several remote sensors, with each sensor able to access only partial knowledge of output information of the master neural network. At each sampling instants, each sensor updates its own measurement and only one sensor is scheduled to transmit its latest information to the controller's side in order to update the control inputs for the slave neural network. Thus, such communication process and control strategy are much more energy-saving comparing with the traditional point-to-point scheme. Sufficient conditions for output feedback control gain matrix, allowable length of sampling intervals, and upper bound of network-induced delays are derived to ensure the quantized synchronization of master-slave chaotic neural networks. Lastly, Chua's circuit system and 4-D Hopfield neural network are simulated to validate the effectiveness of the main results.

Lagrangian analysis of premixed turbulent combustion in hydrogen-air flames

NASA Astrophysics Data System (ADS)

Darragh, Ryan; Poludnenko, Alexei; Hamlington, Peter

2016-11-01

Lagrangian analysis has long been a tool used to analyze non-reacting turbulent flows, and has recently gained attention in the reacting flow and combustion communities. The approach itself allows one to separate local molecular effects, such as those due to reactions or diffusion, from turbulent advective effects along fluid pathlines, or trajectories. Accurate calculation of these trajectories can, however, be rather difficult due to the chaotic nature of turbulent flows and the added complexity of reactions. In order to determine resolution requirements and verify the numerical algorithm, extensive tests are described in this talk for prescribed steady, unsteady, and chaotic flows, as well as for direct numerical simulations (DNS) of non-reacting homogeneous isotropic turbulence. The Lagrangian analysis is then applied to DNS of premixed hydrogen-air flames at two different turbulence intensities for both single- and multi-step chemical mechanisms. Non-monotonic temperature and fuel-mass fraction evolutions are found to exist along trajectories passing through the flame brush. Such non-monotonicity is shown to be due to molecular diffusion resulting from large spatial gradients created by turbulent advection. This work was supported by the Air Force Office of Scientific Research (AFOSR) under Award No. FA9550-14-1-0273, and the Department of Defense (DoD) High Performance Computing Modernization Program (HPCMP) under a Frontier project award.

An Improved Cuckoo Search Optimization Algorithm for the Problem of Chaotic Systems Parameter Estimation

PubMed Central

Wang, Jun; Zhou, Bihua; Zhou, Shudao

2016-01-01

This paper proposes an improved cuckoo search (ICS) algorithm to establish the parameters of chaotic systems. In order to improve the optimization capability of the basic cuckoo search (CS) algorithm, the orthogonal design and simulated annealing operation are incorporated in the CS algorithm to enhance the exploitation search ability. Then the proposed algorithm is used to establish parameters of the Lorenz chaotic system and Chen chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the algorithm can estimate parameters with high accuracy and reliability. Finally, the results are compared with the CS algorithm, genetic algorithm, and particle swarm optimization algorithm, and the compared results demonstrate the method is energy-efficient and superior. PMID:26880874

Bit-level quantum color image encryption scheme with quantum cross-exchange operation and hyper-chaotic system

NASA Astrophysics Data System (ADS)

Zhou, Nanrun; Chen, Weiwei; Yan, Xinyu; Wang, Yunqian

2018-06-01

In order to obtain higher encryption efficiency, a bit-level quantum color image encryption scheme by exploiting quantum cross-exchange operation and a 5D hyper-chaotic system is designed. Additionally, to enhance the scrambling effect, the quantum channel swapping operation is employed to swap the gray values of corresponding pixels. The proposed color image encryption algorithm has larger key space and higher security since the 5D hyper-chaotic system has more complex dynamic behavior, better randomness and unpredictability than those based on low-dimensional hyper-chaotic systems. Simulations and theoretical analyses demonstrate that the presented bit-level quantum color image encryption scheme outperforms its classical counterparts in efficiency and security.

Design and simulation of the micromixer with chaotic advection in twisted microchannels.

PubMed

Jen, Chun-Ping; Wu, Chung-Yi; Lin, Yu-Cheng; Wu, Ching-Yi

2003-05-01

Chaotic mixers with twisted microchannels were designed and simulated numerically in the present study. The phenomenon whereby a simple Eulerian velocity field may generate a chaotic response in the distribution of a Lagrangian marker is termed chaotic advection. Dynamic system theory indicates that chaotic particle motion can occur when a velocity field is either two-dimensional and time-dependent, or three-dimensional. In the present study, micromixers with three-dimensional structures of the twisted microchannel were designed in order to induce chaotic mixing. In addition to the basic T-mixer, three types of micromixers with inclined, oblique and wavelike microchannels were investigated. In the design of each twisted microchannel, the angle of the channels' bottoms alternates in each subsection. When the fluids enter the twisted microchannels, the flow sways around the varying structures within the microchannels. The designs of the twisted microchannels provide a third degree of freedom to the flow field in the microchannel. Therefore, chaotic regimes that lead to chaotic mixing may arise. The numerical results indicate that mixing occurs in the main channel and progressively larger mixing lengths are required as the Peclet number increased. The swaying of the flow in the twisted microchannel causes chaotic advection. Among the four micromixer designs, the micromixer with the inclined channel most improved mixing. Furthermore, using the inclined mixer with six subsections yielded optimum performance, decreasing the mixing length by up to 31% from that of the basic T-mixer.

Chaotic interactions of self-replicating RNA.

PubMed

Forst, C V

1996-03-01

A general system of high-order differential equations describing complex dynamics of replicating biomolecules is given. Symmetry relations and coordinate transformations of general replication systems leading to topologically equivalent systems are derived. Three chaotic attractors observed in Lotka-Volterra equations of dimension n = 3 are shown to represent three cross-sections of one and the same chaotic regime. Also a fractal torus in a generalized three-dimensional Lotka-Volterra Model has been linked to one of the chaotic attractors. The strange attractors are studied in the equivalent four-dimensional catalytic replicator network. The fractal torus has been examined in adapted Lotka-Volterra equations. Analytic expressions are derived for the Lyapunov exponents of the flow in the replicator system. Lyapunov spectra for different pathways into chaos has been calculated. In the generalized Lotka-Volterra system a second inner rest point--coexisting with (quasi)-periodic orbits--can be observed; with an abundance of different bifurcations. Pathways from chaotic tori, via quasi-periodic tori, via limit cycles, via multi-periodic orbits--emerging out of periodic doubling bifurcations--to "simple" chaotic attractors can be found.

Relative Time-scale for Channeling Events Within Chaotic Terrains, Margaritifer Sinus, Mars

NASA Technical Reports Server (NTRS)

Janke, D.

1985-01-01

A relative time scale for ordering channel and chaos forming events was constructed for areas within the Margaritifer Sinus region of Mars. Transection and superposition relationships of channels, chaotic terrain, and the surfaces surrounding them were used to create the relative time scale; crater density studies were not used. Channels and chaos in contact with one another were treated as systems. These systems were in turn treated both separately (in order to understand internal relationships) and as members of the suite of Martian erosional forms (in order to produce a combined, master time scale). Channeling events associated with chaotic terrain development occurred over an extended geomorphic period. The channels can be divided into three convenient groups: those that pre-date intercrater plains development post-plains, pre-chasma systems; and those associated with the development of the Vallis Marineris chasmata. No correlations with cyclic climatic changes, major geologic events in other regions on Mars, or triggering phenomena (for example, specific impact events) were found.

Flavors of Chaos in the Asteroid Belt

NASA Astrophysics Data System (ADS)

Tsiganis, Kleomenis

2016-10-01

The asteroid belt is a natural laboratory for studying chaos, as a large fraction of asteroids actually reside on chaotic orbits. Numerous studies over the past 25 years have unveiled a multitude of dynamical chaos-generating mechanisms, operating on different time-scales and dominating over different regions of the belt. In fact, the distribution of chaotic asteroids in orbital space can be largely understood as the outcome of the combined action of resonant gravitational perturbations and the Yarkovsky effect - two topics on which Paolo Farinella has made an outstanding contribution! - notwithstanding the fact that the different "flavors" of chaos can give rise to a wide range of outcomes, from fast escape (e.g. to NEA space) to slow (~100s My) macroscopic diffusion (e.g. spreading of families) and strange, stable-looking, chaotic orbits (ultra-slow diffusion). In this talk I am going to present an overview of these mechanisms, presenting both analytical and numerical results, and their role in understanding the long-term evolution and stability of individual bodies, asteroid groups and families.

Precisely cyclic sand: self-organization of periodically sheared frictional grains.

PubMed

Royer, John R; Chaikin, Paul M

2015-01-06

The disordered static structure and chaotic dynamics of frictional granular matter has occupied scientists for centuries, yet there are few organizational principles or guiding rules for this highly hysteretic, dissipative material. We show that cyclic shear of a granular material leads to dynamic self-organization into several phases with different spatial and temporal order. Using numerical simulations, we present a phase diagram in strain-friction space that shows chaotic dispersion, crystal formation, vortex patterns, and most unusually a disordered phase in which each particle precisely retraces its unique path. However, the system is not reversible. Rather, the trajectory of each particle, and the entire frictional, many-degrees-of-freedom system, organizes itself into a limit cycle absorbing state. Of particular note is that fact that the cyclic states are spatially disordered, whereas the ordered states are chaotic.

Precisely cyclic sand: Self-organization of periodically sheared frictional grains

PubMed Central

Royer, John R.; Chaikin, Paul M.

2015-01-01

The disordered static structure and chaotic dynamics of frictional granular matter has occupied scientists for centuries, yet there are few organizational principles or guiding rules for this highly hysteretic, dissipative material. We show that cyclic shear of a granular material leads to dynamic self-organization into several phases with different spatial and temporal order. Using numerical simulations, we present a phase diagram in strain–friction space that shows chaotic dispersion, crystal formation, vortex patterns, and most unusually a disordered phase in which each particle precisely retraces its unique path. However, the system is not reversible. Rather, the trajectory of each particle, and the entire frictional, many–degrees-of-freedom system, organizes itself into a limit cycle absorbing state. Of particular note is that fact that the cyclic states are spatially disordered, whereas the ordered states are chaotic. PMID:25538298

Color image encryption using random transforms, phase retrieval, chaotic maps, and diffusion

NASA Astrophysics Data System (ADS)

Annaby, M. H.; Rushdi, M. A.; Nehary, E. A.

2018-04-01

The recent tremendous proliferation of color imaging applications has been accompanied by growing research in data encryption to secure color images against adversary attacks. While recent color image encryption techniques perform reasonably well, they still exhibit vulnerabilities and deficiencies in terms of statistical security measures due to image data redundancy and inherent weaknesses. This paper proposes two encryption algorithms that largely treat these deficiencies and boost the security strength through novel integration of the random fractional Fourier transforms, phase retrieval algorithms, as well as chaotic scrambling and diffusion. We show through detailed experiments and statistical analysis that the proposed enhancements significantly improve security measures and immunity to attacks.

Mixing and segregation of microspheres in microchannel flows of mono- and bidispersed suspensions

NASA Astrophysics Data System (ADS)

Gao, C.; Xu, B.; Gilchrist, J. F.

2009-03-01

We investigate the mixing and segregation of mono- and bidispersed microsphere suspensions in microchannel flows. These flows are common in biological microelectromechanical systems (BioMEMS) applications handling blood or suspensions of DNA. Suspension transport in pressure driven flows is significantly hindered by shear-induced migration, where particles migrate away from the walls and are focused in the center due to multibody hydrodynamic interactions. The microchannels used in this study have geometries that induce chaotic advection in Newtonian fluids. Our results show that mixing in straight, herringbone and staggered herringbone channels depends strongly on volume fraction. Due to this complex interplay of advection and shear-induced migration, a staggered herringbone channel that typically results in chaotic mixing is not always effective for dispersing particles. The maximum degree of segregation is observed in a straight channel once the maximum packing fraction is reached at channel center. We modify a one-dimensional suspension balance model [R. Miller and J. Morris, J. Non-Newtonian Fluid Mech. 135, 149 (2006)] to describe the behavior at the center of the straight channel. The degree of mixing is then calculated as a function of bulk volume fraction, predicting the volume fraction that results in the maximum degree of segregation. In bidispersed suspension flow, it is shown that mixing of the larger species is enhanced in straight and staggered herringbone channels while segregation is enhanced at moderate volume fractions in herringbone channels. This suggests mixing and separations can be tailored by adjusting both the suspension properties and the channel geometry.

Chaotic dynamics of large-scale double-diffusive convection in a porous medium

NASA Astrophysics Data System (ADS)

Kondo, Shutaro; Gotoda, Hiroshi; Miyano, Takaya; Tokuda, Isao T.

2018-02-01

We have studied chaotic dynamics of large-scale double-diffusive convection of a viscoelastic fluid in a porous medium from the viewpoint of dynamical systems theory. A fifth-order nonlinear dynamical system modeling the double-diffusive convection is theoretically obtained by incorporating the Darcy-Brinkman equation into transport equations through a physical dimensionless parameter representing porosity. We clearly show that the chaotic convective motion becomes much more complicated with increasing porosity. The degree of dynamic instability during chaotic convective motion is quantified by two important measures: the network entropy of the degree distribution in the horizontal visibility graph and the Kaplan-Yorke dimension in terms of Lyapunov exponents. We also present an interesting on-off intermittent phenomenon in the probability distribution of time intervals exhibiting nearly complete synchronization.

Polariton Chimeras: Bose-Einstein Condensates with Intrinsic Chaoticity and Spontaneous Long-Range Ordering

NASA Astrophysics Data System (ADS)

Gavrilov, S. S.

2018-01-01

The system of cavity polaritons driven by a plane electromagnetic wave is found to undergo the spontaneous breaking of spatial symmetry, which results in a lifted phase locking with respect to the driving field and, consequently, in the possibility of internal ordering. In particular, periodic spin and intensity patterns arise in polariton wires; they exhibit strong long-range order and can serve as media for signal transmission. Such patterns have the properties of dynamical chimeras: they are formed spontaneously in perfectly homogeneous media and can be partially chaotic. The reported new mechanism of chimera formation requires neither time-delayed feedback loops nor nonlocal interactions.

Stochastic epidemic outbreaks: why epidemics are like lasers

NASA Astrophysics Data System (ADS)

Schwartz, Ira B.; Billings, Lora

2004-05-01

Many diseases, such as childhood diseases, dengue fever, and West Nile virus, appear to oscillate randomly as a function of seasonal environmental or social changes. Such oscillations appear to have a chaotic bursting character, although it is still uncertain how much is due to random fluctuations. Such bursting in the presence of noise is also observed in driven lasers. In this talk, I will show how noise can excite random outbreaks in simple models of seasonally driven outbreaks, as well as lasers. The models for both population dynamics will be shown to share the same class of underlying topology, which plays a major role in the cause of observed stochastic bursting.

Microscopic reversibility and memory in soft crystals undergoing large deformations

NASA Astrophysics Data System (ADS)

Rosenfeld, Liat; Stan, Claudiu; Tang, Sindy K. Y.

2014-11-01

In this study, we explore the transition from reversible to chaotic behavior in an oscillatory shear flow of water-in-oil emulsions. The emulsion was injected through a microchannel and was forced to rearrange due to a central constriction in the channel. We study the motion of the individual droplets and their neighbors in order to determine their ability to retain their original position after several cycles of oscillations. We have found that the emulsion exhibit behaviors that vary from complete reversibility to complete irreversibility depending on the volume fraction, velocity and strain rate. The reversibility, both in the trajectory and the deformation of every drop, is reproducible even when the drops undergo many rearrangement events over distances of >150 droplet diameters. Moreover, the deformability of the drops and the high volume fraction are crucial conditions for the onset of reversibility. We provide here the first direct visualization and physical analysis of this phenomenon. This work is an important step in describing the flow of concentrated emulsions and suspensions in microchannels and is therefore crucial for understanding the behavior of droplets, bubbles and particles in droplet microfluidic applications.

Quantification of chaotic strength and mixing in a micro fluidic system

NASA Astrophysics Data System (ADS)

Kim, Ho Jun; Beskok, Ali

2007-11-01

Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in micro fluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. The 'chaotic electroosmotic stirrer' of Qian and Bau (2002 Anal. Chem. 74 3616-25) is utilized as the benchmark case due to its well-defined flow kinematics. Lagrangian particle tracking methods are utilized to study particle dispersion in the conceptual device using spectral element and fourth-order Runge-Kutta discretizations in space and time, respectively. Stirring efficiency is predicted using the stirring index based on the box counting method, and Poincaré sections are utilized to identify the chaotic and regular regions under various actuation conditions. Finite time Lyapunov exponents are calculated to quantify the chaotic strength, while the probability density function of the stretching field is utilized as an alternative method to demonstrate the statistical analysis of chaotic and partially chaotic cases. Mixing index inverse, based on the standard deviation of scalar species distribution, is utilized as a metric to quantify the mixing efficiency. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing time (tm) is characterized as a function of the Pe number, and tm ~ ln(Pe) scaling is demonstrated for fully chaotic cases, while tm ~ Peα scaling with α ≈ 0.33 and α = 0.5 are observed for partially chaotic and regular cases, respectively. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified.

Forecasting Nonlinear Chaotic Time Series with Function Expression Method Based on an Improved Genetic-Simulated Annealing Algorithm

PubMed Central

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior. PMID:26000011

Spatiotemporal chaos in mixed linear-nonlinear two-dimensional coupled logistic map lattice

NASA Astrophysics Data System (ADS)

Zhang, Ying-Qian; He, Yi; Wang, Xing-Yuan

2018-01-01

We investigate a new spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps for spatial coupling connections based on 2DCML. Here, the coupling methods are including with linear neighborhood coupling and the nonlinear chaotic map coupling of lattices, and the former 2DCML system is only a special case in the proposed system. In this paper the criteria such Kolmogorov-Sinai entropy density and universality, bifurcation diagrams, space-amplitude and snapshot pattern diagrams are provided in order to investigate the chaotic behaviors of the proposed system. Furthermore, we also investigate the parameter ranges of the proposed system which holds those features in comparisons with those of the 2DCML system and the MLNCML system. Theoretical analysis and computer simulation indicate that the proposed system contains features such as the higher percentage of lattices in chaotic behaviors for most of parameters, less periodic windows in bifurcation diagrams and the larger range of parameters for chaotic behaviors, which is more suitable for cryptography.

Chaotic dynamics and its analysis of Hindmarsh-Rose neurons by Shil’nikov approach

NASA Astrophysics Data System (ADS)

Wei, Wei; Zuo, Min

2015-08-01

In this paper, the relationship between external current stimulus and chaotic behaviors of a Hindmarsh-Rose (HR) neuron is considered. In order to find out the range of external current stimulus which will produce chaotic behaviors of an HR neuron, the Shil’nikov technique is employed. The Cardano formula is taken to obtain the threshold of the chaotic motion, and series solution to a differential equation is utilized to obtain the homoclinic orbit of HR neurons. This analysis establishes mathematically the value of external current input in generating chaotic motion of HR neurons by the Shil’nikov method. The numerical simulations are performed to support the theoretical results. Project supported by the Beijing Natural Science Foundation, China (Grant No. 4132005), the National Natural Science Foundation of China (Grant No. 61403006), the Importation and Development of High-Caliber Talents Project of Beijing Municipal Institutions, China (Grant No. YETP1449), and the Project of Scientific and Technological Innovation Platform, China (Grant No. PXM2015_014213_000063).

Experimental demonstration of the real-time online fault monitoring technique for chaos-based passive optical networks

NASA Astrophysics Data System (ADS)

Dou, Xinyu; Yin, Hongxi; Yue, Hehe; Jin, Yu; Shen, Jing; Li, Lin

2015-09-01

In this paper, a real-time online fault monitoring technique for chaos-based passive optical networks (PONs) is proposed and experimentally demonstrated. The fault monitoring is performed by the chaotic communication signal. The proof-of-concept experiments are demonstrated for two PON structures, i.e., wavelength-division-multiplexing (WDM) PON and Ethernet PON (EPON), respectively. For WDM PON, two monitoring approaches are investigated, one deploying a chaotic optical time domain reflectometry (OTDR) for each transmitter, and the other using only one tunable chaotic OTDR. The experimental results show that the faults at beyond 20 km from the OLT can be detected and located. The spatial resolution of the tunable chaotic OTDR is an order of magnitude of centimeter. Meanwhile, the monitoring process can operate in parallel with the chaotic optical secure communications. The proposed technique has benefits of real-time, online, precise fault location, and simple realization, which will significantly reduce the cost of operation, administration and maintenance (OAM) of PON.

Forecasting nonlinear chaotic time series with function expression method based on an improved genetic-simulated annealing algorithm.

PubMed

Wang, Jun; Zhou, Bi-hua; Zhou, Shu-dao; Sheng, Zheng

2015-01-01

The paper proposes a novel function expression method to forecast chaotic time series, using an improved genetic-simulated annealing (IGSA) algorithm to establish the optimum function expression that describes the behavior of time series. In order to deal with the weakness associated with the genetic algorithm, the proposed algorithm incorporates the simulated annealing operation which has the strong local search ability into the genetic algorithm to enhance the performance of optimization; besides, the fitness function and genetic operators are also improved. Finally, the method is applied to the chaotic time series of Quadratic and Rossler maps for validation. The effect of noise in the chaotic time series is also studied numerically. The numerical results verify that the method can forecast chaotic time series with high precision and effectiveness, and the forecasting precision with certain noise is also satisfactory. It can be concluded that the IGSA algorithm is energy-efficient and superior.

ASTEROIDS: Living in the Kingdom of Chaos

NASA Astrophysics Data System (ADS)

Morbidelli, A.

2000-10-01

The existence of chaotic regions in the main asteroid belt, related with the lowest-order mean-motion and secular resonances, has long been known. However, only in the last decade have semi-analytic theories allowed a proper understanding of the chaotic behavior observed in numerical simulations which accurately incorporate the entire planetary system. The most spectacular result has been the discovery that the asteroids in some of these resonance may collide with the Sun on typical time scales of a few million year, their eccentricities being pumped to unity during their chaotic evolution. But the asteroid belt is not simply divided into violent chaotic zones and regular regions. It has been shown that the belt is criss-crossed by a large number of high-order mean-motion resonances with Jupiter or Mars, as well as by `three-body resonances' with Jupiter and Saturn. All these weak resonances cause the slow chaotic drift of the `proper' eccentricities and inclinations. The traces left by this evolution are visible, for example, in the structure of the Eos and Themis asteroid families. Weak chaos may also explain the anomalous dispersion of the eccentricities and inclinations observed in the Flora ``clan." Moreover, due to slow increases in their eccentricities, many asteroids start to cross the orbit of Mars, over a wide range of semimajor axes. The improved knowledge of the asteroid belt's chaotic structure provides, for the first time, an opportunity to build detailed quantitative models of the origin and the orbital distribution of Near-Earth Asteroids and meteorites. In turn, these models seem to imply that the semimajor axes of main-belt asteroids must also slowly evolve with time. For asteroids larger than about 20 km this is due mainly to encounters with Ceres, Pallas, and Vesta, while for smaller bodies the so-called Yarkovsky effect should dominate. Everything moves chaotically in the asteroid belt.

Clustering stock market companies via chaotic map synchronization

NASA Astrophysics Data System (ADS)

Basalto, N.; Bellotti, R.; De Carlo, F.; Facchi, P.; Pascazio, S.

2005-01-01

A pairwise clustering approach is applied to the analysis of the Dow Jones index companies, in order to identify similar temporal behavior of the traded stock prices. To this end, the chaotic map clustering algorithm is used, where a map is associated to each company and the correlation coefficients of the financial time series to the coupling strengths between maps. The simulation of a chaotic map dynamics gives rise to a natural partition of the data, as companies belonging to the same industrial branch are often grouped together. The identification of clusters of companies of a given stock market index can be exploited in the portfolio optimization strategies.

Launching the chaotic realm of iso-fractals: A short remark

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

O'Schmidt, Nathan; Katebi, Reza; Corda, Christian

In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete casemore » examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.« less

Social opinion dynamics is not chaotic

NASA Astrophysics Data System (ADS)

Lim, Chjan; Zhang, Weituo

2016-08-01

Motivated by the research on social opinion dynamics over large and dense networks, a general framework for verifying the monotonicity property of multi-agent dynamics is introduced. This allows a derivation of sociologically meaningful sufficient conditions for monotonicity that are tailor-made for social opinion dynamics, which typically have high nonlinearity. A direct consequence of monotonicity is that social opinion dynamics is nonchaotic. A key part of this framework is the definition of a partial order relation that is suitable for a large class of social opinion dynamics such as the generalized naming games. Comparisons are made to previous techniques to verify monotonicity. Using the results obtained, we extend many of the consequences of monotonicity to this class of social dynamics, including several corollaries on their asymptotic behavior, such as global convergence to consensus and tipping points of a minority fraction of zealots or leaders.

Strong Families, Tidy Houses, and Children's Values in Adult Life: Are "Chaotic", "Crowded" and "Unstable" Homes Really so Bad?

ERIC Educational Resources Information Center

Flouri, Eirini

2009-01-01

Chaotic home systems have been linked with children's adverse psychological and academic outcomes. But, as they represent a departure from the suburban ideal of space, order, and family cohesiveness and stability, they should also be linked with low support for survival values. Using longitudinal data from the 1970 British Cohort Study (BCS70)…

A Chaotic Ordered Hierarchies Consistency Analysis Performance Evaluation Model

NASA Astrophysics Data System (ADS)

Yeh, Wei-Chang

2013-02-01

The Hierarchies Consistency Analysis (HCA) is proposed by Guh in-cooperated along with some case study on a Resort to reinforce the weakness of Analytical Hierarchy Process (AHP). Although the results obtained enabled aid for the Decision Maker to make more reasonable and rational verdicts, the HCA itself is flawed. In this paper, our objective is to indicate the problems of HCA, and then propose a revised method called chaotic ordered HCA (COH in short) which can avoid problems. Since the COH is based upon Guh's method, the Decision Maker establishes decisions in a way similar to that of the original method.

Uncertainty quantification tools for multiphase gas-solid flow simulations using MFIX

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

Fox, Rodney O.; Passalacqua, Alberto

2016-02-01

Computational fluid dynamics (CFD) has been widely studied and used in the scientific community and in the industry. Various models were proposed to solve problems in different areas. However, all models deviate from reality. Uncertainty quantification (UQ) process evaluates the overall uncertainties associated with the prediction of quantities of interest. In particular it studies the propagation of input uncertainties to the outputs of the models so that confidence intervals can be provided for the simulation results. In the present work, a non-intrusive quadrature-based uncertainty quantification (QBUQ) approach is proposed. The probability distribution function (PDF) of the system response can bemore » then reconstructed using extended quadrature method of moments (EQMOM) and extended conditional quadrature method of moments (ECQMOM). The report first explains the theory of QBUQ approach, including methods to generate samples for problems with single or multiple uncertain input parameters, low order statistics, and required number of samples. Then methods for univariate PDF reconstruction (EQMOM) and multivariate PDF reconstruction (ECQMOM) are explained. The implementation of QBUQ approach into the open-source CFD code MFIX is discussed next. At last, QBUQ approach is demonstrated in several applications. The method is first applied to two examples: a developing flow in a channel with uncertain viscosity, and an oblique shock problem with uncertain upstream Mach number. The error in the prediction of the moment response is studied as a function of the number of samples, and the accuracy of the moments required to reconstruct the PDF of the system response is discussed. The QBUQ approach is then demonstrated by considering a bubbling fluidized bed as example application. The mean particle size is assumed to be the uncertain input parameter. The system is simulated with a standard two-fluid model with kinetic theory closures for the particulate phase implemented into MFIX. The effect of uncertainty on the disperse-phase volume fraction, on the phase velocities and on the pressure drop inside the fluidized bed are examined, and the reconstructed PDFs are provided for the three quantities studied. Then the approach is applied to a bubbling fluidized bed with two uncertain parameters, particle-particle and particle-wall restitution coefficients. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities and gas pressure are provided. The PDFs of the response are reconstructed using EQMOM with appropriate kernel density functions. The simulation results are compared to experimental data provided by the 2013 NETL small-scale challenge problem. Lastly, the proposed procedure is demonstrated by considering a riser of a circulating fluidized bed as an example application. The mean particle size is considered to be the uncertain input parameter. Contour plots of the mean and standard deviation of solid volume fraction, solid phase velocities, and granular temperature are provided. Mean values and confidence intervals of the quantities of interest are compared to the experiment results. The univariate and bivariate PDF reconstructions of the system response are performed using EQMOM and ECQMOM.« less

Modelos autoconsistentes de sistemas estelares cuspidales y triaxiales con distribución de velocidades casi isotrópica

NASA Astrophysics Data System (ADS)

Carpintero, D. D.; Muzzio, J. C.; Navone, H. D.; Zorzi, A. F.

It has been shown in many works that it is possible to build stable, self-consistent models of triaxial stellar systems, even with cusps, and containing high percentages of chaotic orbits. Since all these models have been obtained from cold collapses, their velocity distributions are strongly radial. Also, chaos was computed using either Lyapunov exponents or SALI. However, models obtained by adiabatic deformation of spherical systems, in which the velocity distribution is more isotropic, showed a very low level of chaos, though it must be noted that the method of detecting chaos used in this case, namely the variation of orbital frequencies, is less sensitive than the abovementioned methods. In this work, we present models obtained by adiabatic deformation, in which we compute the fraction of chaotic orbits using both Lyapunov exponents and variation of orbital frequencies. Our results show that the percentages of chaotic orbits is significant, though they are smaller than those obtained in models with strong radial velocity components. FULL TEXT IN SPANISH

A comparative analysis of chaotic particle swarm optimizations for detecting single nucleotide polymorphism barcodes.

PubMed

Chuang, Li-Yeh; Moi, Sin-Hua; Lin, Yu-Da; Yang, Cheng-Hong

2016-10-01

Evolutionary algorithms could overcome the computational limitations for the statistical evaluation of large datasets for high-order single nucleotide polymorphism (SNP) barcodes. Previous studies have proposed several chaotic particle swarm optimization (CPSO) methods to detect SNP barcodes for disease analysis (e.g., for breast cancer and chronic diseases). This work evaluated additional chaotic maps combined with the particle swarm optimization (PSO) method to detect SNP barcodes using a high-dimensional dataset. Nine chaotic maps were used to improve PSO method results and compared the searching ability amongst all CPSO methods. The XOR and ZZ disease models were used to compare all chaotic maps combined with PSO method. Efficacy evaluations of CPSO methods were based on statistical values from the chi-square test (χ 2 ). The results showed that chaotic maps could improve the searching ability of PSO method when population are trapped in the local optimum. The minor allele frequency (MAF) indicated that, amongst all CPSO methods, the numbers of SNPs, sample size, and the highest χ 2 value in all datasets were found in the Sinai chaotic map combined with PSO method. We used the simple linear regression results of the gbest values in all generations to compare the all methods. Sinai chaotic map combined with PSO method provided the highest β values (β≥0.32 in XOR disease model and β≥0.04 in ZZ disease model) and the significant p-value (p-value<0.001 in both the XOR and ZZ disease models). The Sinai chaotic map was found to effectively enhance the fitness values (χ 2 ) of PSO method, indicating that the Sinai chaotic map combined with PSO method is more effective at detecting potential SNP barcodes in both the XOR and ZZ disease models. Copyright © 2016 Elsevier B.V. All rights reserved.

Is the normal heart rate ``chaotic'' due to respiration?

NASA Astrophysics Data System (ADS)

Wessel, Niels; Riedl, Maik; Kurths, Jürgen

2009-06-01

The incidence of cardiovascular diseases increases with the growth of the human population and an aging society, leading to very high expenses in the public health system. Therefore, it is challenging to develop sophisticated methods in order to improve medical diagnostics. The question whether the normal heart rate is chaotic or not is an attempt to elucidate the underlying mechanisms of cardiovascular dynamics and therefore a highly controversial topical challenge. In this contribution we demonstrate that linear and nonlinear parameters allow us to separate completely the data sets of the three groups provided for this controversial topic in nonlinear dynamics. The question whether these time series are chaotic or not cannot be answered satisfactorily without investigating the underlying mechanisms leading to them. We give an example of the dominant influence of respiration on heart beat dynamics, which shows that observed fluctuations can be mostly explained by respiratory modulations of heart rate and blood pressure (coefficient of determination: 96%). Therefore, we recommend reformulating the following initial question: "Is the normal heart rate chaotic?" We rather ask the following: "Is the normal heart rate `chaotic' due to respiration?"

Chaos in the sunspot cycle - Analysis and prediction

NASA Technical Reports Server (NTRS)

Mundt, Michael D.; Maguire, W. Bruce, II; Chase, Robert R. P.

1991-01-01

The variability of solar activity over long time scales, given semiquantitatively by measurements of sunspot numbers, is examined as a nonlinear dynamical system. First, a discussion of the data set used and the techniques utilized to reduce the noise and capture the long-term dynamics inherent in the data is presented. Subsequently, an attractor is reconstructed from the data set using the method of time delays. The reconstructed attractor is then used to determine both the dimension of the underlying system and also the largest Lyapunov exponent, which together indicate that the sunspot cycle is indeed chaotic and also low dimensional. In addition, recent techniques of exploiting chaotic dynamics to provide accurate, short-term predictions are utilized in order to improve upon current forecasting methods and also to place theoretical limits on predictability extent. The results are compared to chaotic solar-dynamo models as a possible physically motivated source of this chaotic behavior.

Applying elliptic curve cryptography to a chaotic synchronisation system: neural-network-based approach

NASA Astrophysics Data System (ADS)

Hsiao, Feng-Hsiag

2017-10-01

In order to obtain double encryption via elliptic curve cryptography (ECC) and chaotic synchronisation, this study presents a design methodology for neural-network (NN)-based secure communications in multiple time-delay chaotic systems. ECC is an asymmetric encryption and its strength is based on the difficulty of solving the elliptic curve discrete logarithm problem which is a much harder problem than factoring integers. Because it is much harder, we can get away with fewer bits to provide the same level of security. To enhance the strength of the cryptosystem, we conduct double encryption that combines chaotic synchronisation with ECC. According to the improved genetic algorithm, a fuzzy controller is synthesised to realise the exponential synchronisation and achieves optimal H∞ performance by minimising the disturbances attenuation level. Finally, a numerical example with simulations is given to demonstrate the effectiveness of the proposed approach.

Proving Chaotic Behavior of CBC Mode of Operation

NASA Astrophysics Data System (ADS)

Abidi, Abdessalem; Wang, Qianxue; Bouallegue, Belgacem; Machhout, Mohsen; Guyeux, Christophe

2016-06-01

The cipher block chaining (CBC) mode of operation was invented by IBM (International Business Machine) in 1976. It presents a very popular way of encrypting that is used in various applications. In this paper, we have mathematically proven that, under some conditions, the CBC mode of operation can admit a chaotic behavior according to Devaney. Some cases will be properly studied in order to provide evidence for this idea.

Chaotic coordinates for the Large Helical Device

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

Hudson, S. R., E-mail: shudson@pppl.gov; Suzuki, Y.

The theory of quadratic-flux-minimizing (QFM) surfaces is reviewed, and numerical techniques that allow high-order QFM surfaces to be efficiently constructed for experimentally relevant, non-integrable magnetic fields are described. As a practical example, the chaotic edge of the magnetic field in the Large Helical Device (LHD) is examined. A precise technique for finding the boundary surface is implemented, the hierarchy of partial barriers associated with the near-critical cantori is constructed, and a coordinate system, which we call chaotic coordinates, that is based on a selection of QFM surfaces is constructed that simplifies the description of the magnetic field, so that fluxmore » surfaces become “straight” and islands become “square.”.« less

Design and implementation of EP-based PID controller for chaos synchronization of Rikitake circuit systems.

PubMed

Hou, Yi-You

2017-09-01

This article addresses an evolutionary programming (EP) algorithm technique-based and proportional-integral-derivative (PID) control methods are established to guarantee synchronization of the master and slave Rikitake chaotic systems. For PID synchronous control, the evolutionary programming (EP) algorithm is used to find the optimal PID controller parameters k p , k i , k d by integrated absolute error (IAE) method for the convergence conditions. In order to verify the system performance, the basic electronic components containing operational amplifiers (OPAs), resistors, and capacitors are used to implement the proposed chaotic Rikitake systems. Finally, the experimental results validate the proposed Rikitake chaotic synchronization approach. Copyright © 2017. Published by Elsevier Ltd.

Illusion optics in chaotic light

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

Zhang Suheng; Gan Shu; Xiong Jun

2010-08-15

The time-reversal process provides the possibility to counteract the time evolution of a physical system. Recent research has shown that such a process can occur in the first-order field correlation of chaotic light and result in the spatial interference and phase-reversal diffraction in an unbalanced interferometer. Here we report experimental investigations on the invisibility cloak and illusion phenomena in chaotic light. In an unbalanced interferometer illuminated by thermal light, we have observed the cloak effect and the optical transformation of one object into another object. The experimental results can be understood by the phase-reversal diffraction, and they demonstrate the theoreticalmore » proposal of similar effects in complementary media.« less

A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata

NASA Astrophysics Data System (ADS)

Enayatifar, Rasul; Sadaei, Hossein Javedani; Abdullah, Abdul Hanan; Lee, Malrey; Isnin, Ismail Fauzi

2015-08-01

Currently, there are many studies have conducted on developing security of the digital image in order to protect such data while they are sending on the internet. This work aims to propose a new approach based on a hybrid model of the Tinkerbell chaotic map, deoxyribonucleic acid (DNA) and cellular automata (CA). DNA rules, DNA sequence XOR operator and CA rules are used simultaneously to encrypt the plain-image pixels. To determine rule number in DNA sequence and also CA, a 2-dimension Tinkerbell chaotic map is employed. Experimental results and computer simulations, both confirm that the proposed scheme not only demonstrates outstanding encryption, but also resists various typical attacks.

Gross-Pitaevski map as a chaotic dynamical system.

PubMed

Guarneri, Italo

2017-03-01

The Gross-Pitaevski map is a discrete time, split-operator version of the Gross-Pitaevski dynamics in the circle, for which exponential instability has been recently reported. Here it is studied as a classical dynamical system in its own right. A systematic analysis of Lyapunov exponents exposes strongly chaotic behavior. Exponential growth of energy is then shown to be a direct consequence of rotational invariance and for stationary solutions the full spectrum of Lyapunov exponents is analytically computed. The present analysis includes the "resonant" case, when the free rotation period is commensurate to 2π, and the map has countably many constants of the motion. Except for lowest-order resonances, this case exhibits an integrable-chaotic transition.

Synchronized chaotic targeting and acceleration of surface chemistry in prebiotic hydrothermal microenvironments

PubMed Central

Priye, Aashish; Yu, Yuncheng; Hassan, Yassin A.; Ugaz, Victor M.

2017-01-01

Porous mineral formations near subsea alkaline hydrothermal vents embed microenvironments that make them potential hot spots for prebiotic biochemistry. But, synthesis of long-chain macromolecules needed to support higher-order functions in living systems (e.g., polypeptides, proteins, and nucleic acids) cannot occur without enrichment of chemical precursors before initiating polymerization, and identifying a suitable mechanism has become a key unanswered question in the origin of life. Here, we apply simulations and in situ experiments to show how 3D chaotic thermal convection—flows that naturally permeate hydrothermal pore networks—supplies a robust mechanism for focused accumulation at discrete targeted surface sites. This interfacial enrichment is synchronized with bulk homogenization of chemical species, yielding two distinct processes that are seemingly opposed yet synergistically combine to accelerate surface reaction kinetics by several orders of magnitude. Our results suggest that chaotic thermal convection may play a previously unappreciated role in mediating surface-catalyzed synthesis in the prebiotic milieu. PMID:28119504

Synchronization of an Inertial Neural Network With Time-Varying Delays and Its Application to Secure Communication.

PubMed

Lakshmanan, Shanmugam; Prakash, Mani; Lim, Chee Peng; Rakkiyappan, Rajan; Balasubramaniam, Pagavathigounder; Nahavandi, Saeid

2018-01-01

In this paper, synchronization of an inertial neural network with time-varying delays is investigated. Based on the variable transformation method, we transform the second-order differential equations into the first-order differential equations. Then, using suitable Lyapunov-Krasovskii functionals and Jensen's inequality, the synchronization criteria are established in terms of linear matrix inequalities. Moreover, a feedback controller is designed to attain synchronization between the master and slave models, and to ensure that the error model is globally asymptotically stable. Numerical examples and simulations are presented to indicate the effectiveness of the proposed method. Besides that, an image encryption algorithm is proposed based on the piecewise linear chaotic map and the chaotic inertial neural network. The chaotic signals obtained from the inertial neural network are utilized for the encryption process. Statistical analyses are provided to evaluate the effectiveness of the proposed encryption algorithm. The results ascertain that the proposed encryption algorithm is efficient and reliable for secure communication applications.

Improved synchronization criteria for time-delayed chaotic Lur'e systems using sampled-data control

NASA Astrophysics Data System (ADS)

Duan, Wenyong; Li, Yan; Fu, Xiaorong; Du, Baozhu

2017-02-01

This paper is concerned with the synchronization for a class of time-delayed chaotic Lur’e systems using sampled-data control. Both of time-varying and time-invariant delays are considered. New criteria are proposed in terms of linear matrix inequalities (LMIs) by employing a modified LKF combined with the delay-fraction theory and some novel terms. The criteria are less conservative than some previous ones and a longer sampling period is achieved under the new results. Furthermore, the derived conditions are employed to design a sampled-data controller. The desired controller gain matrix can be obtained by means of the LMI approach. Finally, a numerical examples and simulations on Chua’s circuit is presented to show the effectiveness of the proposed approach.

Mixing Silicate Melts with High Viscosity Contrast by Chaotic Dynamics: Results from a New Experimental Device

NASA Astrophysics Data System (ADS)

de Campos, Cristina; Perugini, Diego; Ertel-Ingrisch, Werner; Dingwell, Donald B.; Poli, Giampiero

2010-05-01

A new experimental device has been developed to perform chaotic mixing between high viscosity melts under controlled fluid-dynamic conditions. The apparatus is based on the Journal Bearing System (JBS). It consists of an outer cylinder hosting the melts of interest and an inner cylinder, which is eccentrically located. Both cylinders can be independently moved to generate chaotic streamlines in the mixing system. Two experiments were performed using as end-members different proportions of a peralkaline haplogranite and a mafic melt, corresponding to the 1 atm eutectic composition in the An-Di binary system. The two melts were stirred together in the JBS for ca. two hours, at 1,400° C and under laminar fluid dynamic condition (Re of the order of 10-7). The viscosity ratio between the two melts, at the beginning of the experiment, was of the order of 103. Optical analyses of experimental samples revealed, at short length scale (of the order of μm), a complex pattern of mixed structures. These consisted of an intimate distribution of filaments; a complex inter-fingering of the two melts. Such features are typically observed in rocks thought to be produced by magma mixing processes. Stretching and folding dynamics between the melts induced chaotic flow fields and generated wide compositional interfaces. In this way, chemical diffusion processes become more efficient, producing melts with highly heterogeneous compositions. A remarkable modulation of compositional fields has been obtained by performing short time-scale experiments and using melts with a high viscosity ratio. This indicates that chaotic mixing of magmas can be a very efficient process in modulating compositional variability in igneous systems, especially under high viscosity ratios and laminar fluid-dynamic regimes. Our experimental device may replicate magma mixing features, observed in natural rocks, and therefore open new frontiers in the study of this important petrologic and volcanological process.

Fermi acceleration in time-dependent billiards: theory of the velocity diffusion in conformally breathing fully chaotic billiards

NASA Astrophysics Data System (ADS)

Batistić, Benjamin; Robnik, Marko

2011-09-01

We study aspects of the Fermi acceleration (the unbounded growth of the energy) in a certain class of time-dependent 2D billiards. Specifically, we look at the conformally breathing billiards (periodic oscillation of the boundary which preserves the shape of the billiard at all times), which are fully chaotic as static (frozen) billiards, and we show that for large velocities around v0 and for not too long times, we observe just normal diffusion of the velocity as a function of the physical (continuous) time, around v0. However, the diffusion is not homogeneous, as the diffusion constant D depends on v0 as a power law D∝1/v30. Taking this into account, we show that to the leading order the average velocity v(n) as a function of the number of collisions n obeys a power law v∝n1/6 thus, the Fermi acceleration exponent is β = 1/6, which is in excellent agreement with the numerical calculations of the fully chaotic oval billiard, the Sinai billiard and the cardioid billiard. The error of the velocity estimates is of the order 1/v2. Thus, the higher the velocity, the better our analytic approximation. Moreover, we derive the underlying universal equation of the velocity dynamics of the time-dependent conformally breathing billiards, correct up to and including the order 1/v in the regime of the large velocity of the particle v. This universal equation does not depend on the dynamical properties of the system (integrability, ergodicity, chaoticity). We present the results of the numerical simulations for three billiards in complete agreement with the theory. We believe that this is a first step towards theoretical understanding of the power law growth and the Fermi acceleration exponents in 2D billiards, although our theory is so far specialized to the conformally breathing fully chaotic billiards.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations.

PubMed

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, R e . Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

On the control of the chaotic attractors of the 2-d Navier-Stokes equations

NASA Astrophysics Data System (ADS)

Smaoui, Nejib; Zribi, Mohamed

2017-03-01

The control problem of the chaotic attractors of the two dimensional (2-d) Navier-Stokes (N-S) equations is addressed in this paper. First, the Fourier Galerkin method based on a reduced-order modelling approach developed by Chen and Price is applied to the 2-d N-S equations to construct a fifth-order system of nonlinear ordinary differential equations (ODEs). The dynamics of the fifth-order system was studied by analyzing the system's attractor for different values of Reynolds number, Re. Then, control laws are proposed to drive the states of the ODE system to a desired attractor. Finally, an adaptive controller is designed to synchronize two reduced order ODE models having different Reynolds numbers and starting from different initial conditions. Simulation results indicate that the proposed control schemes work well.

Stochastic optimization model for order acceptance with multiple demand classes and uncertain demand/supply

NASA Astrophysics Data System (ADS)

Yang, Wen; Fung, Richard Y. K.

2014-06-01

This article considers an order acceptance problem in a make-to-stock manufacturing system with multiple demand classes in a finite time horizon. Demands in different periods are random variables and are independent of one another, and replenishments of inventory deviate from the scheduled quantities. The objective of this work is to maximize the expected net profit over the planning horizon by deciding the fraction of the demand that is going to be fulfilled. This article presents a stochastic order acceptance optimization model and analyses the existence of the optimal promising policies. An example of a discrete problem is used to illustrate the policies by applying the dynamic programming method. In order to solve the continuous problems, a heuristic algorithm based on stochastic approximation (HASA) is developed. Finally, the computational results of a case example illustrate the effectiveness and efficiency of the HASA approach, and make the application of the proposed model readily acceptable.

The Cooling History and Structure of the Ordinary Chondrite Parent Bodies

NASA Technical Reports Server (NTRS)

Benoit, P. H.; Sears, D. W. G.

1996-01-01

Most major meteorite classes exhibit significant ranges of metamorphism. The effects of metamorphism have been extensively characterized, but the heat source(s) and the metamorphic environment are unknown. Proposed beat sources include Al-26, Fe-60, electromagnetic induction, and impact. It is typically assumed that metamorphism occurred in parent bodies of some sort, but it uncertain whether these bodies were highly structured ("onion skins") or were chaotic mixes of material ("rubble piles"). The lack of simple trends of metallographic cooling rates with petrologic type has been considered supportive of both concepts. In this study, we use induced thermoluminescence (TL) as an indicator of thermal history. The TL of ordinary chondrites is produced by sodic feldspar, and the induced TL peak temperature is related to its crystallographic order/disorder. Ordered feldspar has TL peak temperatures of approx. 120 C, and disordered feldspar has TL peak temperatures of approx. 220 C. While ordered feldspar can be easily disordered in the laboratory by heating above 650 C and is easily quenched in the disordered form, producing ordered feldspar requires cooling at geologic cooling rates. We have measured the induced TL properties of 101 equilibrated ordinary chondrites, including 49 H, 29 L, and 23 LL chondrites. For the H chondrites there is an apparent trend of decreasing induced TL peak temperature with increasing petrologic type. H4 chondrites exhibit a tight range of TL peak temperatures, 190 C - 200 C, while H6 chondrites exhibit TL peak temperatures between 180 C and 190 C. H5 chondrites cover the range between H4 and H6, and also extend up to 210 C. Similar results are obtained for LL chondfiles and most L6 chondrites have lower induced TL peak temperatures than L5 chondrites.

Stochastic response and bifurcation of periodically driven nonlinear oscillators by the generalized cell mapping method

NASA Astrophysics Data System (ADS)

Han, Qun; Xu, Wei; Sun, Jian-Qiao

2016-09-01

The stochastic response of nonlinear oscillators under periodic and Gaussian white noise excitations is studied with the generalized cell mapping based on short-time Gaussian approximation (GCM/STGA) method. The solutions of the transition probability density functions over a small fraction of the period are constructed by the STGA scheme in order to construct the GCM over one complete period. Both the transient and steady-state probability density functions (PDFs) of a smooth and discontinuous (SD) oscillator are computed to illustrate the application of the method. The accuracy of the results is verified by direct Monte Carlo simulations. The transient responses show the evolution of the PDFs from being Gaussian to non-Gaussian. The effect of a chaotic saddle on the stochastic response is also studied. The stochastic P-bifurcation in terms of the steady-state PDFs occurs with the decrease of the smoothness parameter, which corresponds to the deterministic pitchfork bifurcation.

Modelling and formation of spatiotemporal patterns of fractional predation system in subdiffusion and superdiffusion scenarios

NASA Astrophysics Data System (ADS)

Owolabi, Kolade M.; Atangana, Abdon

2018-02-01

This paper primarily focused on the question of how population diffusion can affect the formation of the spatial patterns in the spatial fraction predator-prey system by Turing mechanisms. Our numerical findings assert that modeling by fractional reaction-diffusion equations should be considered as an appropriate tool for studying the fundamental mechanisms of complex spatiotemporal dynamics. We observe that pure Hopf instability gives rise to the formation of spiral patterns in 2D and pure Turing instability destroys the spiral pattern and results to the formation of chaotic or spatiotemporal spatial patterns. Existence and permanence of the species is also guaranteed with the 3D simulations at some instances of time for subdiffusive and superdiffusive scenarios.

Chaotic map clustering algorithm for EEG analysis

NASA Astrophysics Data System (ADS)

Bellotti, R.; De Carlo, F.; Stramaglia, S.

2004-03-01

The non-parametric chaotic map clustering algorithm has been applied to the analysis of electroencephalographic signals, in order to recognize the Huntington's disease, one of the most dangerous pathologies of the central nervous system. The performance of the method has been compared with those obtained through parametric algorithms, as K-means and deterministic annealing, and supervised multi-layer perceptron. While supervised neural networks need a training phase, performed by means of data tagged by the genetic test, and the parametric methods require a prior choice of the number of classes to find, the chaotic map clustering gives a natural evidence of the pathological class, without any training or supervision, thus providing a new efficient methodology for the recognition of patterns affected by the Huntington's disease.

Least Squares Shadowing sensitivity analysis of chaotic limit cycle oscillations

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

Wang, Qiqi, E-mail: qiqi@mit.edu; Hu, Rui, E-mail: hurui@mit.edu; Blonigan, Patrick, E-mail: blonigan@mit.edu

2014-06-15

The adjoint method, among other sensitivity analysis methods, can fail in chaotic dynamical systems. The result from these methods can be too large, often by orders of magnitude, when the result is the derivative of a long time averaged quantity. This failure is known to be caused by ill-conditioned initial value problems. This paper overcomes this failure by replacing the initial value problem with the well-conditioned “least squares shadowing (LSS) problem”. The LSS problem is then linearized in our sensitivity analysis algorithm, which computes a derivative that converges to the derivative of the infinitely long time average. We demonstrate ourmore » algorithm in several dynamical systems exhibiting both periodic and chaotic oscillations.« less

Short-term cascaded hydroelectric system scheduling based on chaotic particle swarm optimization using improved logistic map

NASA Astrophysics Data System (ADS)

He, Yaoyao; Yang, Shanlin; Xu, Qifa

2013-07-01

In order to solve the model of short-term cascaded hydroelectric system scheduling, a novel chaotic particle swarm optimization (CPSO) algorithm using improved logistic map is introduced, which uses the water discharge as the decision variables combined with the death penalty function. According to the principle of maximum power generation, the proposed approach makes use of the ergodicity, symmetry and stochastic property of improved logistic chaotic map for enhancing the performance of particle swarm optimization (PSO) algorithm. The new hybrid method has been examined and tested on two test functions and a practical cascaded hydroelectric system. The experimental results show that the effectiveness and robustness of the proposed CPSO algorithm in comparison with other traditional algorithms.

Electric fields yield chaos in microflows

PubMed Central

Posner, Jonathan D.; Pérez, Carlos L.; Santiago, Juan G.

2012-01-01

We present an investigation of chaotic dynamics of a low Reynolds number electrokinetic flow. Electrokinetic flows arise due to couplings of electric fields and electric double layers. In these flows, applied (steady) electric fields can couple with ionic conductivity gradients outside electric double layers to produce flow instabilities. The threshold of these instabilities is controlled by an electric Rayleigh number, Rae. As Rae increases monotonically, we show here flow dynamics can transition from steady state to a time-dependent periodic state and then to an aperiodic, chaotic state. Interestingly, further monotonic increase of Rae shows a transition back to a well-ordered state, followed by a second transition to a chaotic state. Temporal power spectra and time-delay phase maps of low dimensional attractors graphically depict the sequence between periodic and chaotic states. To our knowledge, this is a unique report of a low Reynolds number flow with such a sequence of periodic-to-aperiodic transitions. Also unique is a report of strange attractors triggered and sustained through electric fluid body forces. PMID:22908251

An Exploratory Study of the Butterfly Effect Using Agent-Based Modeling

NASA Technical Reports Server (NTRS)

Khasawneh, Mahmoud T.; Zhang, Jun; Shearer, Nevan E. N.; Rodriquez-Velasquez, Elkin; Bowling, Shannon R.

2010-01-01

This paper provides insights about the behavior of chaotic complex systems, and the sensitive dependence of the system on the initial starting conditions. How much does a small change in the initial conditions of a complex system affect it in the long term? Do complex systems exhibit what is called the "Butterfly Effect"? This paper uses an agent-based modeling approach to address these questions. An existing model from NetLogo library was extended in order to compare chaotic complex systems with near-identical initial conditions. Results show that small changes in initial starting conditions can have a huge impact on the behavior of chaotic complex systems. The term the "butterfly effect" is attributed to the work of Edward Lorenz [1]. It is used to describe the sensitive dependence of the behavior of chaotic complex systems on the initial conditions of these systems. The metaphor refers to the notion that a butterfly flapping its wings somewhere may cause extreme changes in the ecological system's behavior in the future, such as a hurricane.

An Investigation of Traveling-Wave Electrophoresis using a Trigonometric Potential

NASA Astrophysics Data System (ADS)

Vopal, James

Traveling-wave electrophoresis, a technique for microfluidic separations in lab-on-achip devices, is investigated using a trigonometric model that naturally incorporates the spatial periodicity of the device. Traveling-wave electrophoresis can be used to separate high-mobility ions from low-mobility ions in forensic and medical applications, with a separation threshold that can be tuned for specific applications by simply choosing the traveling wave frequency. Our simulations predict plateaus in the average ion velocity verses the mobility, plateaus that correspond to Farey fractions and yield Devil's staircases for non-zero discreteness values. The plateaus indicate that ions with different mobilities can travel with the same average velocity. To determine the conditions for chaos, Lyapunov exponents and contact maps are employed. Through the use of contact maps, the chaotic trajectories are determined to be either narrowband or broadband. Narrowband chaotic trajectories are exhibited in the plateaus of the average velocity, while broadband chaotic trajectories are exhibited where the average velocity varies nonmonotonically with the mobility. Narrowband chaos will be investigated in future work incorporating the role of diffusion. The results of this and future work can be used to develop new tools for electrophoretic separation.

Stochastic Epidemic Outbreaks, or Why Epidemics Behave Like Lasers

NASA Astrophysics Data System (ADS)

Schwartz, Ira; Billings, Lora; Bollt, Erik; Carr, Thomas

2004-03-01

Many diseases, such childhood diseases, dengue fever, and West Nile virus, appear to oscillate randomly as a function of seasonal environmental or social changes. Such oscillations appear to have a chaotic bursting character, although it is still uncertain how much is due to random fluctuations. Such bursting in the presence of noise is also observed in driven lasers. In this talk, I will show how noise can excite random outbreaks in simple models of seasonally driven outbreaks, as well as lasers. The models for both population dynamics will be shown to share the same class of underlying topology, which plays a major role in the cause of observed stochastic bursting. New tools for predicting stcohastic outbreaks will be presented.

Nonlinear fractional order proportion-integral-derivative active disturbance rejection control method design for hypersonic vehicle attitude control

NASA Astrophysics Data System (ADS)

Song, Jia; Wang, Lun; Cai, Guobiao; Qi, Xiaoqiang

2015-06-01

Near space hypersonic vehicle model is nonlinear, multivariable and couples in the reentry process, which are challenging for the controller design. In this paper, a nonlinear fractional order proportion integral derivative (NFOPIλDμ) active disturbance rejection control (ADRC) strategy based on a natural selection particle swarm (NSPSO) algorithm is proposed for the hypersonic vehicle flight control. The NFOPIλDμ ADRC method consists of a tracking-differentiator (TD), an NFOPIλDμ controller and an extended state observer (ESO). The NFOPIλDμ controller designed by combining an FOPIλDμ method and a nonlinear states error feedback control law (NLSEF) is to overcome concussion caused by the NLSEF and conversely compensate the insufficiency for relatively simple and rough signal processing caused by the FOPIλDμ method. The TD is applied to coordinate the contradiction between rapidity and overshoot. By attributing all uncertain factors to unknown disturbances, the ESO can achieve dynamic feedback compensation for these disturbances and thus reduce their effects. Simulation results show that the NFOPIλDμ ADRC method can make the hypersonic vehicle six-degree-of-freedom nonlinear model track desired nominal signals accurately and fast, has good stability, dynamic properties and strong robustness against external environmental disturbances.

Robust Adaptive Synchronization of Ring Configured Uncertain Chaotic FitzHugh–Nagumo Neurons under Direction-Dependent Coupling

PubMed Central

Iqbal, Muhammad; Rehan, Muhammad; Hong, Keum-Shik

2018-01-01

This paper exploits the dynamical modeling, behavior analysis, and synchronization of a network of four different FitzHugh–Nagumo (FHN) neurons with unknown parameters linked in a ring configuration under direction-dependent coupling. The main purpose is to investigate a robust adaptive control law for the synchronization of uncertain and perturbed neurons, communicating in a medium of bidirectional coupling. The neurons are assumed to be different and interconnected in a ring structure. The strength of the gap junctions is taken to be different for each link in the network, owing to the inter-neuronal coupling medium properties. Robust adaptive control mechanism based on Lyapunov stability analysis is employed and theoretical criteria are derived to realize the synchronization of the network of four FHN neurons in a ring form with unknown parameters under direction-dependent coupling and disturbances. The proposed scheme for synchronization of dissimilar neurons, under external electrical stimuli, coupled in a ring communication topology, having all parameters unknown, and subject to directional coupling medium and perturbations, is addressed for the first time as per our knowledge. To demonstrate the efficacy of the proposed strategy, simulation results are provided. PMID:29535622

Time Series Analysis of the Bacillus subtilis Sporulation Network Reveals Low Dimensional Chaotic Dynamics.

PubMed

Lecca, Paola; Mura, Ivan; Re, Angela; Barker, Gary C; Ihekwaba, Adaoha E C

2016-01-01

Chaotic behavior refers to a behavior which, albeit irregular, is generated by an underlying deterministic process. Therefore, a chaotic behavior is potentially controllable. This possibility becomes practically amenable especially when chaos is shown to be low-dimensional, i.e., to be attributable to a small fraction of the total systems components. In this case, indeed, including the major drivers of chaos in a system into the modeling approach allows us to improve predictability of the systems dynamics. Here, we analyzed the numerical simulations of an accurate ordinary differential equation model of the gene network regulating sporulation initiation in Bacillus subtilis to explore whether the non-linearity underlying time series data is due to low-dimensional chaos. Low-dimensional chaos is expectedly common in systems with few degrees of freedom, but rare in systems with many degrees of freedom such as the B. subtilis sporulation network. The estimation of a number of indices, which reflect the chaotic nature of a system, indicates that the dynamics of this network is affected by deterministic chaos. The neat separation between the indices obtained from the time series simulated from the model and those obtained from time series generated by Gaussian white and colored noise confirmed that the B. subtilis sporulation network dynamics is affected by low dimensional chaos rather than by noise. Furthermore, our analysis identifies the principal driver of the networks chaotic dynamics to be sporulation initiation phosphotransferase B (Spo0B). We then analyzed the parameters and the phase space of the system to characterize the instability points of the network dynamics, and, in turn, to identify the ranges of values of Spo0B and of the other drivers of the chaotic dynamics, for which the whole system is highly sensitive to minimal perturbation. In summary, we described an unappreciated source of complexity in the B. subtilis sporulation network by gathering evidence for the chaotic behavior of the system, and by suggesting candidate molecules driving chaos in the system. The results of our chaos analysis can increase our understanding of the intricacies of the regulatory network under analysis, and suggest experimental work to refine our behavior of the mechanisms underlying B. subtilis sporulation initiation control.

Computational Study of Chaotic and Ordered Solutions of the Kuramoto-Sivashinsky Equation

NASA Technical Reports Server (NTRS)

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1996-01-01

We report the results of extensive numerical experiments on the Kuramoto-Sivashinsky equation in the strongly chaotic regime as the viscosity parameter is decreased and increasingly more linearly unstable modes enter the dynamics. General initial conditions are used and evolving states do not assume odd-parity. A large number of numerical experiments are employed in order to obtain quantitative characteristics of the dynamics. We report on different routes to chaos and provide numerical evidence and construction of strange attractors with self-similar characteristics. As the 'viscosity' parameter decreases the dynamics becomes increasingly more complicated and chaotic. In particular it is found that regular behavior in the form of steady state or steady state traveling waves is supported amidst the time-dependent and irregular motions. We show that multimodal steady states emerge and are supported on decreasing windows in parameter space. In addition we invoke a self-similarity property of the equation, to show that these profiles are obtainable from global fixed point attractors of the Kuramoto-Sivashinsky equation at much larger values of the viscosity.

Critical edge between frozen extinction and chaotic life

NASA Astrophysics Data System (ADS)

Monetti, Roberto A.; Albano, Ezequiel V.

1995-12-01

The cellular automata ``game of life'' (GL) proposed by J. Conway simulates the dynamic evolution of a society of living organisms. It has been extensively studied in order to understand the emergence of complexity and diversity from a set of local rules. More recently, the capability of GL to self-oranize into a critical state has opened an interesting debate. In this work we adopt a different approach: by introducing stochastic rules in the GL it is found that ``life'' exhibits a very rich critical behavior. Discontinuous (first-order) irreversible phase transitions (IPT's) between an extinct phase and a steady state supporting life are found. A precise location of the critical edge is achieved by means of an epidemic analysis, which also allows us to determine dynamic critical exponents. Furthermore, by means of a damage spreading study we conclude that the living phase is chaotic. The edge of the frozen-chaotic transition coincides with that of the IPT's life extinction. Close to the edge, fractal spreading of the damage is observed; however, deep inside the living phase such spreading becomes homogeneous. (c) 1995 The American Physical Society

Cascade Error Projection with Low Bit Weight Quantization for High Order Correlation Data

NASA Technical Reports Server (NTRS)

Duong, Tuan A.; Daud, Taher

1998-01-01

In this paper, we reinvestigate the solution for chaotic time series prediction problem using neural network approach. The nature of this problem is such that the data sequences are never repeated, but they are rather in chaotic region. However, these data sequences are correlated between past, present, and future data in high order. We use Cascade Error Projection (CEP) learning algorithm to capture the high order correlation between past and present data to predict a future data using limited weight quantization constraints. This will help to predict a future information that will provide us better estimation in time for intelligent control system. In our earlier work, it has been shown that CEP can sufficiently learn 5-8 bit parity problem with 4- or more bits, and color segmentation problem with 7- or more bits of weight quantization. In this paper, we demonstrate that chaotic time series can be learned and generalized well with as low as 4-bit weight quantization using round-off and truncation techniques. The results show that generalization feature will suffer less as more bit weight quantization is available and error surfaces with the round-off technique are more symmetric around zero than error surfaces with the truncation technique. This study suggests that CEP is an implementable learning technique for hardware consideration.

Wigner time-delay distribution in chaotic cavities and freezing transition.

PubMed

Texier, Christophe; Majumdar, Satya N

2013-06-21

Using the joint distribution for proper time delays of a chaotic cavity derived by Brouwer, Frahm, and Beenakker [Phys. Rev. Lett. 78, 4737 (1997)], we obtain, in the limit of the large number of channels N, the large deviation function for the distribution of the Wigner time delay (the sum of proper times) by a Coulomb gas method. We show that the existence of a power law tail originates from narrow resonance contributions, related to a (second order) freezing transition in the Coulomb gas.

A PRELIMINARY STUDY ON THE FRACTAL PHENOMENON: “DISCONNECTED+ DISCONNECTED=CONNECTED”

NASA Astrophysics Data System (ADS)

Wang, Da; Liu, Shutang; Zhao, Yang

The well-known Parrondo’s paradox: “losing+losing=winning” [G. P. Harmer and D. Abbott, Parrondo’s paradox, Stat. Sci. 14 (2009) 206-213.] indicated that two games with negative gains can generate a new game with positive gain. By extending the Parrondo’s philosophy into chaos research, it was shown that the periodic alteration of two chaotic dynamics results in an ordered dynamics, that is the phenomenon: “chaos+chaos=order” [J. Almeida, D. Peralta-Salas and M. Romera, Can two chaotic systems give rise to order, Physica D 200 124-132 (2005)]. This paper further extends these researches into fractal research by proposing that two disconnected Julia sets can originate a new connected Julia set via alternating order. This new parrondian paradoxical phenomenon can be stated in the Parrondo’s terms as “disconnected+disconnected=connected”.

Chaotic Mixing in Magmatic Systems: a new experiment

NASA Astrophysics Data System (ADS)

de Campos, C. P.; Perugini, D.; Dingwell, D. B.; Poli, G.; Ertel-Ingrisch, W.; Hess, K.

2007-12-01

Previous studies on magma mixing systems have evidenced that mixing processes could be controlled by chaotic dynamics. These processes are thought to be the source of fractal structures propagating within natural magmatic systems, from meter to the micrometer length scale (Perugini et al., 2006. EPSL, 234: 669-680 and references therein). We have developed a device for experimental studies of chaotic mixing dynamics in silicate melts at high temperatures (up to 1700°C). This device has been inspired by the journal bearing or eccentric cylinder geometry for viscous fluids for the study of chaotic mixing in slow flows (Swanson and Ottino, 1990. J. Fluid Mech., 213:227-249). This geometry is thought to be an ideal system for chaotic studies because a) it is experimentally accessible/feasible for silicate rheologies and b) it is subject to an analytical solution for the stream function. In the journal bearing system the flow region, is confined in the torus between the centers of the two cylinders. Their central axes are parallel but not coincident, i. e. the cylinders are eccentric. In order to generate chaos in a flow, the streamlines must be time dependent, resulting in alternating movements between the two cylinders. This means that at least one of the cylinders has alternating rotation directions. The dimension of this new experimental device follows the required main dimensionless numbers for a chaotic flow. Our first experimental goal is to characterize the mixing process in a prototypical system (haplogranite-haplobasalt)under variable mixing protocols. muenchen.de/

Does Planck really rule out monomial inflation?

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

Enqvist, Kari; Karčiauskas, Mindaugas, E-mail: kari.enqvist@helsinki.fi, E-mail: mindaugas.karciauskas@helsinki.fi

2014-02-01

We consider the modifications of monomial chaotic inflation models due to radiative corrections induced by inflaton couplings to bosons and/or fermions necessary for reheating. To the lowest order, ignoring gravitational corrections and treating the inflaton as a classical background field, they are of the Coleman-Weinberg type and parametrized by the renormalization scale μ. In cosmology, there are not enough measurements to fix μ so that we end up with a family of models, each having a slightly different slope of the potential. We demonstrate by explicit calculation that within the family of chaotic φ{sup 2} models, some may be ruledmore » out by Planck whereas some remain perfectly viable. In contrast, radiative corrections do not seem to help chaotic φ{sup 4} models to meet the Planck constraints.« less

Inertio-elastic mixing in a straight microchannel with side wells

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

Hong, Sun Ok; Cooper-White, Justin J.; School of Chemical Engineering, University of Queensland, St Lucia, 4072 QLD

Mixing remains a challenging task in microfluidic channels because of their inherently small length scale. In this work, we propose an efficient microfluidic mixer based on the chaotic vortex dynamics of a viscoelastic flow in a straight channel with side wells. When the inertia and elasticity of a dilute polymer solution are balanced (i.e., the Reynolds number Re and Weissenberg number Wi are both on the order of 10{sup 1}), chaotic vortices appear in the side wells (inertio-elastic flow instability), enhancing the mixing of adjacent fluid streams. However, there is no chaotic vortex motion in Newtonian flows for any flowmore » rate. Efficient mixing by such an inertio-elastic instability is found to be relevant for a wide range of Re values.« less

Role of strategic planning in engineering management

NASA Technical Reports Server (NTRS)

Krishen, Kumar

1993-01-01

Today, more than ever before, engineers are faced with uncertain and sometimes chaotic environments in which to function. The traditional roles of an engineer to design, develop, and streamline a manufacturing process for a product are still valued and relevant. However, the need for an engineer to participate in the process of identifying the product to be developed, the schedule and resources required, and the goal of satisfying the customer, has become paramount to achieving the success of the enterprise. When we include these endeavors in the functions of an engineer, management of 'engineering' takes on a new dimension. In this paper, the ramifications of the changing and increased functions of an engineer and consequent impacts on engineering management are explored. The basic principles which should be invoked in order to embrace the new environment for engineering management are outlined. The ultimate finding of this study is that the enterprise strategic plan should be developed in such a way as to allow engineering management to encompass the full spectrum of the responsibilities of engineers. A consequence of this is that the fundamental elements of the strategic process can best be implemented through a project team or group approach. The paper thus concentrates on three areas: evolving environment, strategic plan, and ways to achieve enterprise success.

The development and application of multi-criteria decision-making tool with consideration of uncertainty: the selection of a management strategy for the bio-degradable fraction in the municipal solid waste.

PubMed

El Hanandeh, Ali; El-Zein, Abbas

2010-01-01

A modified version of the multi-criteria decision aid, ELECTRE III has been developed to account for uncertainty in criteria weightings and threshold values. The new procedure, called ELECTRE-SS, modifies the exploitation phase in ELECTRE III, through a new definition of the pre-order and the introduction of a ranking index (RI). The new approach accommodates cases where incomplete or uncertain preference data are present. The method is applied to a case of selecting a management strategy for the bio-degradable fraction in the municipal solid waste of Sydney. Ten alternatives are compared against 11 criteria. The results show that anaerobic digestion (AD) and composting of paper are less environmentally sound options than recycling. AD is likely to out-perform incineration where a market for heating does not exist. Moreover, landfilling can be a sound alternative, when considering overall performance and conditions of uncertainty.

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method.

PubMed

Wang, Yu; Li, Feng-Ming; Wang, Yi-Ze

2015-06-01

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two buckling cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.

Homoclinic behaviors and chaotic motions of double layered viscoelastic nanoplates based on nonlocal theory and extended Melnikov method

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

Wang, Yu; Wang, Yi-Ze; Li, Feng-Ming, E-mail: fmli@bjut.edu.cn

2015-06-15

The nonlinear dynamical equations are established for the double layered viscoelastic nanoplates (DLNP) subjected to in-plane excitation based on the nonlocal theory and von Kármán large deformation theory. The extended high dimensional homoclinic Melnikov method is employed to study the homoclinic phenomena and chaotic motions for the parametrically excited DLNP system. The criteria for the homoclinic transverse intersection for both the asynchronous and synchronous buckling cases are proposed. Lyapunov exponents and phase portraits are obtained to verify the Melnikov-type analysis. The influences of structural parameters on the transverse homoclinic orbits and homoclinic bifurcation sets are discussed for the two bucklingmore » cases. Some novel phenomena are observed in the investigation. It should be noticed that the nonlocal effect on the homoclinic behaviors and chaotic motions is quite remarkable. Hence, the small scale effect should be taken into account for homoclinic and chaotic analysis for nanostructures. It is significant that the nonlocal effect on the homoclinic phenomena for the asynchronous buckling case is quite different from that for the synchronous buckling case. Moreover, due to the van der Walls interaction between the layers, the nonlocal effect on the homoclinic behaviors and chaotic motions for high order mode is rather tiny under the asynchronous buckling condition.« less

Understanding the Chaotic Behavior of Field Lines using the Simple Map

NASA Astrophysics Data System (ADS)

Saralkar, R.; White, C.; Ali, H.; Punjabi, A.

1998-11-01

The Simple Map is given by x_n+1=x_n-ky_n(1-y_n), y_n+1=y_n+kx_n+1. Different initial values of x and y create different surfaces. We can see at what point the order begins to fade, at what point the surface breaks up and islands form, and at what point chaos occurs. The outer surfaces are chaotic as expected because the plasma is nearing the X-point in the tokamak, where the order begins to break up. We are specifically investigating two areas of the Simple Map. First we want to see what ther surfaces look like if they are magnified near the X-point. We are looking for self-similar structures in which order can be found in chaos, and chaos can be found in order. Our second investigation deals with how neighboring field lines separate in the chaotic region. We are expecting to see the distance between two close points drastically increase as we near the X-point. Reshama Saralkar and Cedric White are HU CFRT 1998 Summer Fusion High School Workshop Participants from the NASA SHARP PLUS Program. RS attends Watkins Mill High School in Gaithersburg, MD. CW attends Gwynn Park High School in Brandywine,MD. They are mentored by Dr. Ali and Dr. Punjabi of HU CFRT. 1. Punjabi et al, Phys Rev Lett 69 3322 (1992) 2. Punjabi et al, J Plasma Phys 52 91 (1994)

Quantum power source: putting in order of a Brownian motion without Maxwell's demon

NASA Astrophysics Data System (ADS)

Aristov, Vitaly V.; Nikulov, A. V.

2003-07-01

The problem of possible violation of the second law of thermodynamics is discussed. It is noted that the task of the well known challenge to the second law called Maxwell's demon is put in order a chaotic perpetual motion and if any ordered Brownian motion exists then the second law can be broken without this hypothetical intelligent entity. The postulate of absolute randomness of any Brownian motion saved the second law in the beginning of the 20th century when it was realized as perpetual motion. This postulate can be proven in the limits of classical mechanics but is not correct according to quantum mechanics. Moreover some enough known quantum phenomena, such as the persistent current at non-zero resistance, are an experimental evidence of the non-chaotic Brownian motion with non-zero average velocity. An experimental observation of a dc quantum power soruce is interperted as evidence of violation of the second law.

Chaos control for the output-constrained system by using adaptive dynamic surface technology and application to the brushless DC motor

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

Luo, Shaohua, E-mail: hua66com@163.com; School of Automation, Chongqing University, Chongqing 400044; Hou, Zhiwei

2015-12-15

In this paper, chaos control is proposed for the output- constrained system with uncertain control gain and time delay and is applied to the brushless DC motor. Using the dynamic surface technology, the controller overcomes the repetitive differentiation of backstepping and boundedness hypothesis of pre-determined control gain by incorporating radial basis function neural network and adaptive technology. The tangent barrier Lyapunov function is employed for time-delay chaotic system to prevent constraint violation. It is proved that the proposed control approach can guarantee asymptotically stable in the sense of uniformly ultimate boundedness without constraint violation. Finally, the effectiveness of the proposedmore » approach is demonstrated on the brushless DC motor example.« less

Temporal chaos in Boussinesq magnetoconvection

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

Bekki, Naoaki; Moriguchi, Hirofumi; Fundamental Science, Gifu National College of Technology, Motosu, Gifu 501-0495

2007-01-15

Two-dimensional Boussinesq magnetoconvection with idealized stress-free boundary conditions is numerically investigated in order to make clear the difference between chaos and turbulence. It is shown that the long-term behavior of magnetoconvection exhibits spatially coherent and temporally chaotic rolls in marked contrast to highly turbulent fluids. It is also shown that heat transport becomes larger anomalously when the polarity reversal of the magnetic field occurs intermittently in the case of temporally chaotic magnetoconvection. It is found that the Poincare return map of the relative maximum temperature fluctuation of partial differential equations as a function of the preceding maximum resembles the famousmore » Lorenz plot in narrow rolls of magnetoconvection. The chaotic behavior of narrow rolls for individual parameter values robustly persists up to rolls about one fifth as wide as they are high near the codimension-two bifurcation point.« less

Ordering process in the diffusively coupled logistic lattice

NASA Astrophysics Data System (ADS)

Conrado, Claudine V.; Bohr, Tomas

1991-08-01

We study the ordering process in a lattice of diffusively coupled logistic maps for increasing lattice size. Within a window of parameters, the system goes into a weakly chaotic state with long range "antiferromagnetic" order. This happens for arbitrary lattice size L and the ordering time behaves as t ~ L2 as we would expect from a picture of diffusing defects.

Phase transition of Boolean networks with partially nested canalizing functions

NASA Astrophysics Data System (ADS)

Jansen, Kayse; Matache, Mihaela Teodora

2013-07-01

We generate the critical condition for the phase transition of a Boolean network governed by partially nested canalizing functions for which a fraction of the inputs are canalizing, while the remaining non-canalizing inputs obey a complementary threshold Boolean function. Past studies have considered the stability of fully or partially nested canalizing functions paired with random choices of the complementary function. In some of those studies conflicting results were found with regard to the presence of chaotic behavior. Moreover, those studies focus mostly on ergodic networks in which initial states are assumed equally likely. We relax that assumption and find the critical condition for the sensitivity of the network under a non-ergodic scenario. We use the proposed mathematical model to determine parameter values for which phase transitions from order to chaos occur. We generate Derrida plots to show that the mathematical model matches the actual network dynamics. The phase transition diagrams indicate that both order and chaos can occur, and that certain parameters induce a larger range of values leading to order versus chaos. The edge-of-chaos curves are identified analytically and numerically. It is shown that the depth of canalization does not cause major dynamical changes once certain thresholds are reached; these thresholds are fairly small in comparison to the connectivity of the nodes.

Predicting the response of seven Asian glaciers to future climate scenarios using a simple linear glacier model

NASA Astrophysics Data System (ADS)

Ren, Diandong; Karoly, David J.

2008-03-01

Observations from seven Central Asian glaciers (35-55°N; 70-95°E) are used, together with regional temperature data, to infer uncertain parameters for a simple linear model of the glacier length variations. The glacier model is based on first order glacier dynamics and requires the knowledge of reference states of forcing and glacier perturbation magnitude. An adjoint-based variational method is used to optimally determine the glacier reference states in 1900 and the uncertain glacier model parameters. The simple glacier model is then used to estimate the glacier length variations until 2060 using regional temperature projections from an ensemble of climate model simulations for a future climate change scenario (SRES A2). For the period 2000-2060, all glaciers are projected to experience substantial further shrinkage, especially those with gentle slopes (e.g., Glacier Chogo Lungma retreats ˜4 km). Although nearly one-third of the year 2000 length will be reduced for some small glaciers, the existence of the glaciers studied here is not threatened by year 2060. The differences between the individual glacier responses are large. No straightforward relationship is found between glacier size and the projected fractional change of its length.

Fourier's law for quasi-one-dimensional chaotic quantum systems

NASA Astrophysics Data System (ADS)

Seligman, Thomas H.; Weidenmüller, Hans A.

2011-05-01

We derive Fourier's law for a completely coherent quasi-one-dimensional chaotic quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the level density and, thus, inversely proportional to the length of the system.

Chaotic time series analysis in economics: Balance and perspectives

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

Faggini, Marisa, E-mail: mfaggini@unisa.it

2014-12-15

The aim of the paper is not to review the large body of work concerning nonlinear time series analysis in economics, about which much has been written, but rather to focus on the new techniques developed to detect chaotic behaviours in economic data. More specifically, our attention will be devoted to reviewing some of these techniques and their application to economic and financial data in order to understand why chaos theory, after a period of growing interest, appears now not to be such an interesting and promising research area.

Multisynchronization of chaotic oscillators via nonlinear observer approach.

PubMed

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L

2014-01-01

The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology.

Multisynchronization of Chaotic Oscillators via Nonlinear Observer Approach

PubMed Central

Aguilar-López, Ricardo; Martínez-Guerra, Rafael; Mata-Machuca, Juan L.

2014-01-01

The goal of this work is to synchronize a class of chaotic oscillators in a master-slave scheme, under different initial conditions, considering several slaves systems. The Chen oscillator is employed as a benchmark model and a nonlinear observer is proposed to reach synchronicity between the master and the slaves' oscillators. The proposed observer contains a proportional and integral form of a bounded function of the synchronization error in order to provide asymptotic synchronization with a satisfactory performance. Numerical experiments were carried out to show the operation of the considered methodology. PMID:24578671

Transport properties in nontwist area-preserving maps

DOE PAGES

Szezech Jr., J. D.; Caldas, I. L.; Lopes, S. R.; ...

2009-10-23

Nontwist systems, common in the dynamical descriptions of fluids and plasmas, possess a shearless curve with a concomitant transport barrier that eliminates or reduces chaotic transport, even after its breakdown. In order to investigate the transport properties of nontwist systems, we analyze the barrier escape time and barrier transmissivity for the standard nontwist map, a paradigm of such systems. We interpret the sensitive dependence of these quantities upon map parameters by investigating chaotic orbit stickiness and the associated role played by the dominant crossing of stable and unstable manifolds.

Robust synchronization of master-slave chaotic systems using approximate model: An experimental study.

PubMed

Ahmed, Hafiz; Salgado, Ivan; Ríos, Héctor

2018-02-01

Robust synchronization of master slave chaotic systems are considered in this work. First an approximate model of the error system is obtained using the ultra-local model concept. Then a Continuous Singular Terminal Sliding-Mode (CSTSM) Controller is designed for the purpose of synchronization. The proposed approach is output feedback-based and uses fixed-time higher order sliding-mode (HOSM) differentiator for state estimation. Numerical simulation and experimental results are given to show the effectiveness of the proposed technique. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

A case study in bifurcation theory

NASA Astrophysics Data System (ADS)

Khmou, Youssef

This short paper is focused on the bifurcation theory found in map functions called evolution functions that are used in dynamical systems. The most well-known example of discrete iterative function is the logistic map that puts into evidence bifurcation and chaotic behavior of the topology of the logistic function. We propose a new iterative function based on Lorentizan function and its generalized versions, based on numerical study, it is found that the bifurcation of the Lorentzian function is of second-order where it is characterized by the absence of chaotic region.

Hierarchical collapse of regular islands via dissipation

NASA Astrophysics Data System (ADS)

Jousseph, C. A. C.; Abdulack, S. A.; Manchein, C.; Beims, M. W.

2018-03-01

In this work we investigate how regular islands localized in a mixed phase-space of generic area-preserving Hamiltonian systems are affected by a small amount of dissipation. Mainly we search for a universality (hierarchy) in the convergence of higher-order resonances and their periods when dissipation increases. One very simple scenario is already known: when subjected to small dissipation, stable periodic points become sinks attracting almost all the surrounding orbits, destroying all invariant curves which divide the phase-space in chaotic and regular domains. However, performing numerical experiments with the paradigmatic Chirikov-Taylor standard mapping we show that this presumably simple scenario can be rather complicated. The first, not trivial, scenario is what happens to chaotic trajectories, since they can be attracted by the sinks or by chaotic attractors, in cases when they exist. We show that this depends very much on how basins of attraction are formed as dissipation increases. In addition, we demonstrate that higher-order resonances are usually first affected by small dissipation when compared to lower-order resonances from the conservative case. Nevertheless, this is not a generic behaviour. We show that a local hierarchical collapse of resonances, as dissipation increases, is related to the area of the islands from the conservative case surrounding the periodic orbits. All observed resonance destructions occur via the bifurcation phenomena and are quantified here by determining the largest finite-time Lyapunov exponent.

Describing the Neuron Axons Network of the Human Brain by Continuous Flow Models

NASA Astrophysics Data System (ADS)

Hizanidis, J.; Katsaloulis, P.; Verganelakis, D. A.; Provata, A.

2014-12-01

The multifractal spectrum Dq (Rényi dimensions) is used for the analysis and comparison between the Neuron Axons Network (NAN) of healthy and pathological human brains because it conveys information about the statistics in many scales, from the very rare to the most frequent network configurations. Comparison of the Fractional Anisotropy Magnetic Resonance Images between healthy and pathological brains is performed with and without noise reduction. Modelling the complex structure of the NAN in the human brain is undertaken using the dynamics of the Lorenz model in the chaotic regime. The Lorenz multifractal spectra capture well the human brain characteristics in the large negative q's which represent the rare network configurations. In order to achieve a closer approximation in the positive part of the spectrum (q > 0) two independent modifications are considered: a) redistribution of the dense parts of the Lorenz model's phase space into their neighbouring areas and b) inclusion of additive uniform noise in the Lorenz model. Both modifications, independently, drive the Lorenz spectrum closer to the human NAN one in the positive q region without destroying the already good correspondence of the negative spectra. The modelling process shows that the unmodified Lorenz model in its full chaotic regime has a phase space distribution with high fluctuations in its dense parts, while the fluctuations in the human brain NAN are smoother. The induced modifications (phase space redistribution or additive noise) moderate the fluctuations only in the positive part of the Lorenz spectrum leading to a faithful representation of the human brain axons network in all scales.

Chaotic dynamics outside Saturn’s main rings: The case of Atlas

NASA Astrophysics Data System (ADS)

Renner, Stéfan; Cooper, Nicholas J.; El Moutamid, Maryame; Evans, Mike W.; Murray, Carl D.; Sicardy, Bruno

2014-11-01

We revisit in detail the dynamics of Atlas. From a fit to new Cassini ISS astrometric observations spanning February 2004 to August 2013, we estimate GM_Atlas=0.384+/-0.001 x 10^(-3)km^3s^(-2), a value 13% smaller than the previously published estimate but with an order of magnitude reduction in the uncertainty. Our numerically-derived orbit shows that Atlas is currently librating in both a 54:53 corotation eccentricity resonance (CER) and a 54:53 Lindblad eccentricity resonance (LER) with Prometheus. We demonstrate that the orbit of Atlas is chaotic, with a Lyapunov time of order 10 years, as a direct consequence of the coupled resonant interaction (CER/LER) with Prometheus. The interactions between the two resonances is investigated using the CoraLin analytical model (El Moutamid et al., 2014), showing that the chaotic zone fills almost all the corotation site occupied by the satellite’s orbit. Four 70 :67 apse-type mean motion resonances with Pandora are also overlapping, but these resonances have a much weaker effect on Atlas.We estimate the capture probabilities of Atlas into resonances with Prometheus as the orbits expand through tidal effects, and discuss the implications for the orbital evolution.

Competitive Modes for the Detection of Chaotic Parameter Regimes in the General Chaotic Bilinear System of Lorenz Type

NASA Astrophysics Data System (ADS)

Mallory, Kristina; van Gorder, Robert A.

We study chaotic behavior of solutions to the bilinear system of Lorenz type developed by Celikovsky and Vanecek [1994] through an application of competitive modes. This bilinear system of Lorenz type is one possible canonical form holding the Lorenz equation as a special case. Using a competitive modes analysis, which is a completely analytical method allowing one to identify parameter regimes for which chaos may occur, we are able to demonstrate a number of parameter regimes which admit a variety of distinct chaotic behaviors. Indeed, we are able to draw some interesting conclusions which relate the behavior of the mode frequencies arising from writing the state variables for the Celikovsky-Vanecek model as coupled oscillators, and the types of emergent chaotic behaviors observed. The competitive modes analysis is particularly useful if all but one of the model parameters are fixed, and the remaining free parameter is used to modify the chaos observed, in a manner analogous to a bifurcation parameter. Through a thorough application of the method, we are able to identify several parameter regimes which give new dynamics (such as specific forms of chaos) which were not observed or studied previously in the Celikovsky-Vanecek model. Therefore, the results demonstrate the advantage of the competitive modes approach for detecting new parameter regimes leading to chaos in third-order dynamical systems.

Plenoptic imaging with second-order correlations of light

NASA Astrophysics Data System (ADS)

Pepe, Francesco V.; Scarcelli, Giuliano; Garuccio, Augusto; D'Angelo, Milena

2016-01-01

Plenoptic imaging is a promising optical modality that simultaneously captures the location and the propagation direction of light in order to enable tridimensional imaging in a single shot. We demonstrate that it is possible to implement plenoptic imaging through second-order correlations of chaotic light, thus enabling to overcome the typical limitations of classical plenoptic devices.

Theoretical and numerical studies of chaotic mixing

NASA Astrophysics Data System (ADS)

Kim, Ho Jun

Theoretical and numerical studies of chaotic mixing are performed to circumvent the difficulties of efficient mixing, which come from the lack of turbulence in microfluidic devices. In order to carry out efficient and accurate parametric studies and to identify a fully chaotic state, a spectral element algorithm for solution of the incompressible Navier-Stokes and species transport equations is developed. Using Taylor series expansions in time marching, the new algorithm employs an algebraic factorization scheme on multi-dimensional staggered spectral element grids, and extends classical conforming Galerkin formulations to nonconforming spectral elements. Lagrangian particle tracking methods are utilized to study particle dispersion in the mixing device using spectral element and fourth order Runge-Kutta discretizations in space and time, respectively. Comparative studies of five different techniques commonly employed to identify the chaotic strength and mixing efficiency in microfluidic systems are presented to demonstrate the competitive advantages and shortcomings of each method. These are the stirring index based on the box counting method, Poincare sections, finite time Lyapunov exponents, the probability density function of the stretching field, and mixing index inverse, based on the standard deviation of scalar species distribution. Series of numerical simulations are performed by varying the Peclet number (Pe) at fixed kinematic conditions. The mixing length (lm) is characterized as function of the Pe number, and lm ∝ ln(Pe) scaling is demonstrated for fully chaotic cases. Employing the aforementioned techniques, optimum kinematic conditions and the actuation frequency of the stirrer that result in the highest mixing/stirring efficiency are identified in a zeta potential patterned straight micro channel, where a continuous flow is generated by superposition of a steady pressure driven flow and time periodic electroosmotic flow induced by a stream-wise AC electric field. Finally, it is shown that the invariant manifold of hyperbolic periodic point determines the geometry of fast mixing zones in oscillatory flows in two-dimensional cavity.

Deterministic diffusion in flower-shaped billiards.

PubMed

Harayama, Takahisa; Klages, Rainer; Gaspard, Pierre

2002-08-01

We propose a flower-shaped billiard in order to study the irregular parameter dependence of chaotic normal diffusion. Our model is an open system consisting of periodically distributed obstacles in the shape of a flower, and it is strongly chaotic for almost all parameter values. We compute the parameter dependent diffusion coefficient of this model from computer simulations and analyze its functional form using different schemes, all generalizing the simple random walk approximation of Machta and Zwanzig. The improved methods we use are based either on heuristic higher-order corrections to the simple random walk model, on lattice gas simulation methods, or they start from a suitable Green-Kubo formula for diffusion. We show that dynamical correlations, or memory effects, are of crucial importance in reproducing the precise parameter dependence of the diffusion coefficent.

Near-Earth asteroid satellite spins under spin-orbit coupling

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

Naidu, Shantanu P.; Margot, Jean-Luc

We develop a fourth-order numerical integrator to simulate the coupled spin and orbital motions of two rigid bodies having arbitrary mass distributions under the influence of their mutual gravitational potential. We simulate the dynamics of components in well-characterized binary and triple near-Earth asteroid systems and use surface of section plots to map the possible spin configurations of the satellites. For asynchronous satellites, the analysis reveals large regions of phase space where the spin state of the satellite is chaotic. For synchronous satellites, we show that libration amplitudes can reach detectable values even for moderately elongated shapes. The presence of chaoticmore » regions in the phase space has important consequences for the evolution of binary asteroids. It may substantially increase spin synchronization timescales, explain the observed fraction of asychronous binaries, delay BYORP-type evolution, and extend the lifetime of binaries. The variations in spin rate due to large librations also affect the analysis and interpretation of light curve and radar observations.« less

Behaviour of Lyapunov exponents near crisis points in the dissipative standard map

NASA Astrophysics Data System (ADS)

Pompe, B.; Leven, R. W.

1988-11-01

We numerically study the behaviour of the largest Lyapunov characteristic exponent λ1 in dependence on a control parameter in the 2D standard map with dissipation. In order to investigate the system's motion in parameter intervals slightly above crisis points we introduce "partial" Lyapunov exponents which characterize the average exponential divergence of nearby orbits on a semi-attractor at a boundary crisis and on distinct parts of a "large" chaotic attractor near an interior crisis. In the former case we find no significant difference between λ1 in the pre-crisis regime and the partial Lyapunov exponent describing transient chaotic motions slightly above the crisis. For the latter case we give a quantitative description of the drastic increase of λ1. Moreover, a formula which connects the critical exponent of a chaotic transient above a boundary crisis with a pointwise dimension is derived.

Impact of Noise on a Dynamical System: Prediction and Uncertainties from a Swarm-Optimized Neural Network

PubMed Central

López-Caraballo, C. H.; Lazzús, J. A.; Salfate, I.; Rojas, P.; Rivera, M.; Palma-Chilla, L.

2015-01-01

An artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey-Glass chaotic time series in the short-term x(t + 6). The performance prediction was evaluated and compared with other studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called stochastic hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute the uncertainties of predictions for noisy Mackey-Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level (σ N) from 0.01 to 0.1. PMID:26351449

Impact of Noise on a Dynamical System: Prediction and Uncertainties from a Swarm-Optimized Neural Network.

PubMed

López-Caraballo, C H; Lazzús, J A; Salfate, I; Rojas, P; Rivera, M; Palma-Chilla, L

2015-01-01

An artificial neural network (ANN) based on particle swarm optimization (PSO) was developed for the time series prediction. The hybrid ANN+PSO algorithm was applied on Mackey-Glass chaotic time series in the short-term x(t + 6). The performance prediction was evaluated and compared with other studies available in the literature. Also, we presented properties of the dynamical system via the study of chaotic behaviour obtained from the predicted time series. Next, the hybrid ANN+PSO algorithm was complemented with a Gaussian stochastic procedure (called stochastic hybrid ANN+PSO) in order to obtain a new estimator of the predictions, which also allowed us to compute the uncertainties of predictions for noisy Mackey-Glass chaotic time series. Thus, we studied the impact of noise for several cases with a white noise level (σ(N)) from 0.01 to 0.1.

A new kind of metal detector based on chaotic oscillator

NASA Astrophysics Data System (ADS)

Hu, Wenjing

2017-12-01

The sensitivity of a metal detector greatly depends on the identification ability to weak signals from the probe. In order to improve the sensitivity of metal detectors, this paper applies the Duffing chaotic oscillator to metal detectors based on its characteristic which is very sensitive to weak periodic signals. To make a suitable Duffing system for detectors, this paper computes two Lyapunov characteristics exponents of the Duffing oscillator, which help to obtain the threshold of the Duffing system in the critical state accurately and give quantitative criteria for chaos. Meanwhile, a corresponding simulation model of the chaotic oscillator is made by the Simulink tool box of Matlab. Simulation results shows that Duffing oscillator is very sensitive to sinusoidal signals in high frequency cases. And experimental results show that the measurable diameter of metal particles is about 1.5mm. It indicates that this new method can feasibly and effectively improve the metal detector sensitivity.

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape.

PubMed

Gilpin, William; Feldman, Marcus W

2017-07-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the "edge of chaos" while creating a wide distribution of opportunities for speciation during epochs of disruptive selection-a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies.

Relevance of deterministic chaos theory to studies in functioning of dynamical systems

NASA Astrophysics Data System (ADS)

Glagolev, S. N.; Bukhonova, S. M.; Chikina, E. D.

2018-03-01

The paper considers chaotic behavior of dynamical systems typical for social and economic processes. Approaches to analysis and evaluation of system development processes are studies from the point of view of controllability and determinateness. Explanations are given for necessity to apply non-standard mathematical tools to explain states of dynamical social and economic systems on the basis of fractal theory. Features of fractal structures, such as non-regularity, self-similarity, dimensionality and fractionality are considered.

The security energy encryption in wireless power transfer

NASA Astrophysics Data System (ADS)

Sadzali, M. N.; Ali, A.; Azizan, M. M.; Albreem, M. A. M.

2017-09-01

This paper presents a concept of security in wireless power transfer (WPT) by applying chaos theory. Chaos theory is applied as a security system in order to safeguard the transfer of energy from a transmitter to the intended receiver. The energy encryption of the wireless power transfer utilizes chaos theory to generate the possibility of a logistic map for the chaotic security key. The simulation for energy encryption wireless power transfer system was conducted by using MATLAB and Simulink. By employing chaos theory, the chaotic key ensures the transmission of energy from transmitter to its intended receiver.

Qualitative and quantitative behaviour of planetary systems; Proceedings of the 3rd Alexander von Humboldt Colloquium on Celestial Mechanics, Ramsau, Austria, Mar. 29-Apr. 4, 1992

NASA Astrophysics Data System (ADS)

Dvorak, R.; Henrard, J.

1993-06-01

Topics addressed include planetary theories, the Sitnikov problem, asteroids, resonance, general dynamical systems, and chaos and stability. Particular attention is given to recent progress in the theory and application of symplectic integrators, a computer-aided analysis of the Sitnikov problem, the chaotic behavior of trajectories for the asteroidal resonances, and the resonant motion in the restricted three-body problem. Also discussed are the second order long-period motion of Hyperion, meteorites from the asteroid 6 Hebe, and least squares parameter estimation in chaotic differential equations.

Analysis of chaotic saddles in a nonlinear vibro-impact system

NASA Astrophysics Data System (ADS)

Feng, Jinqian

2017-07-01

In this paper, a computational investigation of chaotic saddles in a nonlinear vibro-impact system is presented. For a classical Duffing vibro-impact oscillator, we employ the bisection procedure and an improved stagger-and-step method to present evidence of visual chaotic saddles on the fractal basin boundary and in the internal basin, respectively. The results show that the period saddles play an important role in the evolution of chaotic saddle. The dynamics mechanics of three types of bifurcation such as saddle-node bifurcation, chaotic saddle crisis bifurcation and interior chaotic crisis bifurcation are discussed. The results reveal that the period saddle created at saddle-node bifurcation is responsible for the switch of the internal chaotic saddle to the boundary chaotic saddle. At chaotic saddle crisis bifurcation, a large chaotic saddle can divide into two different chaotic saddle connected by a period saddle. The intersection points between stable and unstable manifolds of this period saddle supply access for chaotic orbits from one chaotic saddle to another and eventually induce the coupling of these two chaotic saddle. Interior chaotic crisis bifurcation is associated with the intersection of stable and unstable manifolds of the period saddle connecting two chaotic invariant sets. In addition, the gaps in chaotic saddle is responsible for the fractal structure.

A novel high-resolution chaotic lidar with optical injection to chaotic laser diode

NASA Astrophysics Data System (ADS)

Wang, Yun-cai; Wang, An-bang

2008-03-01

A novel chaotic lidar with high resolution is proposed and studied theoretically. In chaotic lidar system, the chaotic laser emitted from chaotic laser diode is split into two beams: the probe and the reference light. The ranging is achieved by correlating the reference waveform with the delayed probe waveform backscattered from the target. In chaotic lidar systems presented previously, the chaotic signal source is laser diode with optical feedback or with optical injection by another one. The ranging resolution is limited by the bandwidth of chaotic laser which determined by the configuration of chaotic signal source. We proposed a novel chaotic lidar which ranging resolution is enhanced significantly by external optical injected chaotic laser diode. With the bandwidth-enhanced chaotic laser, the range resolution of the chaotic lidar system with optical injection is roughly two times compared with that of without optical injection. The resolution increases with injection strength increasing in a certain frequency detuning range.

Characterizing Strength of Chaotic Dynamics and Numerical Simulation Relevant to Modified Taylor-Couette Flow with Hourglass Geometry

NASA Astrophysics Data System (ADS)

Hou, Yu; Kowalski, Adam; Schroder, Kjell; Halmstad, Andrew; Olsen, Thomas; Wiener, Richard

2006-05-01

We characterize the strength of chaos in two different regimes of Modified Taylor-Couette flow with Hourglass Geometry: the formation of Taylor Vortices with laminar flow and with turbulent flow. We measure the strength of chaos by calculating the correlation dimension and the Kaplan-Yorke dimension based upon the Lyapunov Exponents of each system. We determine the reliability of our calculations by considering data from a chaotic electronic circuit. In order to predict the behavior of the Modified Taylor-Couette flow system, we employ simulations based upon an idealized Reaction-Diffusion model with a third order non-linearity in the reaction rate. Variation of reaction rate with length corresponds to variation of the effective Reynolds Number along the Taylor-Couette apparatus. We present preliminary results and compare to experimental data.

Problem-Based Learning and Use of Higher-Order Thinking by Emergency Medical Technicians

ERIC Educational Resources Information Center

Rosenberger, Paul

2013-01-01

Emergency Medical Technicians (EMTs) often handle chaotic life-and-death situations that require higher-order thinking skills. Improving the pass rate of EMT students depends on many factors, including the use of proven and effective teaching methods. Results from recent research about effective teaching have suggested that the instructional…

Chaotic nature of the spin-glass phase

NASA Technical Reports Server (NTRS)

Bray, A. J.; Moore, M. A.

1987-01-01

The microscopic structure of the ordered phase of spin glasses is investigated theoretically in the framework of the T = 0 fixed-point model (McMillan, 1984; Fisher and Huse, 1986; and Bray and Moore, 1986). The sensitivity of the ground state to changes in the interaction strengths at T = 0 is explored, and it is found that for sufficiently large length scales the ground state is unstable against arbitrarily weak perturbations to the bonds. Explicit results are derived for d = 1, and the implications for d = 2 and d = 3 are considered in detail. It is concluded that there is no hidden order pattern for spin glasses at all T less than T(C), the ordered-phase spin correlations being chaotic functions of spin separation at fixed temperature or of temperature (for a given pair of spins) at scale lengths L greater than (T delta T) exp -1/zeta, where zeta = d(s)/2 - y, d(s) is the interfacial fractal dimension, and -y is the thermal eigenvalue at T = 0.

The controversial nuclear matrix: a balanced point of view.

PubMed

Martelli, A M; Falcieri, E; Zweyer, M; Bortul, R; Tabellini, G; Cappellini, A; Cocco, L; Manzoli, L

2002-10-01

The nuclear matrix is defined as the residual framework after the removal of the nuclear envelope, chromatin, and soluble components by sequential extractions. According to several investigators the nuclear matrix provides the structural basis for intranuclear order. However, the existence itself and the nature of this structure is still uncertain. Although the techniques used for the visualization of the nuclear matrix have improved over the years, it is still unclear to what extent the isolated nuclear matrix corresponds to an in vivo existing structure. Therefore, considerable skepticism continues to surround the nuclear matrix fraction as an accurate representation of the situation in living cells. Here, we summarize the experimental evidence in favor of, or against, the presence of a diffuse nucleoskeleton as a facilitating organizational nonchromatin structure of the nucleus.

Dual-threshold segmentation using Arimoto entropy based on chaotic bee colony optimization

NASA Astrophysics Data System (ADS)

Li, Li

2018-03-01

In order to extract target from complex background more quickly and accurately, and to further improve the detection effect of defects, a method of dual-threshold segmentation using Arimoto entropy based on chaotic bee colony optimization was proposed. Firstly, the method of single-threshold selection based on Arimoto entropy was extended to dual-threshold selection in order to separate the target from the background more accurately. Then intermediate variables in formulae of Arimoto entropy dual-threshold selection was calculated by recursion to eliminate redundant computation effectively and to reduce the amount of calculation. Finally, the local search phase of artificial bee colony algorithm was improved by chaotic sequence based on tent mapping. The fast search for two optimal thresholds was achieved using the improved bee colony optimization algorithm, thus the search could be accelerated obviously. A large number of experimental results show that, compared with the existing segmentation methods such as multi-threshold segmentation method using maximum Shannon entropy, two-dimensional Shannon entropy segmentation method, two-dimensional Tsallis gray entropy segmentation method and multi-threshold segmentation method using reciprocal gray entropy, the proposed method can segment target more quickly and accurately with superior segmentation effect. It proves to be an instant and effective method for image segmentation.

Probing the statistics of transport in the Hénon Map

NASA Astrophysics Data System (ADS)

Alus, O.; Fishman, S.; Meiss, J. D.

2016-09-01

The phase space of an area-preserving map typically contains infinitely many elliptic islands embedded in a chaotic sea. Orbits near the boundary of a chaotic region have been observed to stick for long times, strongly influencing their transport properties. The boundary is composed of invariant "boundary circles." We briefly report recent results of the distribution of rotation numbers of boundary circles for the Hénon quadratic map and show that the probability of occurrence of small integer entries of their continued fraction expansions is larger than would be expected for a number chosen at random. However, large integer entries occur with probabilities distributed proportionally to the random case. The probability distributions of ratios of fluxes through island chains is reported as well. These island chains are neighbours in the sense of the Meiss-Ott Markov-tree model. Two distinct universality families are found. The distributions of the ratio between the flux and orbital period are also presented. All of these results have implications for models of transport in mixed phase space.

Towards a definition of life.

PubMed

Macklem, Peter T; Seely, Andrew

2010-01-01

This article offers a new definition of life as a "self-contained, self-regulating, self-organizing, self-reproducing, interconnected, open thermodynamic network of component parts which performs work, existing in a complex regime which combines stability and adaptability in the phase transition between order and chaos, as a plant, animal, fungus, or microbe." Open thermodynamic networks, which create and maintain order and are used by all organisms to perform work, import energy from and export entropy into the environment. Intra- and extracellular interconnected networks also confer order. Although life obeys the laws of physics and chemistry, the design of living organisms is not determined by these laws, but by Darwinian selection of the fittest designs. Over a short range of normalized energy consumption, open thermodynamic systems change from deeply ordered to chaotic, and life is found in this phase transition, where a dynamic balance between stability and adaptability allows for homeokinesis. Organisms and cells move within the phase transition with changes in metabolic rate. Seeds, spores and cryo-preserved tissue are well within the ordered regime, while health probably cannot be maintained with displacements into the chaotic regime. Understanding life in these terms may provide new insights into what constitutes health and lead to new theories of disease.

Wave Chaos and HPM Effects on Electronic Systems

DTIC Science & Technology

2013-08-13

if one examines these pas- sages, one will find that, as the orbit length approaches infinity, (i) the fraction of time spent by the orbit in the...as the orbits in a complete quarter circle billiard having the same radius R (see Fig. 3.2(a)). These orbits are tangent to a circular caustic 62 with...a radius Cr. If the caustic radius Cr > ρ0, (see Fig. 3.1) this orbit is trapped in the cap, and is integrable. There are also chaotic orbits that

Revealing the Character of Orbits in a Binary System Consisting of a Primary Galaxy and a Satellite Companion

NASA Astrophysics Data System (ADS)

Zotos, Euaggelos E.

2013-02-01

In this article, we present a galactic gravitational model of three degrees of freedom (3D), in order to study and reveal the character of the orbits of the stars, in a binary stellar system composed of a primary quiet or active galaxy and a small satellite companion galaxy. Our main dynamical analysis will be focused on the behaviour of the primary galaxy. We investigate in detail the regular or chaotic nature of motion, in two different cases: (i) the time-independent model in both 2D and 3D dynamical systems and (ii) the time-evolving 3D model. For the description of the structure of the 2D system, we use the classical method of the Poincaré (x, px ), y = 0, py < 0 phase plane. In order to study the structure of the phase space of the 3D system, we take sections in the plane y = 0 of the 3D orbits, whose initial conditions differ from the plane parent periodic orbits, only by the z component. The set of the four-dimensional points in the (x, px , z, pz ) phase space is projected on the (z, pz ) plane. The maximum Lyapunov characteristic exponent is used in order to make an estimation of the chaoticity of our galactic system, in both 2D and 3D dynamical models. Our numerical calculations indicate that the percentage of the chaotic orbits increases when the primary galaxy has a dense and massive nucleus. The presence of the dense galactic core also increases the stellar velocities near the center of the galaxy. Moreover, for small values of the distance R between the two bodies, low-energy stars display chaotic motion, near the central region of the galaxy, while for larger values of the distance R, the motion in active galaxies is entirely regular for low-energy stars. Our simulations suggest that in galaxies with a satellite companion, the chaotic nature of motion is not only a result of the galactic interaction between the primary galaxy and its companion, but also a result caused by the presence of the dense nucleus in the core of the primary galaxy. Theoretical arguments are presented in order to support and interpret the numerically derived outcomes. Furthermore, we follow the 3D evolution of the primary galaxy, when mass is transported adiabatically from the disk to the nucleus. Our numerical results are in satisfactory agreement with observational data obtained from the M51-type binary stellar systems. A comparison between the present research and similar and earlier work is also made.

Saturnʼs Inner Satellites: Orbits, Masses, and the Chaotic Motion of Atlas from New Cassini Imaging Observations

NASA Astrophysics Data System (ADS)

Cooper, N. J.; Renner, S.; Murray, C. D.; Evans, M. W.

2015-01-01

We present numerically derived orbits and mass estimates for the inner Saturnian satellites, Atlas, Prometheus, Pandora, Janus, and Epimetheus from a fit to 2580 new Cassini Imaging Science Subsystem astrometric observations spanning 2004 February to 2013 August. The observations are provided as machine-readable and Virtual Observatory tables. We estimate G{{M}Atlas} = (0.384 ± 0.001) × 10-3 km3 s-2, a value 13% smaller than the previously published estimate but with an order of magnitude reduction in the uncertainty. We also find G{{M}Prometheus} = (10.677 ± 0.006) × 10-3 km3 s-2, G{{M}Pandora} = (9.133 ± 0.009) × 10-3 km3 s-2, G{{M}Janus} = (126.51 ± 0.03) × 10-3 km3 s-2, and G{{M}Epimetheus} = (35.110 ± 0.009) × 10-3 km3 s-2, consistent with previously published values, but also with significant reductions in uncertainties. We show that Atlas is currently librating in both the 54:53 co-rotation-eccentricity resonance (CER) and the 54:53 inner Lindblad (ILR) resonance with Prometheus, making it the latest example of a coupled CER-ILR system, in common with the Saturnian satellites Anthe, Aegaeon, and Methone, and possibly Neptune's ring arcs. We further demonstrate that Atlas's orbit is chaotic, with a Lyapunov time of ˜10 years, and show that its chaotic behavior is a direct consequence of the coupled resonant interaction with Prometheus, rather than being an indirect effect of the known chaotic interaction between Prometheus and Pandora. We provide an updated analysis of the second-order resonant perturbations involving Prometheus, Pandora, and Epimetheus based on the new observations, showing that these resonant arguments are librating only when Epimetheus is the innermost of the co-orbital pair, Janus and Epimetheus. We also find evidence that the known chaotic changes in the orbits of Prometheus and Pandora are not confined to times of apse anti-alignment.

A phase transition induces chaos in a predator-prey ecosystem with a dynamic fitness landscape

PubMed Central

2017-01-01

In many ecosystems, natural selection can occur quickly enough to influence the population dynamics and thus future selection. This suggests the importance of extending classical population dynamics models to include such eco-evolutionary processes. Here, we describe a predator-prey model in which the prey population growth depends on a prey density-dependent fitness landscape. We show that this two-species ecosystem is capable of exhibiting chaos even in the absence of external environmental variation or noise, and that the onset of chaotic dynamics is the result of the fitness landscape reversibly alternating between epochs of stabilizing and disruptive selection. We draw an analogy between the fitness function and the free energy in statistical mechanics, allowing us to use the physical theory of first-order phase transitions to understand the onset of rapid cycling in the chaotic predator-prey dynamics. We use quantitative techniques to study the relevance of our model to observational studies of complex ecosystems, finding that the evolution-driven chaotic dynamics confer community stability at the “edge of chaos” while creating a wide distribution of opportunities for speciation during epochs of disruptive selection—a potential observable signature of chaotic eco-evolutionary dynamics in experimental studies. PMID:28678792

AN AMMONIA EMISSION INVENTORY FOR FERTILIZER APPLICATION IN THE UNITED STATES. (R826371C006)

EPA Science Inventory

Fertilizer application represents a significant fraction of ammonia emissions from all sources in the United States. Previously published ammonia inventories have generally suffered from poor spatial and temporal resolution, erroneous activity levels, and highly uncertain emis...

Inadequacy representation of flamelet-based RANS model for turbulent non-premixed flame

NASA Astrophysics Data System (ADS)

Lee, Myoungkyu; Oliver, Todd; Moser, Robert

2017-11-01

Stochastic representations for model inadequacy in RANS-based models of non-premixed jet flames are developed and explored. Flamelet-based RANS models are attractive for engineering applications relative to higher-fidelity methods because of their low computational costs. However, the various assumptions inherent in such models introduce errors that can significantly affect the accuracy of computed quantities of interest. In this work, we develop an approach to represent the model inadequacy of the flamelet-based RANS model. In particular, we pose a physics-based, stochastic PDE for the triple correlation of the mixture fraction. This additional uncertain state variable is then used to construct perturbations of the PDF for the instantaneous mixture fraction, which is used to obtain an uncertain perturbation of the flame temperature. A hydrogen-air non-premixed jet flame is used to demonstrate the representation of the inadequacy of the flamelet-based RANS model. This work was supported by DARPA-EQUiPS(Enabling Quantification of Uncertainty in Physical Systems) program.

Exploring plenoptic properties of correlation imaging with chaotic light

NASA Astrophysics Data System (ADS)

Pepe, Francesco V.; Vaccarelli, Ornella; Garuccio, Augusto; Scarcelli, Giuliano; D'Angelo, Milena

2017-11-01

In a setup illuminated by chaotic light, we consider different schemes that enable us to perform imaging by measuring second-order intensity correlations. The most relevant feature of the proposed protocols is the ability to perform plenoptic imaging, namely to reconstruct the geometrical path of light propagating in the system, by imaging both the object and the focusing element. This property allows us to encode, in a single data acquisition, both multi-perspective images of the scene and light distribution in different planes between the scene and the focusing element. We unveil the plenoptic property of three different setups, explore their refocusing potentialities and discuss their practical applications.

File compression and encryption based on LLS and arithmetic coding

NASA Astrophysics Data System (ADS)

Yu, Changzhi; Li, Hengjian; Wang, Xiyu

2018-03-01

e propose a file compression model based on arithmetic coding. Firstly, the original symbols, to be encoded, are input to the encoder one by one, we produce a set of chaotic sequences by using the Logistic and sine chaos system(LLS), and the values of this chaotic sequences are randomly modified the Upper and lower limits of current symbols probability. In order to achieve the purpose of encryption, we modify the upper and lower limits of all character probabilities when encoding each symbols. Experimental results show that the proposed model can achieve the purpose of data encryption while achieving almost the same compression efficiency as the arithmetic coding.

A Novel Color Image Encryption Algorithm Based on Quantum Chaos Sequence

NASA Astrophysics Data System (ADS)

Liu, Hui; Jin, Cong

2017-03-01

In this paper, a novel algorithm of image encryption based on quantum chaotic is proposed. The keystreams are generated by the two-dimensional logistic map as initial conditions and parameters. And then general Arnold scrambling algorithm with keys is exploited to permute the pixels of color components. In diffusion process, a novel encryption algorithm, folding algorithm, is proposed to modify the value of diffused pixels. In order to get the high randomness and complexity, the two-dimensional logistic map and quantum chaotic map are coupled with nearest-neighboring coupled-map lattices. Theoretical analyses and computer simulations confirm that the proposed algorithm has high level of security.

Quantum mushroom billiards

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

Barnett, Alex H.; Betcke, Timo; School of Mathematics, University of Manchester, Manchester, M13 9PL

2007-12-15

We report the first large-scale statistical study of very high-lying eigenmodes (quantum states) of the mushroom billiard proposed by L. A. Bunimovich [Chaos 11, 802 (2001)]. The phase space of this mixed system is unusual in that it has a single regular region and a single chaotic region, and no KAM hierarchy. We verify Percival's conjecture to high accuracy (1.7%). We propose a model for dynamical tunneling and show that it predicts well the chaotic components of predominantly regular modes. Our model explains our observed density of such superpositions dying as E{sup -1/3} (E is the eigenvalue). We compare eigenvaluemore » spacing distributions against Random Matrix Theory expectations, using 16 000 odd modes (an order of magnitude more than any existing study). We outline new variants of mesh-free boundary collocation methods which enable us to achieve high accuracy and high mode numbers ({approx}10{sup 5}) orders of magnitude faster than with competing methods.« less

Various Attractors, Coexisting Attractors and Antimonotonicity in a Simple Fourth-Order Memristive Twin-T Oscillator

NASA Astrophysics Data System (ADS)

Zhou, Ling; Wang, Chunhua; Zhang, Xin; Yao, Wei

By replacing the resistor in a Twin-T network with a generalized flux-controlled memristor, this paper proposes a simple fourth-order memristive Twin-T oscillator. Rich dynamical behaviors can be observed in the dynamical system. The most striking feature is that this system has various periodic orbits and various chaotic attractors generated by adjusting parameter b. At the same time, coexisting attractors and antimonotonicity are also detected (especially, two full Feigenbaum remerging trees in series are observed in such autonomous chaotic systems). Their dynamical features are analyzed by phase portraits, Lyapunov exponents, bifurcation diagrams and basin of attraction. Moreover, hardware experiments on a breadboard are carried out. Experimental measurements are in accordance with the simulation results. Finally, a multi-channel random bit generator is designed for encryption applications. Numerical results illustrate the usefulness of the random bit generator.

Dancing Protein Clouds: The Strange Biology and Chaotic Physics of Intrinsically Disordered Proteins*

PubMed Central

2016-01-01

Biologically active but floppy proteins represent a new reality of modern protein science. These intrinsically disordered proteins (IDPs) and hybrid proteins containing ordered and intrinsically disordered protein regions (IDPRs) constitute a noticeable part of any given proteome. Functionally, they complement ordered proteins, and their conformational flexibility and structural plasticity allow them to perform impossible tricks and be engaged in biological activities that are inaccessible to well folded proteins with their unique structures. The major goals of this minireview are to show that, despite their simplified amino acid sequences, IDPs/IDPRs are complex entities often resembling chaotic systems, are structurally and functionally heterogeneous, and can be considered an important part of the structure-function continuum. Furthermore, IDPs/IDPRs are everywhere, and are ubiquitously engaged in various interactions characterized by a wide spectrum of binding scenarios and an even wider spectrum of structural and functional outputs. PMID:26851286

Plastic dynamics of the Al0.5CoCrCuFeNi high entropy alloy at cryogenic temperatures: Jerky flow, stair-like fluctuation, scaling behavior, and non-chaotic state

NASA Astrophysics Data System (ADS)

Guo, Xiaoxiang; Xie, Xie; Ren, Jingli; Laktionova, Marina; Tabachnikova, Elena; Yu, Liping; Cheung, Wing-Sum; Dahmen, Karin A.; Liaw, Peter K.

2017-12-01

This study investigates the plastic behavior of the Al0.5CoCrCuFeNi high-entropy alloy at cryogenic temperatures. The samples are uniaxially compressed at 4.2 K, 7.5 K, and 9 K. A jerky evolution of stress and stair-like fluctuation of strain are observed during plastic deformation. A scaling relationship is detected between the released elastic energy and strain-jump sizes. Furthermore, the dynamical evolution of serrations is characterized by the largest Lyapunov exponent. The largest Lyapunov exponents of the serrations at the three temperatures are all negative, which indicates that the dynamical regime is non-chaotic. This trend reflects an ordered slip process, and this ordered slip process exhibits a more disordered slip process, as the temperature decreases from 9 K to 4.2 K or 7.5 K.

A chaotic model for advertising diffusion problem with competition

NASA Astrophysics Data System (ADS)

Ip, W. H.; Yung, K. L.; Wang, Dingwei

2012-08-01

In this article, the author extends Dawid and Feichtinger's chaotic advertising diffusion model into the duopoly case. A computer simulation system is used to test this enhanced model. Based on the analysis of simulation results, it is found that the best advertising strategy in duopoly is to increase the advertising investment to reach the best Win-Win situation where the oscillation of market portion will not occur. In order to effectively arrive at the best situation, we define a synthetic index and two thresholds. An estimation method for the parameters of the index and thresholds is proposed in this research. We can reach the Win-Win situation by simply selecting the control parameters to make the synthetic index close to the threshold of min-oscillation state. The numerical example and computational results indicated that the proposed chaotic model is useful to describe and analyse advertising diffusion process in duopoly, it is an efficient tool for the selection and optimisation of advertising strategy.

ORIGIN OF THE CHAOTIC MOTION OF THE SATURNIAN SATELLITE ATLAS

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

Renner, S.; Vienne, A.; Cooper, N. J.

2016-05-01

We revisit the dynamics of Atlas. Using Cassini ISS astrometric observations spanning 2004 February to 2013 August, Cooper et al. found evidence that Atlas is currently perturbed by both a 54:53 corotation eccentricity resonance (CER) and a 54:53 Lindblad eccentricity resonance (LER) with Prometheus. They demonstrated that the orbit of Atlas is chaotic, with a Lyapunov time of order 10 years, as a direct consequence of the coupled resonant interaction (CER/LER) with Prometheus. Here we investigate the interactions between the two resonances using the CoraLin analytical model, showing that the chaotic zone fills almost all the corotation sites occupied bymore » the satellite's orbit. Four 70:67 apse-type mean motion resonances with Pandora are also overlapping, but these resonances have a much weaker effect. Frequency analysis allows us to highlight the coupling between the 54:53 resonances, and confirms that a simplified system including the perturbations due to Prometheus and Saturn's oblateness only captures the essential features of the dynamics.« less

Origin of the Chaotic Motion of the Saturnian Satellite Atlas

NASA Astrophysics Data System (ADS)

Renner, S.; Cooper, N. J.; El Moutamid, M.; Sicardy, B.; Vienne, A.; Murray, C. D.; Saillenfest, M.

2016-05-01

We revisit the dynamics of Atlas. Using Cassini ISS astrometric observations spanning 2004 February to 2013 August, Cooper et al. found evidence that Atlas is currently perturbed by both a 54:53 corotation eccentricity resonance (CER) and a 54:53 Lindblad eccentricity resonance (LER) with Prometheus. They demonstrated that the orbit of Atlas is chaotic, with a Lyapunov time of order 10 years, as a direct consequence of the coupled resonant interaction (CER/LER) with Prometheus. Here we investigate the interactions between the two resonances using the CoraLin analytical model, showing that the chaotic zone fills almost all the corotation sites occupied by the satellite's orbit. Four 70:67 apse-type mean motion resonances with Pandora are also overlapping, but these resonances have a much weaker effect. Frequency analysis allows us to highlight the coupling between the 54:53 resonances, and confirms that a simplified system including the perturbations due to Prometheus and Saturn's oblateness only captures the essential features of the dynamics.

Scale invariance in chaotic time series: Classical and quantum examples

NASA Astrophysics Data System (ADS)

Landa, Emmanuel; Morales, Irving O.; Stránský, Pavel; Fossion, Rubén; Velázquez, Victor; López Vieyra, J. C.; Frank, Alejandro

Important aspects of chaotic behavior appear in systems of low dimension, as illustrated by the Map Module 1. It is indeed a remarkable fact that all systems tha make a transition from order to disorder display common properties, irrespective of their exacta functional form. We discuss evidence for 1/f power spectra in the chaotic time series associated in classical and quantum examples, the one-dimensional map module 1 and the spectrum of 48Ca. A Detrended Fluctuation Analysis (DFA) method is applied to investigate the scaling properties of the energy fluctuations in the spectrum of 48Ca obtained with a large realistic shell model calculation (ANTOINE code) and with a random shell model (TBRE) calculation also in the time series obtained with the map mod 1. We compare the scale invariant properties of the 48Ca nuclear spectrum sith similar analyses applied to the RMT ensambles GOE and GDE. A comparison with the corresponding power spectra is made in both cases. The possible consequences of the results are discussed.

Virtual Libraries: Interactive Support Software and an Application in Chaotic Models.

ERIC Educational Resources Information Center

Katsirikou, Anthi; Skiadas, Christos; Apostolou, Apostolos; Rompogiannakis, Giannis

This paper begins with a discussion of the characteristics and the singularity of chaotic systems, including dynamic systems theory, chaotic orbit, fractals, chaotic attractors, and characteristics of chaotic systems. The second section addresses the digital libraries (DL) concept and the appropriateness of chaotic models, including definition and…

Urey Prize Lecture - Chaotic dynamics in the solar system

NASA Technical Reports Server (NTRS)

Wisdom, Jack

1987-01-01

Attention is given to solar system cases in which chaotic solutions of Newton's equations are important, as in chaotic rotation and orbital evolution. Hyperion is noted to be tumbling chaotically; chaotic orbital evolution is suggested to be of fundamental importance to an accounting for the Kirkwood gaps in asteroid distribution and for the phase space boundary of the chaotic zone at the 3/1 mean-motion commensurability with Jupiter. In addition, chaotic trajectories in the 2/1 chaotic zone reach very high eccentricities by a route that carries them to high inclinations temporarily.

Chaotic simulated annealing by a neural network with a variable delay: design and application.

PubMed

Chen, Shyan-Shiou

2011-10-01

In this paper, we have three goals: the first is to delineate the advantages of a variably delayed system, the second is to find a more intuitive Lyapunov function for a delayed neural network, and the third is to design a delayed neural network for a quadratic cost function. For delayed neural networks, most researchers construct a Lyapunov function based on the linear matrix inequality (LMI) approach. However, that approach is not intuitive. We provide a alternative candidate Lyapunov function for a delayed neural network. On the other hand, if we are first given a quadratic cost function, we can construct a delayed neural network by suitably dividing the second-order term into two parts: a self-feedback connection weight and a delayed connection weight. To demonstrate the advantage of a variably delayed neural network, we propose a transiently chaotic neural network with variable delay and show numerically that the model should possess a better searching ability than Chen-Aihara's model, Wang's model, and Zhao's model. We discuss both the chaotic and the convergent phases. During the chaotic phase, we simply present bifurcation diagrams for a single neuron with a constant delay and with a variable delay. We show that the variably delayed model possesses the stochastic property and chaotic wandering. During the convergent phase, we not only provide a novel Lyapunov function for neural networks with a delay (the Lyapunov function is independent of the LMI approach) but also establish a correlation between the Lyapunov function for a delayed neural network and an objective function for the traveling salesman problem. © 2011 IEEE

The chaotic dynamical aperture

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

Lee, S.Y.; Tepikian, S.

1985-10-01

Nonlinear magnetic forces become more important for particles in the modern large accelerators. These nonlinear elements are introduced either intentionally to control beam dynamics or by uncontrollable random errors. Equations of motion in the nonlinear Hamiltonian are usually non-integrable. Because of the nonlinear part of the Hamiltonian, the tune diagram of accelerators is a jungle. Nonlinear magnet multipoles are important in keeping the accelerator operation point in the safe quarter of the hostile jungle of resonant tunes. Indeed, all the modern accelerator design have taken advantages of nonlinear mechanics. On the other hand, the effect of the uncontrollable random multipolesmore » should be evaluated carefully. A powerful method of studying the effect of these nonlinear multipoles is using a particle tracking calculation, where a group of test particles are tracing through these magnetic multipoles in the accelerator hundreds to millions of turns in order to test the dynamical aperture of the machine. These methods are extremely useful in the design of a large accelerator such as SSC, LEP, HERA and RHIC. These calculations unfortunately take tremendous amount of computing time. In this paper, we try to apply the existing method in the nonlinear dynamics to study the possible alternative solution. When the Hamiltonian motion becomes chaotic, the tune of the machine becomes undefined. The aperture related to the chaotic orbit can be identified as chaotic dynamical aperture. We review the method of determining chaotic orbit and apply the method to nonlinear problems in accelerator physics. We then discuss the scaling properties and effect of random sextupoles.« less

Cooperative path planning for multi-USV based on improved artificial bee colony algorithm

NASA Astrophysics Data System (ADS)

Cao, Lu; Chen, Qiwei

2018-03-01

Due to the complex constraints, more uncertain factors and critical real-time demand of path planning for multiple unmanned surface vehicle (multi-USV), an improved artificial bee colony (I-ABC) algorithm were proposed to solve the model of cooperative path planning for multi-USV. First the Voronoi diagram of battle field space is conceived to generate the optimal area of USVs paths. Then the chaotic searching algorithm is used to initialize the collection of paths, which is regard as foods of the ABC algorithm. With the limited data, the initial collection can search the optimal area of paths perfectly. Finally simulations of the multi-USV path planning under various threats have been carried out. Simulation results verify that the I-ABC algorithm can improve the diversity of nectar source and the convergence rate of algorithm. It can increase the adaptability of dynamic battlefield and unexpected threats for USV.

Wave-Particle Dynamics of Wave Breaking in the Self-Excited Dust Acoustic Wave

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

Teng, L.-W.; Chang, M.-C.; Tseng, Y.-P.

2009-12-11

The wave-particle microdynamics in the breaking of the self-excited dust acoustic wave growing in a dusty plasma liquid is investigated through directly tracking dust micromotion. It is found that the nonlinear wave growth and steepening stop as the mean oscillating amplitude of dust displacement reaches about 1/k (k is the wave number), where the vertical neighboring dust trajectories start to crossover and the resonant wave heating with uncertain crest trapping onsets. The dephased dust oscillations cause the abrupt dropping and broadening of the wave crest after breaking, accompanied by the transition from the liquid phase with coherent dust oscillation tomore » the gas phase with chaotic dust oscillation. Corkscrew-shaped phase-space distributions measured at the fixed phases of the wave oscillation cycle clearly indicate how dusts move in and constitute the evolving waveform through dust-wave interaction.« less

Wave-Particle Dynamics of Wave Breaking in the Self-Excited Dust Acoustic Wave

NASA Astrophysics Data System (ADS)

Teng, Lee-Wen; Chang, Mei-Chu; Tseng, Yu-Ping; I, Lin

2009-12-01

The wave-particle microdynamics in the breaking of the self-excited dust acoustic wave growing in a dusty plasma liquid is investigated through directly tracking dust micromotion. It is found that the nonlinear wave growth and steepening stop as the mean oscillating amplitude of dust displacement reaches about 1/k (k is the wave number), where the vertical neighboring dust trajectories start to crossover and the resonant wave heating with uncertain crest trapping onsets. The dephased dust oscillations cause the abrupt dropping and broadening of the wave crest after breaking, accompanied by the transition from the liquid phase with coherent dust oscillation to the gas phase with chaotic dust oscillation. Corkscrew-shaped phase-space distributions measured at the fixed phases of the wave oscillation cycle clearly indicate how dusts move in and constitute the evolving waveform through dust-wave interaction.

Defect structure of epitaxial layers of III nitrides as determined by analyzing the shape of X-ray diffraction peaks

NASA Astrophysics Data System (ADS)

Kyutt, R. T.

2017-04-01

The shape of X-ray diffraction epitaxial layers with high dislocation densities has been studied experimentally. Measurements with an X-ray diffractometer were performed in double- and triple-crystal setups with both Cu K α and Mo K α radiation. Epitaxial layers (GaN, AlN, AlGaN, ZnO, etc.) with different degrees of structural perfection grown by various methods on sapphire, silicon, and silicon carbide substrates have been examined. The layer thickness varied in the range of 0.5-30 μm. It has been found that the center part of peaks is well approximated by the Voigt function with different Lorentz fractions, while the wing intensity drops faster and may be represented by a power function (with the index that varies from one structure to another). A well-marked dependence on the ordering of dislocations was observed. The drop in intensity in the majority of structures with a regular system and regular threading dislocations was close to the theoretically predicted law Δθ-3; the intensity in films with a chaotic distribution decreased much faster. The dependence of the peak shape on the order of reflection, the diffraction geometry, and the epitaxial layer thickness was also examined.

Tracking Radionuclide Fractionation in the First Atomic Explosion Using Stable Elements

DOE PAGES

Bonamici, Chloë E.; Hervig, Richard L.; Kinman, William S.

2017-08-25

Compositional analysis of postdetonation fallout is a tool for forensic identification of nuclear devices. However, the relationship between device composition and fallout composition is difficult to interpret because of the complex combination of physical mixing, nuclear reactions, and chemical fractionations that occur in the chaotic nuclear fireball. By using a combination of in situ microanalytical techniques (electron microprobe analysis and secondary ion mass spectrometry), we show that some heavy stable elements (Rb, Sr, Zr, Ba, Cs, Ba, La, Ce, Nd, Sm, Dy, Lu, U, Th) in glassy fallout from the first nuclear test, Trinity, are reliable chemical proxies for radionuclidesmore » generated during the explosion. Stable-element proxies show that radionuclides from the Trinity device were chemically, but not isotopically, fractionated by condensation. Moreover, stable-element proxies delineate chemical fractionation trends that can be used to connect present-day fallout composition to past fireball composition. Stable-element proxies therefore offer a novel approach for elucidating the phenomenology of the nuclear fireball as it relates to the formation of debris and the fixation of device materials within debris.« less

Tracking Radionuclide Fractionation in the First Atomic Explosion Using Stable Elements

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

Bonamici, Chloë E.; Hervig, Richard L.; Kinman, William S.

Compositional analysis of postdetonation fallout is a tool for forensic identification of nuclear devices. However, the relationship between device composition and fallout composition is difficult to interpret because of the complex combination of physical mixing, nuclear reactions, and chemical fractionations that occur in the chaotic nuclear fireball. By using a combination of in situ microanalytical techniques (electron microprobe analysis and secondary ion mass spectrometry), we show that some heavy stable elements (Rb, Sr, Zr, Ba, Cs, Ba, La, Ce, Nd, Sm, Dy, Lu, U, Th) in glassy fallout from the first nuclear test, Trinity, are reliable chemical proxies for radionuclidesmore » generated during the explosion. Stable-element proxies show that radionuclides from the Trinity device were chemically, but not isotopically, fractionated by condensation. Moreover, stable-element proxies delineate chemical fractionation trends that can be used to connect present-day fallout composition to past fireball composition. Stable-element proxies therefore offer a novel approach for elucidating the phenomenology of the nuclear fireball as it relates to the formation of debris and the fixation of device materials within debris.« less

Tracking Radionuclide Fractionation in the First Atomic Explosion Using Stable Elements.

PubMed

Bonamici, Chloë E; Hervig, Richard L; Kinman, William S

2017-09-19

Compositional analysis of postdetonation fallout is a tool for forensic identification of nuclear devices. However, the relationship between device composition and fallout composition is difficult to interpret because of the complex combination of physical mixing, nuclear reactions, and chemical fractionations that occur in the chaotic nuclear fireball. Using a combination of in situ microanalytical techniques (electron microprobe analysis and secondary ion mass spectrometry), we show that some heavy stable elements (Rb, Sr, Zr, Ba, Cs, Ba, La, Ce, Nd, Sm, Dy, Lu, U, Th) in glassy fallout from the first nuclear test, Trinity, are reliable chemical proxies for radionuclides generated during the explosion. Stable-element proxies show that radionuclides from the Trinity device were chemically, but not isotopically, fractionated by condensation. Furthermore, stable-element proxies delineate chemical fractionation trends that can be used to connect present-day fallout composition to past fireball composition. Stable-element proxies therefore offer a novel approach for elucidating the phenomenology of the nuclear fireball as it relates to the formation of debris and the fixation of device materials within debris.

Secondary chaotic terrain formation in the higher outflow channels of southern circum-Chryse, Mars

USGS Publications Warehouse

Rodriguez, J.A.P.; Kargel, J.S.; Tanaka, K.L.; Crown, D.A.; Berman, D.C.; Fairen, A.G.; Baker, V.R.; Furfaro, R.; Candelaria, P.; Sasaki, S.

2011-01-01

Higher outflow channel dissection in the martian region of southern circum-Chryse appears to have extended from the Late Hesperian to the Middle Amazonian Epoch. These outflow channels were excavated within the upper 1. km of the cryolithosphere, where no liquid water is expected to have existed during these geologic epochs. In accordance with previous work, our examination of outflow channel floor morphologies suggests the upper crust excavated by the studied outflow channels consisted of a thin (a few tens of meters) layer of dry geologic materials overlying an indurated zone that extends to the bases of the investigated outflow channels (1. km in depth). We find that the floors of these outflow channels contain widespread secondary chaotic terrains (i.e., chaotic terrains produced by the destruction of channel-floor materials). These chaotic terrains occur within the full range of outflow channel dissection and tend to form clusters. Our examination of the geology of these chaotic terrains suggests that their formation did not result in the generation of floods. Nevertheless, despite their much smaller dimensions, these chaotic terrains are comprised of the same basic morphologic elements (e.g., mesas, knobs, and smooth deposits within scarp-bound depressions) as those located in the initiation zones of the outflow channels, which suggests that their formation must have involved the release of ground volatiles. We propose that these chaotic terrains developed not catastrophically but gradually and during multiple episodes of nested surface collapse. In order to explain the formation of secondary chaotic terrains within zones of outflow channel dissection, we propose that the regional Martian cryolithosphere contained widespread lenses of volatiles in liquid form. In this model, channel floor collapse and secondary chaotic terrain formation would have taken place as a consequence of instabilities arising during their exhumation by outflow channel dissection. Within relatively warm upper crustal materials in volcanic settings, or within highly saline crustal materials where cryopegs developed, lenses of volatiles in liquid form within the cryolithosphere could have formed, and/or remained stable.In addition, our numerical simulations suggest that low thermal conductivity, dry fine-grained porous geologic materials just a few tens of meters in thickness (e.g., dunes, sand sheets, some types of regolith materials), could have produced high thermal anomalies resulting in subsurface melting. The existence of a global layer of dry geologic materials overlying the cryolithosphere would suggest that widespread lenses of fluids existed (and may still exist) at shallow depths wherever these materials are fine-grained and porous. The surface ages of the investigated outflow channels and chaotic terrains span a full 500 to 700. Myr. Chaotic terrains similar in dimensions and morphology to secondary chaotic terrains are not observed conspicuously throughout the surface of Mars, suggesting that intra-cryolithospheric fluid lenses may form relatively stable systems. The existence of widespread groundwater lenses at shallow depths of burial has tremendous implications for exobiological studies and future human exploration. We find that the clear geomorphologic anomaly that the chaotic terrains and outflow channels of southern Chryse form within the Martian landscape could have been a consequence of large-scale resurfacing resulting from anomalously extensive subsurface melt in this region of the planet produced by high concentrations of salts within the regional upper crust. Crater count statistics reveal that secondary chaotic terrains and the outflow channels within which they occur have overlapping ages, suggesting that the instabilities leading to their formation rapidly dissipated, perhaps as the thickness of the cryolithosphere was reset following the disruption of the upper crustal thermal structure produced during outflow channel ex

Insights on chaotic dynamics: mixing experiments between natural silicate melts from Vulcano island (Aeolian Islands, Italy)

NASA Astrophysics Data System (ADS)

Rossi, Stefano; Morgavi, Daniele; Vetere, Francesco; Petrelli, Maurizio; Perugini, Diego

2017-04-01

keywords: Magma mixing, chaotic dynamics, time series experiments Magma mixing is a petrologic phenomenon which is recognized as potential trigger of highly explosive eruptions and its evidence is commonly observable in natural rocks. Here we tried to replicate the dynamic conditions of mixing performing a set of chaotic mixing experiments between shoshonitic and rhyolitic magmas from Vulcano island. Vulcano is the southernmost island of the Aeolian Archipelago (Aeolian Islands, Italy); it is completely built by volcanic rocks with variable degree of evolution ranging from basalt to rhyolite (e.g. Keller 1980; Ellam et al. 1988; De Astis 1995; De Astis et al. 2013) and its magmatic activity dates back to about 120 ky. Last eruption occurred in 1888-1890. The chaotic mixing experiments were performed by using the new ChaOtic Magma Mixing Apparatus (COMMA), held at the Department of Physics and Geology, University of Perugia. This new experimental device allows to track the evolution of the mixing process and the associated modulation of chemical composition between different magmas. Experiments were performed at 1200°C and atmospheric pressure with a viscosity ratio higher than three orders of magnitude. The experimental protocol was chosen to ensure the occurrence of chaotic dynamics in the system and the run duration was progressively increased (e.g. 10.5 h, 21 h, 42 h). The products of each experiment are crystal-free glasses in which the variation of major elements was investigated along different profiles using electron microprobe (EMPA) at Institute für Mineralogie, Leibniz Universität of Hannover (Germany). The efficiency of the mixing process is estimated by calculating the decrease of concentration variance in time and it is shown that the variance of major elements exponentially decays. Our results confirm and quantify how different chemical elements homogenize in the melt at differing rates. It is also observable that the mixing structures generated during the mixing experiments are topologically identical to those observed in natural mixed volcanic rocks.

X-ray signatures: New time scales and spectral features

NASA Technical Reports Server (NTRS)

Boldt, E. A.

1977-01-01

The millisecond bursts from Cyg X-1 are investigated and the overall chaotic variability for the bulk of the Cyg X-1 emission is compared to that of Sco X-1, showing that the essential character is remarkably similar (i.e. shot noise) although the fundamental time scales involved differ widely, from a fraction of a second (for Cyg X-1) to a fraction of a day (for Sco X-1). Recent OSO-8 observations of spectra features attributable to iron are reviewed. In particular, line emission is discussed within the context of a model for thermal radiation by a hot evolved gas in systems as different as supernova remnants and clusters of galaxies. Newly observed spectral structure in the emission from the X-ray pulsar Her X-1 is reported.

Research of Uncertainty Reasoning in Pineapple Disease Identification System

NASA Astrophysics Data System (ADS)

Liu, Liqun; Fan, Haifeng

In order to deal with the uncertainty of evidences mostly existing in pineapple disease identification system, a reasoning model based on evidence credibility factor was established. The uncertainty reasoning method is discussed,including: uncertain representation of knowledge, uncertain representation of rules, uncertain representation of multi-evidences and update of reasoning rules. The reasoning can fully reflect the uncertainty in disease identification and reduce the influence of subjective factors on the accuracy of the system.

Sexy is What You Make it: Organizational Culture and U.S. Army Special Forces

DTIC Science & Technology

2014-06-01

terrorist groups, criminal elements and any number of hybrids” (ARSOF 2022, 2013, p. 4). In order to be prepared for employment in this uncertain...range of military operations throughout an ever-changing, uncertain environment that is both global in spread and volatile in nature . In order to be...approaches to dealing with situations that become second nature to employees in an organization. It encompasses the beliefs, values, norms

The properties of borderlines in discontinuous conservative systems

NASA Astrophysics Data System (ADS)

Wang, X.-M.; Fang, Z.-J.

2006-02-01

The properties of the set of borderline images in discontinuous conservative systems are commonly investigated. The invertible system in which a stochastic web was found in 1999 is re-discussed here. The result shows that the set of images of the borderline actually forms the same stochastic web. The web has two typical local fine structures. Firstly, in some parts of the web the borderline crosses the manifold of hyperbolic points so that the chaotic diffusion is damped greatly; secondly, in other parts of phase space many holes and elliptic islands appear in the stochastic layer. This local structure shows infinite self-similarity. The noninvertible system in which the so-called chaotic quasi-attractor was found in [X.-M. Wang et al., Eur. Phys. J. D 19, 119 (2002)] is also studied here. The numerical investigation shows that such a chaotic quasi-attractor is confined by the preceding lower order images of the borderline. The mechanism of this confinement is revealed: a forbidden zone exists that any orbit can not visit, which is the sub-phase space of one side of the first image of the borderline. Each order of the images of the forbidden zone can be qualitatively divided into two sub-phase regions: one is the so-called escaping region that provides the orbit with an escaping channel, the other is the so-called dissipative region where the contraction of phase space occurs.

Stability analysis of fuzzy parametric uncertain systems.

PubMed

Bhiwani, R J; Patre, B M

2011-10-01

In this paper, the determination of stability margin, gain and phase margin aspects of fuzzy parametric uncertain systems are dealt. The stability analysis of uncertain linear systems with coefficients described by fuzzy functions is studied. A complexity reduced technique for determining the stability margin for FPUS is proposed. The method suggested is dependent on the order of the characteristic polynomial. In order to find the stability margin of interval polynomials of order less than 5, it is not always necessary to determine and check all four Kharitonov's polynomials. It has been shown that, for determining stability margin of FPUS of order five, four, and three we require only 3, 2, and 1 Kharitonov's polynomials respectively. Only for sixth and higher order polynomials, a complete set of Kharitonov's polynomials are needed to determine the stability margin. Thus for lower order systems, the calculations are reduced to a large extent. This idea has been extended to determine the stability margin of fuzzy interval polynomials. It is also shown that the gain and phase margin of FPUS can be determined analytically without using graphical techniques. Copyright © 2011 ISA. Published by Elsevier Ltd. All rights reserved.

A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

2018-03-01

A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

Breaking chaotic secure communication using a spectrogram

NASA Astrophysics Data System (ADS)

Yang, Tao; Yang, Lin-Bao; Yang, Chun-Mei

1998-10-01

We present the results of breaking a kind of chaotic secure communication system called chaotic switching scheme, also known as chaotic shift keying, in which a binary message signal is scrambled by two chaotic attractors. The spectrogram which can reveal the energy evolving process in the spectral-temporal space is used to distinguish the two different chaotic attractors, which are qualitatively and statistically similar in phase space. Then mathematical morphological filters are used to decode the binary message signal without the knowledge of the binary message signal and the transmitter. The computer experimental results are provided to show how our method works when both the chaotic and hyper-chaotic transmitter are used.

Altered humin compositions under organic and inorganic fertilization on an intensively cultivated sandy loam soil

USDA-ARS?s Scientific Manuscript database

Humin is the largest and also the least understood fraction of soil organic matter. The humin structure and its correlation with microbiological properties are particularly uncertain. We applied advanced solid-state 13C nuclear magnetic resonance (NMR) spectroscopy to investigate the structural chan...

Physicians’ Perspectives on the Uncertainties and Implications of Chromosomal Microarray Testing of Children and Families

PubMed Central

Reiff, Marian; Ross, Kathryn; Mulchandani, Surabhi; Propert, Kathleen Joy; Pyeritz, Reed E.; Spinner, Nancy B.; Bernhardt, Barbara A.

2012-01-01

Chromosomal microarray analysis (CMA) has improved the diagnostic rate of genomic disorders in pediatric populations, but can produce uncertain and unexpected findings. This paper explores clinicians’ perspectives and identifies challenges in effectively interpreting results and communicating with families about CMA. Responses to an online survey were obtained from 40 clinicians who had ordered CMA. Content included practice characteristics and perceptions, and queries about a hypothetical case involving uncertain and incidental findings. Data were analyzed using non-parametric statistical tests. Clinicians’ comfort levels differed significantly for explaining uncertain, abnormal, and normal CMA results, with lowest levels for uncertain results. Despite clinical guidelines recommending informed consent, many clinicians did not consider it pertinent to discuss the potential for CMA to reveal information concerning biological parentage or predisposition to late-onset disease, in a hypothetical case. Many non-genetics professionals ordering CMA did not feel equipped to interpret the results for patients, and articulated needs for education and access to genetics professionals. This exploratory study highlights key challenges in the practice of genomic medicine, and identifies needs for education, disseminated practice guidelines, and access to genetics professionals, especially when dealing with uncertain or unexpected findings. PMID:22989118

Studying the VCSEL to VCSEL injection locking for enhanced chromatic dispersion compensation

NASA Astrophysics Data System (ADS)

Li, Linfu

2010-11-01

In order to supply a theoretical guide for digital chaotic telecommunication, the technique of Optical injection locking (OIL) of semiconductor lasers on the chaotic communication have been investigated based on the theoretical models used to describe the dynamics of solitary VCSEL subjected to the external optical injection and signal transmission in fiber. The numerical simulation results show that, the frequency chirp and time-resolved chirp are reduced in magnitude, using a VCSEL laser as master and another VCSEL as slave, it leads to a no-penalty transmission over 50 km of uncompensated in SSMF at 10Gb/s, and it could be higher rate and more remote if there were appropriate compensation.

Hybrid electronic/optical synchronized chaos communication system.

PubMed

Toomey, J P; Kane, D M; Davidović, A; Huntington, E H

2009-04-27

A hybrid electronic/optical system for synchronizing a chaotic receiver to a chaotic transmitter has been demonstrated. The chaotic signal is generated electronically and injected, in addition to a constant bias current, to a semiconductor laser to produce an optical carrier for transmission. The optical chaotic carrier is photodetected to regenerate an electronic signal for synchronization in a matched electronic receiver The system has been successfully used for the transmission and recovery of a chaos masked message that is added to the chaotic optical carrier. Past demonstrations of synchronized chaos based, secure communication systems have used either an electronic chaotic carrier or an optical chaotic carrier (such as the chaotic output of various nonlinear laser systems). This is the first electronic/optical hybrid system to be demonstrated. We call this generation of a chaotic optical carrier by electronic injection.

On the Chaotic Vibrations of Electrostatically Actuated Arch Micro/Nano Resonators: A Parametric Study

NASA Astrophysics Data System (ADS)

Tajaddodianfar, Farid; Hairi Yazdi, Mohammad Reza; Pishkenari, Hossein Nejat

Motivated by specific applications, electrostatically actuated bistable arch shaped micro-nano resonators have attracted growing attention in the research community in recent years. Nevertheless, some issues relating to their nonlinear dynamics, including the possibility of chaos, are still not well known. In this paper, we investigate the chaotic vibrations of a bistable resonator comprised of a double clamped initially curved microbeam under combined harmonic AC and static DC distributed electrostatic actuation. A reduced order equation obtained by the application of the Galerkin method to the nonlinear partial differential equation of motion, given in the framework of Euler-Bernoulli beam theory, is used for the investigation in this paper. We numerically integrate the obtained equation to study the chaotic vibrations of the proposed system. Moreover, we investigate the effects of various parameters including the arch curvature, the actuation parameters and the quality factor of the resonator, which are effective in the formation of both static and dynamic behaviors of the system. Using appropriate numerical tools, including Poincaré maps, bifurcation diagrams, Fourier spectrum and Lyapunov exponents we scrutinize the effects of various parameters on the formation of chaotic regions in the parametric space of the resonator. Results of this work provide better insight into the problem of nonlinear dynamics of the investigated family of bistable micro/nano resonators, and facilitate the design of arch resonators for applications such as filters.

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

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

Saiki, Yoshitaka, E-mail: yoshi.saiki@r.hit-u.ac.jp; Yamada, Michio; Chian, Abraham C.-L.

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originatemore » from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.« less

Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation.

PubMed

Saiki, Yoshitaka; Yamada, Michio; Chian, Abraham C-L; Miranda, Rodrigo A; Rempel, Erico L

2015-10-01

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

NASA Astrophysics Data System (ADS)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-06-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Complex-enhanced chaotic signals with time-delay signature suppression based on vertical-cavity surface-emitting lasers subject to chaotic optical injection

NASA Astrophysics Data System (ADS)

Chen, Jianjun; Duan, Yingni; Zhong, Zhuqiang

2018-03-01

A chaotic system is constructed on the basis of vertical-cavity surface-emitting lasers (VCSELs), where a slave VCSEL subject to chaotic optical injection (COI) from a master VCSEL with the external feedback. The complex degree (CD) and time-delay signature (TDS) of chaotic signals generated by this chaotic system are investigated numerically via permutation entropy (PE) and self-correlation function (SF) methods, respectively. The results show that, compared with master VCSEL subject to optical feedback, complex-enhanced chaotic signals with TDS suppression can be achieved for S-VCSEL subject to COI. Meanwhile, the influences of several controllable parameters on the evolution maps of CD of chaotic signals are carefully considered. It is shown that the CD of chaotic signals for S-VCSEL is always higher than that for M-VCSEL due to the CIO effect. The TDS of chaotic signals can be significantly suppressed by choosing the reasonable parameters in this system. Furthermore, TDS suppression and high CD chaos can be obtained simultaneously in the specific parameter ranges. The results confirm that this chaotic system may effectively improve the security of a chaos-based communication scheme.

Understanding genetic regulatory networks

NASA Astrophysics Data System (ADS)

Kauffman, Stuart

2003-04-01

Random Boolean networks (RBM) were introduced about 35 years ago as first crude models of genetic regulatory networks. RBNs are comprised of N on-off genes, connected by a randomly assigned regulatory wiring diagram where each gene has K inputs, and each gene is controlled by a randomly assigned Boolean function. This procedure samples at random from the ensemble of all possible NK Boolean networks. The central ideas are to study the typical, or generic properties of this ensemble, and see 1) whether characteristic differences appear as K and biases in Boolean functions are introducted, and 2) whether a subclass of this ensemble has properties matching real cells. Such networks behave in an ordered or a chaotic regime, with a phase transition, "the edge of chaos" between the two regimes. Networks with continuous variables exhibit the same two regimes. Substantial evidence suggests that real cells are in the ordered regime. A key concept is that of an attractor. This is a reentrant trajectory of states of the network, called a state cycle. The central biological interpretation is that cell types are attractors. A number of properties differentiate the ordered and chaotic regimes. These include the size and number of attractors, the existence in the ordered regime of a percolating "sea" of genes frozen in the on or off state, with a remainder of isolated twinkling islands of genes, a power law distribution of avalanches of gene activity changes following perturbation to a single gene in the ordered regime versus a similar power law distribution plus a spike of enormous avalanches of gene changes in the chaotic regime, and the existence of branching pathway of "differentiation" between attractors induced by perturbations in the ordered regime. Noise is serious issue, since noise disrupts attractors. But numerical evidence suggests that attractors can be made very stable to noise, and meanwhile, metaplasias may be a biological manifestation of noise. As we learn more about the wiring diagram and constraints on rules controlling real genes, we can build refined ensembles reflecting these properties, study the generic properties of the refined ensembles, and hope to gain insight into the dynamics of real cells.

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys

PubMed Central

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K.

2016-01-01

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk. PMID:27435922

Self-similar random process and chaotic behavior in serrated flow of high entropy alloys

DOE PAGES

Chen, Shuying; Yu, Liping; Ren, Jingli; ...

2016-07-20

Here, the statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al 0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, andmore » there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.« less

Self-Similar Random Process and Chaotic Behavior In Serrated Flow of High Entropy Alloys.

PubMed

Chen, Shuying; Yu, Liping; Ren, Jingli; Xie, Xie; Li, Xueping; Xu, Ying; Zhao, Guangfeng; Li, Peizhen; Yang, Fuqian; Ren, Yang; Liaw, Peter K

2016-07-20

The statistical and dynamic analyses of the serrated-flow behavior in the nanoindentation of a high-entropy alloy, Al0.5CoCrCuFeNi, at various holding times and temperatures, are performed to reveal the hidden order associated with the seemingly-irregular intermittent flow. Two distinct types of dynamics are identified in the high-entropy alloy, which are based on the chaotic time-series, approximate entropy, fractal dimension, and Hurst exponent. The dynamic plastic behavior at both room temperature and 200 °C exhibits a positive Lyapunov exponent, suggesting that the underlying dynamics is chaotic. The fractal dimension of the indentation depth increases with the increase of temperature, and there is an inflection at the holding time of 10 s at the same temperature. A large fractal dimension suggests the concurrent nucleation of a large number of slip bands. In particular, for the indentation with the holding time of 10 s at room temperature, the slip process evolves as a self-similar random process with a weak negative correlation similar to a random walk.

Kinetic Simulations of the Lowest-order Unstable Mode of Relativistic Magnetostatic Equilibria

NASA Astrophysics Data System (ADS)

Nalewajko, Krzysztof; Zrake, Jonathan; Yuan, Yajie; East, William E.; Blandford, Roger D.

2016-08-01

We present the results of particle-in-cell numerical pair plasma simulations of relativistic two-dimensional magnetostatic equilibria known as the “Arnold-Beltrami-Childress” fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of “X-point collapse” first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers are disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process, leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers. The maximum particle energy is proportional to the mean magnetization, which is attributed partly to the increase of the effective electric field and partly to the increase of the acceleration timescale. We describe in detail the evolving structure of the dynamical current layers and report on the conservation of magnetic helicity. These results can be applied to highly magnetized astrophysical environments, where ideal plasma instabilities trigger rapid magnetic dissipation with efficient particle acceleration and flares of high-energy radiation.

KINETIC SIMULATIONS OF THE LOWEST-ORDER UNSTABLE MODE OF RELATIVISTIC MAGNETOSTATIC EQUILIBRIA

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

Nalewajko, Krzysztof; Zrake, Jonathan; Yuan, Yajie

2016-08-01

We present the results of particle-in-cell numerical pair plasma simulations of relativistic two-dimensional magnetostatic equilibria known as the “Arnold–Beltrami–Childress” fields. In particular, we focus on the lowest-order unstable configuration consisting of two minima and two maxima of the magnetic vector potential. Breaking of the initial symmetry leads to exponential growth of the electric energy and to the formation of two current layers, which is consistent with the picture of “X-point collapse” first described by Syrovatskii. Magnetic reconnection within the layers heats a fraction of particles to very high energies. After the saturation of the linear instability, the current layers aremore » disrupted and the system evolves chaotically, diffusing the particle energies in a stochastic second-order Fermi process, leading to the formation of power-law energy distributions. The power-law slopes harden with the increasing mean magnetization, but they are significantly softer than those produced in simulations initiated from Harris-type layers. The maximum particle energy is proportional to the mean magnetization, which is attributed partly to the increase of the effective electric field and partly to the increase of the acceleration timescale. We describe in detail the evolving structure of the dynamical current layers and report on the conservation of magnetic helicity. These results can be applied to highly magnetized astrophysical environments, where ideal plasma instabilities trigger rapid magnetic dissipation with efficient particle acceleration and flares of high-energy radiation.« less

Chaos in driven Alfvén systems: unstable periodic orbits and chaotic saddles

NASA Astrophysics Data System (ADS)

Chian, A. C.-L.; Santana, W. M.; Rempel, E. L.; Borotto, F. A.; Hada, T.; Kamide, Y.

2007-01-01

The chaotic dynamics of Alfvén waves in space plasmas governed by the derivative nonlinear Schrödinger equation, in the low-dimensional limit described by stationary spatial solutions, is studied. A bifurcation diagram is constructed, by varying the driver amplitude, to identify a number of nonlinear dynamical processes including saddle-node bifurcation, boundary crisis, and interior crisis. The roles played by unstable periodic orbits and chaotic saddles in these transitions are analyzed, and the conversion from a chaotic saddle to a chaotic attractor in these dynamical processes is demonstrated. In particular, the phenomenon of gap-filling in the chaotic transition from weak chaos to strong chaos via an interior crisis is investigated. A coupling unstable periodic orbit created by an explosion, within the gaps of the chaotic saddles embedded in a chaotic attractor following an interior crisis, is found numerically. The gap-filling unstable periodic orbits are responsible for coupling the banded chaotic saddle (BCS) to the surrounding chaotic saddle (SCS), leading to crisis-induced intermittency. The physical relevance of chaos for Alfvén intermittent turbulence observed in the solar wind is discussed.

Remote sensing data assimilation for a prognostic phenology model

Treesearch

R. Stockli; T. Rutishauser; D. Dragoni; J. O' Keefe; P. E. Thornton; M. Jolly; L. Lu; A. S. Denning

2008-01-01

Predicting the global carbon and water cycle requires a realistic representation of vegetation phenology in climate models. However most prognostic phenology models are not yet suited for global applications, and diagnostic satellite data can be uncertain and lack predictive power. We present a framework for data assimilation of Fraction of Photosynthetically Active...

Bifurcation analysis of a discrete-time ratio-dependent predator-prey model with Allee Effect

NASA Astrophysics Data System (ADS)

Cheng, Lifang; Cao, Hongjun

2016-09-01

A discrete-time predator-prey model with Allee effect is investigated in this paper. We consider the strong and the weak Allee effect (the population growth rate is negative and positive at low population density, respectively). From the stability analysis and the bifurcation diagrams, we get that the model with Allee effect (strong or weak) growth function and the model with logistic growth function have somewhat similar bifurcation structures. If the predator growth rate is smaller than its death rate, two species cannot coexist due to having no interior fixed points. When the predator growth rate is greater than its death rate and other parameters are fixed, the model can have two interior fixed points. One is always unstable, and the stability of the other is determined by the integral step size, which decides the species coexistence or not in some extent. If we increase the value of the integral step size, then the bifurcated period doubled orbits or invariant circle orbits may arise. So the numbers of the prey and the predator deviate from one stable state and then circulate along the period orbits or quasi-period orbits. When the integral step size is increased to a critical value, chaotic orbits may appear with many uncertain period-windows, which means that the numbers of prey and predator will be chaotic. In terms of bifurcation diagrams and phase portraits, we know that the complexity degree of the model with strong Allee effect decreases, which is related to the fact that the persistence of species can be determined by the initial species densities.

Changing PLA Processes, Not PLA

ERIC Educational Resources Information Center

Suopis, Cynthia A.

2009-01-01

Margaret J. Wheatley, the organizational consultant who wrote the 1999 classic, "Leadership and the New Science: Discovering Order in a Chaotic World," laments about the rigid structures and processes that often strangle organizations rendering them incapable of change. Wheatley asserts that organizations lack faith that their purpose…

Tangent Adjoint Methods In a Higher-Order Space-Time Discontinuous-Galerkin Solver For Turbulent Flows

NASA Technical Reports Server (NTRS)

Diosady, Laslo; Murman, Scott; Blonigan, Patrick; Garai, Anirban

2017-01-01

Presented space-time adjoint solver for turbulent compressible flows. Confirmed failure of traditional sensitivity methods for chaotic flows. Assessed rate of exponential growth of adjoint for practical 3D turbulent simulation. Demonstrated failure of short-window sensitivity approximations.

Dancing Protein Clouds: The Strange Biology and Chaotic Physics of Intrinsically Disordered Proteins.

PubMed

Uversky, Vladimir N

2016-03-25

Biologically active but floppy proteins represent a new reality of modern protein science. These intrinsically disordered proteins (IDPs) and hybrid proteins containing ordered and intrinsically disordered protein regions (IDPRs) constitute a noticeable part of any given proteome. Functionally, they complement ordered proteins, and their conformational flexibility and structural plasticity allow them to perform impossible tricks and be engaged in biological activities that are inaccessible to well folded proteins with their unique structures. The major goals of this minireview are to show that, despite their simplified amino acid sequences, IDPs/IDPRs are complex entities often resembling chaotic systems, are structurally and functionally heterogeneous, and can be considered an important part of the structure-function continuum. Furthermore, IDPs/IDPRs are everywhere, and are ubiquitously engaged in various interactions characterized by a wide spectrum of binding scenarios and an even wider spectrum of structural and functional outputs. © 2016 by The American Society for Biochemistry and Molecular Biology, Inc.

A semi-symmetric image encryption scheme based on the function projective synchronization of two hyperchaotic systems

PubMed Central

Li, Jinqing; Qi, Hui; Cong, Ligang; Yang, Huamin

2017-01-01

Both symmetric and asymmetric color image encryption have advantages and disadvantages. In order to combine their advantages and try to overcome their disadvantages, chaos synchronization is used to avoid the key transmission for the proposed semi-symmetric image encryption scheme. Our scheme is a hybrid chaotic encryption algorithm, and it consists of a scrambling stage and a diffusion stage. The control law and the update rule of function projective synchronization between the 3-cell quantum cellular neural networks (QCNN) response system and the 6th-order cellular neural network (CNN) drive system are formulated. Since the function projective synchronization is used to synchronize the response system and drive system, Alice and Bob got the key by two different chaotic systems independently and avoid the key transmission by some extra security links, which prevents security key leakage during the transmission. Both numerical simulations and security analyses such as information entropy analysis, differential attack are conducted to verify the feasibility, security, and efficiency of the proposed scheme. PMID:28910349

Solving Partial Differential Equations in a data-driven multiprocessor environment

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

Gaudiot, J.L.; Lin, C.M.; Hosseiniyar, M.

1988-12-31

Partial differential equations can be found in a host of engineering and scientific problems. The emergence of new parallel architectures has spurred research in the definition of parallel PDE solvers. Concurrently, highly programmable systems such as data-how architectures have been proposed for the exploitation of large scale parallelism. The implementation of some Partial Differential Equation solvers (such as the Jacobi method) on a tagged token data-flow graph is demonstrated here. Asynchronous methods (chaotic relaxation) are studied and new scheduling approaches (the Token No-Labeling scheme) are introduced in order to support the implementation of the asychronous methods in a data-driven environment.more » New high-level data-flow language program constructs are introduced in order to handle chaotic operations. Finally, the performance of the program graphs is demonstrated by a deterministic simulation of a message passing data-flow multiprocessor. An analysis of the overhead in the data-flow graphs is undertaken to demonstrate the limits of parallel operations in dataflow PDE program graphs.« less

Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: Basic theory and applications

NASA Astrophysics Data System (ADS)

Doungmo Goufo, Emile Franc

2016-08-01

After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function E α , β ( z ) , z ∈ ℂ ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89, 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on Eα,β(z). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β. Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of Eα,β(z), certainly opening new doors to modeling with two-parameter derivatives.

Chaotic processes using the two-parameter derivative with non-singular and non-local kernel: Basic theory and applications.

PubMed

Doungmo Goufo, Emile Franc

2016-08-01

After having the issues of singularity and locality addressed recently in mathematical modelling, another question regarding the description of natural phenomena was raised: How influent is the second parameter β of the two-parameter Mittag-Leffler function Eα,β(z), z∈ℂ? To answer this question, we generalize the newly introduced one-parameter derivative with non-singular and non-local kernel [A. Atangana and I. Koca, Chaos, Solitons Fractals 89, 447 (2016); A. Atangana and D. Bealeanu (e-print)] by developing a similar two-parameter derivative with non-singular and non-local kernel based on Eα , β(z). We exploit the Agarwal/Erdelyi higher transcendental functions together with their Laplace transforms to explicitly establish the Laplace transform's expressions of the two-parameter derivatives, necessary for solving related fractional differential equations. Explicit expression of the associated two-parameter fractional integral is also established. Concrete applications are done on atmospheric convection process by using Lorenz non-linear simple system. Existence result for the model is provided and a numerical scheme established. As expected, solutions exhibit chaotic behaviors for α less than 0.55, and this chaos is not interrupted by the impact of β. Rather, this second parameter seems to indirectly squeeze and rotate the solutions, giving an impression of twisting. The whole graphics seem to have completely changed its orientation to a particular direction. This is a great observation that clearly shows the substantial impact of the second parameter of Eα , β(z), certainly opening new doors to modeling with two-parameter derivatives.

On order and chaos in the mergers of galaxies

NASA Astrophysics Data System (ADS)

Vandervoort, Peter O.

2018-03-01

This paper describes a low-dimensional model of the merger of two galaxies. The governing equations are the complete sets of moment equations of the first and second orders derived from the collisionless Boltzmann equations representing the galaxies. The moment equations reduce to an equation governing the relative motion of the galaxies, tensor virial equations, and equations governing the kinetic energy tensors. We represent the galaxies as heterogeneous ellipsoids with Gaussian stratifications of their densities, and we represent the mean stellar motions in terms of velocity fields that sustain those densities consistently with the equation of continuity. We reduce and solve the governing equations for a head-on encounter of a dwarf galaxy with a giant galaxy. That reduction includes the effect of dynamical friction on the relative motion of the galaxies. Our criterion for chaotic behaviour is sensitivity of the motion to small changes in the initial conditions. In a survey of encounters and mergers of a dwarf galaxy with a giant galaxy, chaotic behaviour arises mainly in non-linear oscillations of the dwarf galaxy. The encounter disrupts the dwarf, excites chaotic oscillations of the dwarf, or excites regular oscillations. Dynamical friction can drive a merger to completion within a Hubble time only if the dwarf is sufficiently massive. The survey of encounters and mergers is the basis for a simple model of the evolution of a `Local Group' consisting of a giant galaxy and a population of dwarf galaxies bound to the giant as satellites on radial orbits.

Implementation of an integrated op-amp based chaotic neuron model and observation of its chaotic dynamics

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

Jung, Jinwoo; Lee, Jewon; Song, Hanjung

2011-03-15

This paper presents a fully integrated circuit implementation of an operational amplifier (op-amp) based chaotic neuron model with a bipolar output function, experimental measurements, and analyses of its chaotic behavior. The proposed chaotic neuron model integrated circuit consists of several op-amps, sample and hold circuits, a nonlinear function block for chaotic signal generation, a clock generator, a nonlinear output function, etc. Based on the HSPICE (circuit program) simulation results, approximated empirical equations for analyses were formulated. Then, the chaotic dynamical responses such as bifurcation diagrams, time series, and Lyapunov exponent were calculated using these empirical equations. In addition, we performedmore » simulations about two chaotic neuron systems with four synapses to confirm neural network connections and got normal behavior of the chaotic neuron such as internal state bifurcation diagram according to the synaptic weight variation. The proposed circuit was fabricated using a 0.8-{mu}m single poly complementary metal-oxide semiconductor technology. Measurements of the fabricated single chaotic neuron with {+-}2.5 V power supplies and a 10 kHz sampling clock frequency were carried out and compared with the simulated results.« less

Partially chaotic orbits in a perturbed cubic force model

NASA Astrophysics Data System (ADS)

Muzzio, J. C.

2017-11-01

Three types of orbits are theoretically possible in autonomous Hamiltonian systems with 3 degrees of freedom: fully chaotic (they only obey the energy integral), partially chaotic (they obey an additional isolating integral besides energy) and regular (they obey two isolating integrals besides energy). The existence of partially chaotic orbits has been denied by several authors, however, arguing either that there is a sudden transition from regularity to full chaoticity or that a long enough follow-up of a supposedly partially chaotic orbit would reveal a fully chaotic nature. This situation needs clarification, because partially chaotic orbits might play a significant role in the process of chaotic diffusion. Here we use numerically computed Lyapunov exponents to explore the phase space of a perturbed three-dimensional cubic force toy model, and a generalization of the Poincaré maps to show that partially chaotic orbits are actually present in that model. They turn out to be double orbits joined by a bifurcation zone, which is the most likely source of their chaos, and they are encapsulated in regions of phase space bounded by regular orbits similar to each one of the components of the double orbit.

A modified hybrid uncertain analysis method for dynamic response field of the LSOAAC with random and interval parameters

NASA Astrophysics Data System (ADS)

Zi, Bin; Zhou, Bin

2016-07-01

For the prediction of dynamic response field of the luffing system of an automobile crane (LSOAAC) with random and interval parameters, a hybrid uncertain model is introduced. In the hybrid uncertain model, the parameters with certain probability distribution are modeled as random variables, whereas, the parameters with lower and upper bounds are modeled as interval variables instead of given precise values. Based on the hybrid uncertain model, the hybrid uncertain dynamic response equilibrium equation, in which different random and interval parameters are simultaneously included in input and output terms, is constructed. Then a modified hybrid uncertain analysis method (MHUAM) is proposed. In the MHUAM, based on random interval perturbation method, the first-order Taylor series expansion and the first-order Neumann series, the dynamic response expression of the LSOAAC is developed. Moreover, the mathematical characteristics of extrema of bounds of dynamic response are determined by random interval moment method and monotonic analysis technique. Compared with the hybrid Monte Carlo method (HMCM) and interval perturbation method (IPM), numerical results show the feasibility and efficiency of the MHUAM for solving the hybrid LSOAAC problems. The effects of different uncertain models and parameters on the LSOAAC response field are also investigated deeply, and numerical results indicate that the impact made by the randomness in the thrust of the luffing cylinder F is larger than that made by the gravity of the weight in suspension Q . In addition, the impact made by the uncertainty in the displacement between the lower end of the lifting arm and the luffing cylinder a is larger than that made by the length of the lifting arm L .

Detection of chaos: New approach to atmospheric pollen time-series analysis

NASA Astrophysics Data System (ADS)

Bianchi, M. M.; Arizmendi, C. M.; Sanchez, J. R.

1992-09-01

Pollen and spores are biological particles that are ubiquitous to the atmosphere and are pathologically significant, causing plant diseases and inhalant allergies. One of the main objectives of aerobiological surveys is forecasting. Prediction models are required in order to apply aerobiological knowledge to medical or agricultural practice; a necessary condition of these models is not to be chaotic. The existence of chaos is detected through the analysis of a time series. The time series comprises hourly counts of atmospheric pollen grains obtained using a Burkard spore trap from 1987 to 1989 at Mar del Plata. Abraham's method to obtain the correlation dimension was applied. A low and fractal dimension shows chaotic dynamics. The predictability of models for atomspheric pollen forecasting is discussed.

Generation of chaotic radiation in a driven traveling wave tube amplifier with time-delayed feedback

NASA Astrophysics Data System (ADS)

Marchewka, Chad; Larsen, Paul; Bhattacharjee, Sudeep; Booske, John; Sengele, Sean; Ryskin, Nikita; Titov, Vladimir

2006-01-01

The application of chaos in communications and radar offers new and interesting possibilities. This article describes investigations on the generation of chaos in a traveling wave tube (TWT) amplifier and the experimental parameters responsible for sustaining stable chaos. Chaos is generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction of the TWT output power back to the input in a delayed feedback configuration. A driver wave provides a constant external force to the system making it behave like a forced nonlinear oscillator. The effects of the feedback bandwidth, intensity, and phase are described. The study illuminates the different transitions to chaos and the effect of parameters such as the frequency and intensity of the driver wave. The detuning frequency, i.e., difference frequency between the driver wave and the natural oscillation of the system, has been identified as being an important physical parameter for controlling evolution to chaos. Among the observed routes to chaos, besides the more common period doubling, a new route called loss of frequency locking occurs when the driving frequency is adjacent to a natural oscillation mode. The feedback bandwidth controls the nonlinear dynamics of the system, particularly the number of natural oscillation modes. A computational model has been developed to simulate the experiments and reasonably good agreement is obtained between them. Experiments are described that demonstrate the feasibility of chaotic communications using two TWTs, where one is operated as a driven chaotic oscillator and the other as a time-delayed, open-loop amplifier.

Iron isotope fractionation during magmatic differentiation in Kilauea Iki lava lake.

PubMed

Teng, Fang-Zhen; Dauphas, Nicolas; Helz, Rosalind T

2008-06-20

Magmatic differentiation helps produce the chemical and petrographic diversity of terrestrial rocks. The extent to which magmatic differentiation fractionates nonradiogenic isotopes is uncertain for some elements. We report analyses of iron isotopes in basalts from Kilauea Iki lava lake, Hawaii. The iron isotopic compositions (56Fe/54Fe) of late-stagemeltveins are 0.2 permil (per thousand) greater than values for olivine cumulates. Olivine phenocrysts are up to 1.2 per thousand lighter than those of whole rocks. These results demonstrate that iron isotopes fractionate during magmatic differentiation at both whole-rock and crystal scales. This characteristic of iron relative to the characteristics of magnesium and lithium, for which no fractionation has been found, may be related to its complex redox chemistry in magmatic systems and makes iron a potential tool for studying planetary differentiation.

Iron isotope fractionation during magmatic differentiation in Kilauea Iki lava lake

USGS Publications Warehouse

Teng, F.-Z.; Dauphas, N.; Helz, R.T.

2008-01-01

Magmatic differentiation helps produce the chemical and petrographic diversity of terrestrial rocks. The extent to which magmatic differentiation fractionates nonradiogenic isotopes is uncertain for some elements. We report analyses of iron isotopes in basalts from Kilauea Iki lava lake, Hawaii. The iron isotopic compositions (56Fe/54Fe) of late-stage melt veins are 0.2 per mil (???) greater than values for olivine cumulates. Olivine phenocrysts are up to 1.2??? lighter than those of whole rocks. These results demonstrate that iron isotopes fractionate during magmatic differentiation at both whole-rock and crystal scales. This characteristic of iron relative to the characteristics of magnesium and lithium, for which no fractionation has been found, may be related to its complex redox chemistry in magmatic systems and makes iron a potential tool for studying planetary differentiation.

Superconductivity-induced macroscopic resonant tunneling.

PubMed

Goorden, M C; Jacquod, Ph; Weiss, J

2008-02-15

We show analytically and by numerical simulations that the conductance through pi-biased chaotic Josephson junctions is enhanced by several orders of magnitude in the short-wavelength regime. We identify the mechanism behind this effect as macroscopic resonant tunneling through a macroscopic number of low-energy quasidegenerate Andreev levels.

Uncertain relational reasoning in the parietal cortex.

PubMed

Ragni, Marco; Franzmeier, Imke; Maier, Simon; Knauff, Markus

2016-04-01

The psychology of reasoning is currently transitioning from the study of deductive inferences under certainty to inferences that have degrees of uncertainty in both their premises and conclusions; however, only a few studies have explored the cortical basis of uncertain reasoning. Using transcranial magnetic stimulation (TMS), we show that areas in the right superior parietal lobe (rSPL) are necessary for solving spatial relational reasoning problems under conditions of uncertainty. Twenty-four participants had to decide whether a single presented order of objects agreed with a given set of indeterminate premises that could be interpreted in more than one way. During the presentation of the order, 10-Hz TMS was applied over the rSPL or a sham control site. Right SPL TMS during the inference phase disrupted performance in uncertain relational reasoning. Moreover, we found differences in the error rates between preferred mental models, alternative models, and inconsistent models. Our results suggest that different mechanisms are involved when people reason spatially and evaluate different kinds of uncertain conclusions. Copyright © 2016 Elsevier Inc. All rights reserved.

Non-symmetric forms of non-linear vibrations of flexible cylindrical panels and plates under longitudinal load and additive white noise

NASA Astrophysics Data System (ADS)

Krysko, V. A.; Awrejcewicz, J.; Krylova, E. Yu; Papkova, I. V.; Krysko, A. V.

2018-06-01

Parametric non-linear vibrations of flexible cylindrical panels subjected to additive white noise are studied. The governing Marguerre equations are investigated using the finite difference method (FDM) of the second-order accuracy and the Runge-Kutta method. The considered mechanical structural member is treated as a system of many/infinite number of degrees of freedom (DoF). The dependence of chaotic vibrations on the number of DoFs is investigated. Reliability of results is guaranteed by comparing the results obtained using two qualitatively different methods to reduce the problem of PDEs (partial differential equations) to ODEs (ordinary differential equations), i.e. the Faedo-Galerkin method in higher approximations and the 4th and 6th order FDM. The Cauchy problem obtained by the FDM is eventually solved using the 4th-order Runge-Kutta methods. The numerical experiment yielded, for a certain set of parameters, the non-symmetric vibration modes/forms with and without white noise. In particular, it has been illustrated and discussed that action of white noise on chaotic vibrations implies quasi-periodicity, whereas the previously non-symmetric vibration modes are closer to symmetric ones.

Chaotic phase synchronization in bursting-neuron models driven by a weak periodic force

NASA Astrophysics Data System (ADS)

Ando, Hiroyasu; Suetani, Hiromichi; Kurths, Jürgen; Aihara, Kazuyuki

2012-07-01

We investigate the entrainment of a neuron model exhibiting a chaotic spiking-bursting behavior in response to a weak periodic force. This model exhibits two types of oscillations with different characteristic time scales, namely, long and short time scales. Several types of phase synchronization are observed, such as 1:1 phase locking between a single spike and one period of the force and 1:l phase locking between the period of slow oscillation underlying bursts and l periods of the force. Moreover, spiking-bursting oscillations with chaotic firing patterns can be synchronized with the periodic force. Such a type of phase synchronization is detected from the position of a set of points on a unit circle, which is determined by the phase of the periodic force at each spiking time. We show that this detection method is effective for a system with multiple time scales. Owing to the existence of both the short and the long time scales, two characteristic phenomena are found around the transition point to chaotic phase synchronization. One phenomenon shows that the average time interval between successive phase slips exhibits a power-law scaling against the driving force strength and that the scaling exponent has an unsmooth dependence on the changes in the driving force strength. The other phenomenon shows that Kuramoto's order parameter before the transition exhibits stepwise behavior as a function of the driving force strength, contrary to the smooth transition in a model with a single time scale.

Chaotic dynamics of flexible Euler-Bernoulli beams

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

Awrejcewicz, J., E-mail: awrejcew@p.lodz.pl; Krysko, A. V., E-mail: anton.krysko@gmail.com; Kutepov, I. E., E-mail: iekutepov@gmail.com

2013-12-15

Mathematical modeling and analysis of spatio-temporal chaotic dynamics of flexible simple and curved Euler-Bernoulli beams are carried out. The Kármán-type geometric non-linearity is considered. Algorithms reducing partial differential equations which govern the dynamics of studied objects and associated boundary value problems are reduced to the Cauchy problem through both Finite Difference Method with the approximation of O(c{sup 2}) and Finite Element Method. The obtained Cauchy problem is solved via the fourth and sixth-order Runge-Kutta methods. Validity and reliability of the results are rigorously discussed. Analysis of the chaotic dynamics of flexible Euler-Bernoulli beams for a series of boundary conditions ismore » carried out with the help of the qualitative theory of differential equations. We analyze time histories, phase and modal portraits, autocorrelation functions, the Poincaré and pseudo-Poincaré maps, signs of the first four Lyapunov exponents, as well as the compression factor of the phase volume of an attractor. A novel scenario of transition from periodicity to chaos is obtained, and a transition from chaos to hyper-chaos is illustrated. In particular, we study and explain the phenomenon of transition from symmetric to asymmetric vibrations. Vibration-type charts are given regarding two control parameters: amplitude q{sub 0} and frequency ω{sub p} of the uniformly distributed periodic excitation. Furthermore, we detected and illustrated how the so called temporal-space chaos is developed following the transition from regular to chaotic system dynamics.« less

A new two-scroll chaotic attractor with three quadratic nonlinearities, its adaptive control and circuit design

NASA Astrophysics Data System (ADS)

Lien, C.-H.; Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D new two-scroll chaotic attractor with three quadratic nonlinearities is investigated in this paper. First, the qualitative and dynamical properties of the new two-scroll chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new two-scroll dissipative chaotic system has three unstable equilibrium points. As an engineering application, global chaos control of the new two-scroll chaotic system with unknown system parameters is designed via adaptive feedback control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic two-scroll attractor model.

Porn in Prison: How Does It Get in? Who Receives It?

ERIC Educational Resources Information Center

Tewksbury, Richard; DeMichele, Matthew

2005-01-01

Prison administrators are faced with the arduous task of maintaining order in an environment that is often characterized as chaotic. This task is made increasingly more difficult as administrators must observe individual rights, operate within rapidly diminishing budgets, and satisfy shifting philosophical penal goals--oscillating between…

Orderly Thinking about a Chaotic System.

ERIC Educational Resources Information Center

Cohen, Arthur M.

Half of all students who begin college in America--and an even higher proportion of underrepresetned minorities--matriculate at community colleges. If the bachelor's degree is a requisite for major social and economic advancement, then transfer must be an essential community college mission. Calculating the transfer rate is important as a measure…

Video encryption using chaotic masks in joint transform correlator

NASA Astrophysics Data System (ADS)

Saini, Nirmala; Sinha, Aloka

2015-03-01

A real-time optical video encryption technique using a chaotic map has been reported. In the proposed technique, each frame of video is encrypted using two different chaotic random phase masks in the joint transform correlator architecture. The different chaotic random phase masks can be obtained either by using different iteration levels or by using different seed values of the chaotic map. The use of different chaotic random phase masks makes the decryption process very complex for an unauthorized person. Optical, as well as digital, methods can be used for video encryption but the decryption is possible only digitally. To further enhance the security of the system, the key parameters of the chaotic map are encoded using RSA (Rivest-Shamir-Adleman) public key encryption. Numerical simulations are carried out to validate the proposed technique.

Condition-based diagnosis of mechatronic systems using a fractional calculus approach

NASA Astrophysics Data System (ADS)

Gutiérrez-Carvajal, Ricardo Enrique; Flávio de Melo, Leonimer; Maurício Rosário, João; Tenreiro Machado, J. A.

2016-07-01

While fractional calculus (FC) is as old as integer calculus, its application has been mainly restricted to mathematics. However, many real systems are better described using FC equations than with integer models. FC is a suitable tool for describing systems characterised by their fractal nature, long-term memory and chaotic behaviour. It is a promising methodology for failure analysis and modelling, since the behaviour of a failing system depends on factors that increase the model's complexity. This paper explores the proficiency of FC in modelling complex behaviour by tuning only a few parameters. This work proposes a novel two-step strategy for diagnosis, first modelling common failure conditions and, second, by comparing these models with real machine signals and using the difference to feed a computational classifier. Our proposal is validated using an electrical motor coupled with a mechanical gear reducer.

Visibility graphlet approach to chaotic time series

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

Mutua, Stephen; Computer Science Department, Masinde Muliro University of Science and Technology, P.O. Box 190-50100, Kakamega; Gu, Changgui, E-mail: gu-changgui@163.com, E-mail: hjyang@ustc.edu.cn

Many novel methods have been proposed for mapping time series into complex networks. Although some dynamical behaviors can be effectively captured by existing approaches, the preservation and tracking of the temporal behaviors of a chaotic system remains an open problem. In this work, we extended the visibility graphlet approach to investigate both discrete and continuous chaotic time series. We applied visibility graphlets to capture the reconstructed local states, so that each is treated as a node and tracked downstream to create a temporal chain link. Our empirical findings show that the approach accurately captures the dynamical properties of chaotic systems.more » Networks constructed from periodic dynamic phases all converge to regular networks and to unique network structures for each model in the chaotic zones. Furthermore, our results show that the characterization of chaotic and non-chaotic zones in the Lorenz system corresponds to the maximal Lyapunov exponent, thus providing a simple and straightforward way to analyze chaotic systems.« less

A novel double-convection chaotic attractor, its adaptive control and circuit simulation

NASA Astrophysics Data System (ADS)

Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

Nonlinear dynamics analysis of the spur gear system for railway locomotive

NASA Astrophysics Data System (ADS)

Wang, Junguo; He, Guangyue; Zhang, Jie; Zhao, Yongxiang; Yao, Yuan

2017-02-01

Considering the factors such as the nonlinearity backlash, static transmission error and time-varying meshing stiffness, a three-degree-of-freedom torsional vibration model of spur gear transmission system for a typical locomotive is developed, in which the wheel/rail adhesion torque is considered as uncertain but bounded parameter. Meantime, the Ishikawa method is used for analysis and calculation of the time-varying mesh stiffness of the gear pair in meshing process. With the help of bifurcation diagrams, phase plane diagrams, Poincaré maps, time domain response diagrams and amplitude-frequency spectrums, the effects of the pinion speed and stiffness on the dynamic behavior of gear transmission system for locomotive are investigated in detail by using the numerical integration method. Numerical examples reveal various types of nonlinear phenomena and dynamic evolution mechanism involving one-period responses, multi-periodic responses, bifurcation and chaotic responses. Some research results present useful information to dynamic design and vibration control of the gear transmission system for railway locomotive.

Characterizing chaotic melodies in automatic music composition

NASA Astrophysics Data System (ADS)

Coca, Andrés E.; Tost, Gerard O.; Zhao, Liang

2010-09-01

In this paper, we initially present an algorithm for automatic composition of melodies using chaotic dynamical systems. Afterward, we characterize chaotic music in a comprehensive way as comprising three perspectives: musical discrimination, dynamical influence on musical features, and musical perception. With respect to the first perspective, the coherence between generated chaotic melodies (continuous as well as discrete chaotic melodies) and a set of classical reference melodies is characterized by statistical descriptors and melodic measures. The significant differences among the three types of melodies are determined by discriminant analysis. Regarding the second perspective, the influence of dynamical features of chaotic attractors, e.g., Lyapunov exponent, Hurst coefficient, and correlation dimension, on melodic features is determined by canonical correlation analysis. The last perspective is related to perception of originality, complexity, and degree of melodiousness (Euler's gradus suavitatis) of chaotic and classical melodies by nonparametric statistical tests.

A nonlinear controller design for permanent magnet motors using a synchronization-based technique inspired from the Lorenz system.

PubMed

Zaher, Ashraf A

2008-03-01

The dynamic behavior of a permanent magnet synchronous machine (PMSM) is analyzed. Nominal and special operating conditions are explored to show that the PMSM can experience chaos. A nonlinear controller is introduced to control these unwanted chaotic oscillations and to bring the PMSM to a stable steady state. The designed controller uses a pole-placement approach to force the closed-loop system to follow the performance of a simple first-order linear system with zero steady-state error to a desired set point. The similarity between the mathematical model of the PMSM and the famous chaotic Lorenz system is utilized to design a synchronization-based state observer using only the angular speed for feedback. Simulation results verify the effectiveness of the proposed controller in eliminating the chaotic oscillations while using a single feedback signal. The superiority of the proposed controller is further demonstrated by comparing it with a conventional PID controller. Finally, a laboratory-based experiment was conducted using the MCK2812 C Pro-MS(BL) motion control kit to confirm the theoretical results and to verify both the causality and versatility of the proposed controller.

Counting statistics of chaotic resonances at optical frequencies: Theory and experiments

NASA Astrophysics Data System (ADS)

Lippolis, Domenico; Wang, Li; Xiao, Yun-Feng

2017-07-01

A deformed dielectric microcavity is used as an experimental platform for the analysis of the statistics of chaotic resonances, in the perspective of testing fractal Weyl laws at optical frequencies. In order to surmount the difficulties that arise from reading strongly overlapping spectra, we exploit the mixed nature of the phase space at hand, and only count the high-Q whispering-gallery modes (WGMs) directly. That enables us to draw statistical information on the more lossy chaotic resonances, coupled to the high-Q regular modes via dynamical tunneling. Three different models [classical, Random-Matrix-Theory (RMT) based, semiclassical] to interpret the experimental data are discussed. On the basis of least-squares analysis, theoretical estimates of Ehrenfest time, and independent measurements, we find that a semiclassically modified RMT-based expression best describes the experiment in all its realizations, particularly when the resonator is coupled to visible light, while RMT alone still works quite well in the infrared. In this work we reexamine and substantially extend the results of a short paper published earlier [L. Wang et al., Phys. Rev. E 93, 040201(R) (2016), 10.1103/PhysRevE.93.040201].

Chaotic particle swarm optimization with mutation for classification.

PubMed

Assarzadeh, Zahra; Naghsh-Nilchi, Ahmad Reza

2015-01-01

In this paper, a chaotic particle swarm optimization with mutation-based classifier particle swarm optimization is proposed to classify patterns of different classes in the feature space. The introduced mutation operators and chaotic sequences allows us to overcome the problem of early convergence into a local minima associated with particle swarm optimization algorithms. That is, the mutation operator sharpens the convergence and it tunes the best possible solution. Furthermore, to remove the irrelevant data and reduce the dimensionality of medical datasets, a feature selection approach using binary version of the proposed particle swarm optimization is introduced. In order to demonstrate the effectiveness of our proposed classifier, mutation-based classifier particle swarm optimization, it is checked out with three sets of data classifications namely, Wisconsin diagnostic breast cancer, Wisconsin breast cancer and heart-statlog, with different feature vector dimensions. The proposed algorithm is compared with different classifier algorithms including k-nearest neighbor, as a conventional classifier, particle swarm-classifier, genetic algorithm, and Imperialist competitive algorithm-classifier, as more sophisticated ones. The performance of each classifier was evaluated by calculating the accuracy, sensitivity, specificity and Matthews's correlation coefficient. The experimental results show that the mutation-based classifier particle swarm optimization unequivocally performs better than all the compared algorithms.

Modulated heat pulse propagation and partial transport barriers in chaotic magnetic fields

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

Castillo-Negrete, Diego del; Blazevski, Daniel

2016-04-15

Direct numerical simulations of the time dependent parallel heat transport equation modeling heat pulses driven by power modulation in three-dimensional chaotic magnetic fields are presented. The numerical method is based on the Fourier formulation of a Lagrangian-Green's function method that provides an accurate and efficient technique for the solution of the parallel heat transport equation in the presence of harmonic power modulation. The numerical results presented provide conclusive evidence that even in the absence of magnetic flux surfaces, chaotic magnetic field configurations with intermediate levels of stochasticity exhibit transport barriers to modulated heat pulse propagation. In particular, high-order islands andmore » remnants of destroyed flux surfaces (Cantori) act as partial barriers that slow down or even stop the propagation of heat waves at places where the magnetic field connection length exhibits a strong gradient. Results on modulated heat pulse propagation in fully stochastic fields and across magnetic islands are also presented. In qualitative agreement with recent experiments in large helical device and DIII-D, it is shown that the elliptic (O) and hyperbolic (X) points of magnetic islands have a direct impact on the spatio-temporal dependence of the amplitude of modulated heat pulses.« less

Axial distribution of plasma fluctuations, plasma parameters, deposition rate and grain size during copper deposition

NASA Astrophysics Data System (ADS)

Gopikishan, S.; Banerjee, I.; Pathak, Anand; Mahapatra, S. K.

2017-08-01

Floating potential fluctuations, plasma parameters and deposition rate have been investigated as a function of axial distance during deposition of copper in direct current (DC) magnetron sputtering system. Fluctuations were analyzed using phase space, power spectra and amplitude bifurcation plots. It has been observed that the fluctuations are modified from chaotic to ordered state with increase in the axial distance from cathode. Plasma parameters such as electron density (ne), electron temperature (Te) and deposition rate (Dr) were measured and correlated with plasma fluctuations. It was found that more the deposition rate, greater the grain size, higher the electron density, higher the electron temperature and more chaotic the oscillations near the cathode. This observation could be helpful to the thin film technology industry to optimize the required film.

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

NASA Astrophysics Data System (ADS)

Fernandez, P.; Wang, Q.

2017-12-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

Disturbance observer based active and adaptive synchronization of energy resource chaotic system.

PubMed

Wei, Wei; Wang, Meng; Li, Donghai; Zuo, Min; Wang, Xiaoyi

2016-11-01

In this paper, synchronization of a three-dimensional energy resource chaotic system is considered. For the sake of achieving the synchronization between the drive and response systems, two different nonlinear control approaches, i.e. active control with known parameters and adaptive control with unknown parameters, have been designed. In order to guarantee the transient performance, finite-time boundedness (FTB) and finite-time stability (FTS) are introduced in the design of active control and adaptive control, respectively. Simultaneously, in view of the existence of disturbances, a new disturbance observer is proposed to estimate the disturbance. The conditions of the asymptotic stability for the closed-loop system are obtained. Numerical simulations are provided to illustrate the proposed approaches. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Noise, chaos, and (ɛ, τ)-entropy per unit time

NASA Astrophysics Data System (ADS)

Gaspard, Pierre; Wang, Xiao-Jing

1993-12-01

The degree of dynamical randomness of different time processes is characterized in terms of the (ε, τ)-entropy per unit time. The (ε, τ)-entropy is the amount of information generated per unit time, at different scales τ of time and ε of the observables. This quantity generalizes the Kolmogorov-Sinai entropy per unit time from deterministic chaotic processes, to stochastic processes such as fluctuations in mesoscopic physico-chemical phenomena or strong turbulence in macroscopic spacetime dynamics. The random processes that are characterized include chaotic systems, Bernoulli and Markov chains, Poisson and birth-and-death processes, Ornstein-Uhlenbeck and Yaglom noises, fractional Brownian motions, different regimes of hydrodynamical turbulence, and the Lorentz-Boltzmann process of nonequilibrium statistical mechanics. We also extend the (ε, τ)-entropy to spacetime processes like cellular automata, Conway's game of life, lattice gas automata, coupled maps, spacetime chaos in partial differential equations, as well as the ideal, the Lorentz, and the hard sphere gases. Through these examples it is demonstrated that the (ε, τ)-entropy provides a unified quantitative measure of dynamical randomness to both chaos and noises, and a method to detect transitions between dynamical states of different degrees of randomness as a parameter of the system is varied.

Stages of chaotic synchronization.

PubMed

Tang, D. Y.; Dykstra, R.; Hamilton, M. W.; Heckenberg, N. R.

1998-09-01

In an experimental investigation of the response of a chaotic system to a chaotic driving force, we have observed synchronization of chaos of the response system in the forms of generalized synchronization, phase synchronization, and lag synchronization to the driving signal. In this paper we compare the features of these forms of synchronized chaos and study their relations and physical origins. We found that different forms of chaotic synchronization could be interpreted as different stages of nonlinear interaction between the coupled chaotic systems. (c) 1998 American Institute of Physics.

Ordered and disordered dynamics in monolayers of rolling particles.

PubMed

Kim, Byungsoo; Putkaradze, Vakhtang

2010-12-10

We consider the ordered and disordered dynamics for monolayers of rolling self-interacting particles modeling water molecules. The rolling constraint represents a simplified model of a strong, but rapidly decaying bond with the surface. We show the existence and nonlinear stability of ordered lattice states, as well as disturbance propagation through and chaotic vibrations of these states. We study the dynamics of disordered gas states and show that there is a surprising and universal linear connection between distributions of angular and linear velocity, allowing definition of temperature.

Experimental investigation of linear and nonlinear wave systems: A quantum chaos approach

NASA Astrophysics Data System (ADS)

Neicu, Toni

2002-09-01

An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and chaotic regions in its phase space. We observed periodic orbits in the spectral properties of the acoustic plate, the first such definitive acoustic experiment. We also solved numerically the linear wave equation of the acoustic plate for the first few hundred eigenmodes. The Fourier transform of the eigenvalues show peaks corresponding to the principal periodic orbits of the classical billiard. The signatures of the periodic orbits in the spectra were unambiguously verified by deforming one edge of the plate and observing that only the peaks corresponding to the orbits that hit this edge changed. The statistical measures of the eigenvalues are intermediate between universal forms for completely integrable and chaotic systems. The density distribution of the eigenfunctions agrees with the Porter-Thomas formula of chaotic systems. The viscosity dependence and effects of nonlinearity on the Faraday surface wave patterns in a stadium geometry were also investigated. The ray dynamics inside the stadium, a paradigm of quantum chaos, is completely chaotic. The majority of the observed patterns of the orbits resemble three eigenstates of the stadium: the bouncing ball, longitudinal, and bowtie patterns. We observed many disordered patterns that increase with the viscosity. The experimental results were analyzed using recent theoretical work that explains the suppression of certain modes. The theory also predicts that the perimeter dissipation is too strong for whispering gallery modes, which contradicts our observations of these modes for a fluid with low viscosity. Novel vortex patterns were observed in a strongly nonlinear, dissipative granular system of vertically vibrated rods. Above a critical packing fraction, moving domains of nearly vertical rods were seen to coexist with horizontal rods. The vertical domains coarsen to form several large vortices, which were driven by the anisotropy and inclination of the rods.

Chaotic Stochasticity: A Ubiquitous Source of Unpredictability in Epidemics

NASA Astrophysics Data System (ADS)

Rand, D. A.; Wilson, H. B.

1991-11-01

We address the question of whether or not childhood epidemics such as measles and chickenpox are chaotic, and argue that the best explanation of the observed unpredictability is that it is a manifestation of what we call chaotic stochasticity. Such chaos is driven and made permanent by the fluctuations from the mean field encountered in epidemics, or by extrinsic stochastic noise, and is dependent upon the existence of chaotic repellors in the mean field dynamics. Its existence is also a consequence of the near extinctions in the epidemic. For such systems, chaotic stochasticity is likely to be far more ubiquitous than the presence of deterministic chaotic attractors. It is likely to be a common phenomenon in biological dynamics.

Studies in astronomical time series analysis. IV - Modeling chaotic and random processes with linear filters

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1990-01-01

While chaos arises only in nonlinear systems, standard linear time series models are nevertheless useful for analyzing data from chaotic processes. This paper introduces such a model, the chaotic moving average. This time-domain model is based on the theorem that any chaotic process can be represented as the convolution of a linear filter with an uncorrelated process called the chaotic innovation. A technique, minimum phase-volume deconvolution, is introduced to estimate the filter and innovation. The algorithm measures the quality of a model using the volume covered by the phase-portrait of the innovation process. Experiments on synthetic data demonstrate that the algorithm accurately recovers the parameters of simple chaotic processes. Though tailored for chaos, the algorithm can detect both chaos and randomness, distinguish them from each other, and separate them if both are present. It can also recover nonminimum-delay pulse shapes in non-Gaussian processes, both random and chaotic.

Generating a Double-Scroll Attractor by Connecting a Pair of Mutual Mirror-Image Attractors via Planar Switching Control

NASA Astrophysics Data System (ADS)

Sun, Changchun; Chen, Zhongtang; Xu, Qicheng

2017-12-01

An original three-dimensional (3D) smooth continuous chaotic system and its mirror-image system with eight common parameters are constructed and a pair of symmetric chaotic attractors can be generated simultaneously. Basic dynamical behaviors of two 3D chaotic systems are investigated respectively. A double-scroll chaotic attractor by connecting the pair of mutual mirror-image attractors is generated via a novel planar switching control approach. Chaos can also be controlled to a fixed point, a periodic orbit and a divergent orbit respectively by switching between two chaotic systems. Finally, an equivalent 3D chaotic system by combining two 3D chaotic systems with a switching law is designed by utilizing a sign function. Two circuit diagrams for realizing the double-scroll attractor are depicted by employing an improved module-based design approach.

A new 4-D chaotic hyperjerk system, its synchronization, circuit design and applications in RNG, image encryption and chaos-based steganography

NASA Astrophysics Data System (ADS)

Vaidyanathan, S.; Akgul, A.; Kaçar, S.; Çavuşoğlu, U.

2018-02-01

Hyperjerk systems have received significant interest in the literature because of their simple structure and complex dynamical properties. This work presents a new chaotic hyperjerk system having two exponential nonlinearities. Dynamical properties of the chaotic hyperjerk system are discovered through equilibrium point analysis, bifurcation diagram, dissipativity and Lyapunov exponents. Moreover, an adaptive backstepping controller is designed for the synchronization of the chaotic hyperjerk system. Also, a real circuit of the chaotic hyperjerk system has been carried out to show the feasibility of the theoretical hyperjerk model. The chaotic hyperjerk system can also be useful in scientific fields such as Random Number Generators (RNGs), data security, data hiding, etc. In this work, three implementations of the chaotic hyperjerk system, viz. RNG, image encryption and sound steganography have been performed by using complex dynamics characteristics of the system.

An Artificial Bee Colony Algorithm for Uncertain Portfolio Selection

PubMed Central

Chen, Wei

2014-01-01

Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts' evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm. PMID:25089292

An artificial bee colony algorithm for uncertain portfolio selection.

PubMed

Chen, Wei

2014-01-01

Portfolio selection is an important issue for researchers and practitioners. In this paper, under the assumption that security returns are given by experts' evaluations rather than historical data, we discuss the portfolio adjusting problem which takes transaction costs and diversification degree of portfolio into consideration. Uncertain variables are employed to describe the security returns. In the proposed mean-variance-entropy model, the uncertain mean value of the return is used to measure investment return, the uncertain variance of the return is used to measure investment risk, and the entropy is used to measure diversification degree of portfolio. In order to solve the proposed model, a modified artificial bee colony (ABC) algorithm is designed. Finally, a numerical example is given to illustrate the modelling idea and the effectiveness of the proposed algorithm.

Design and experiment of controlled bistable vortex induced vibration energy harvesting systems operating in chaotic regions

NASA Astrophysics Data System (ADS)

Huynh, B. H.; Tjahjowidodo, T.; Zhong, Z.-W.; Wang, Y.; Srikanth, N.

2018-01-01

Vortex induced vibration based energy harvesting systems have gained interests in these recent years due to its potential as a low water current energy source. However, the effectiveness of the system is limited only at a certain water current due to the resonance principle that governs the concept. In order to extend the working range, a bistable spring to support the structure is introduced on the system. The improvement on the performance is essentially dependent on the bistable gap as one of the main parameters of the nonlinear spring. A sufficiently large bistable gap will result in a significant performance improvement. Unfortunately, a large bistable gap might also increase a chance of chaotic responses, which in turn will result in diminutive harvested power. To mitigate the problem, an appropriate control structure is required to stabilize the chaotic vibrations of a VIV energy converter with the bistable supporting structure. Based on the nature of the double-well potential energy in a bistable spring, the ideal control structure will attempt to drive the responses to inter-well periodic vibrations in order to maximize the harvested power. In this paper, the OGY control algorithm is designed and implemented to the system. The control strategy is selected since it requires only a small perturbation in a structural parameter to execute the control effort, thus, minimum power is needed to drive the control input. Facilitated by a wake oscillator model, the bistable VIV system is modelled as a 4-dimensional autonomous continuous-time dynamical system. To implement the controller strategy, the system is discretized at a period estimated from the subspace hyperplane intersecting to the chaotic trajectory, whereas the fixed points that correspond to the desired periodic orbits are estimated by the recurrence method. Simultaneously, the Jacobian and sensitivity matrices are estimated by the least square regression method. Based on the defined fixed point and the linearized model, the control gain matrix is calculated using the pole placement technique. The results show that the OGY controller is capable of stabilizing the chaotic responses by driving them to the desired inter-well period-one periodic vibrations and it is also shown that the harvested power is successfully improved. For validation purpose, a real-time experiment was carried out on a computer-based forced-feedback testing platform to validate the applicability of the controller in real-time applications. The experimental results confirm the feasibility of the controller to stabilize the responses.

ALMA Observations of Molecular Clouds in Three Group-centered Elliptical Galaxies: NGC 5846, NGC 4636, and NGC 5044

NASA Astrophysics Data System (ADS)

Temi, Pasquale; Amblard, Alexandre; Gitti, Myriam; Brighenti, Fabrizio; Gaspari, Massimo; Mathews, William G.; David, Laurence

2018-05-01

We present new ALMA CO(2–1) observations of two well-studied group-centered elliptical galaxies: NGC 4636 and NGC 5846. In addition, we include a revised analysis of Cycle 0 ALMA observations of the central galaxy in the NGC 5044 group. We find evidence that molecular gas is a common presence in bright group-centered galaxies (BGG). CO line widths are broader than Galactic molecular clouds, and using the reference Milky Way X CO, the total molecular mass ranges from 2.6 × 105 M ⊙ in NGC 4636 to 6.1 × 107 M ⊙ in NGC 5044. Complementary observations using the ALMA Compact Array do not exhibit any detection of a CO diffuse component at the sensitivity level achieved by current exposures. The origin of the detected molecular features is still uncertain, but these ALMA observations suggest that they are the end product of the hot gas cooling process and not the result of merger events. Some of the molecular clouds are associated with dust features as revealed by HST dust extinction maps, suggesting that these clouds formed from dust-enhanced cooling. The global nonlinear condensation may be triggered via the chaotic turbulent field or buoyant uplift. The large virial parameter of the molecular structures and correlation with the warm ({10}3{--}{10}5 {{K}})/hot (≥106) phase velocity dispersion provide evidence that they are unbound giant molecular associations drifting in the turbulent field, consistent with numerical predictions of the chaotic cold accretion process. Alternatively, the observed large CO line widths may be generated by molecular gas flowing out from cloud surfaces due to heating by the local hot gas atmosphere.

Dynamics, Analysis and Implementation of a Multiscroll Memristor-Based Chaotic Circuit

NASA Astrophysics Data System (ADS)

Alombah, N. Henry; Fotsin, Hilaire; Ngouonkadi, E. B. Megam; Nguazon, Tekou

This article introduces a novel four-dimensional autonomous multiscroll chaotic circuit which is derived from the actual simplest memristor-based chaotic circuit. A fourth circuit element — another inductor — is introduced to generate the complex behavior observed. A systematic study of the chaotic behavior is performed with the help of some nonlinear tools such as Lyapunov exponents, phase portraits, and bifurcation diagrams. Multiple scroll attractors are observed in Matlab, Pspice environments and also experimentally. We also observe the phenomenon of antimonotonicity, periodic and chaotic bubbles, multiple periodic-doubling bifurcations, Hopf bifurcations, crises and the phenomenon of intermittency. The chaotic dynamics of this circuit is realized by laboratory experiments, Pspice simulations, numerical and analytical investigations. It is observed that the results from the three environments agree to a great extent. This topology is likely convenient to be used to intentionally generate chaos in memristor-based chaotic circuit applications, given the fact that multiscroll chaotic systems have found important applications as broadband signal generators, pseudorandom number generators for communication engineering and also in biometric authentication.

From Determinism and Probability to Chaos: Chaotic Evolution towards Philosophy and Methodology of Chaotic Optimization

PubMed Central

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed. PMID:25879067

From determinism and probability to chaos: chaotic evolution towards philosophy and methodology of chaotic optimization.

PubMed

Pei, Yan

2015-01-01

We present and discuss philosophy and methodology of chaotic evolution that is theoretically supported by chaos theory. We introduce four chaotic systems, that is, logistic map, tent map, Gaussian map, and Hénon map, in a well-designed chaotic evolution algorithm framework to implement several chaotic evolution (CE) algorithms. By comparing our previous proposed CE algorithm with logistic map and two canonical differential evolution (DE) algorithms, we analyse and discuss optimization performance of CE algorithm. An investigation on the relationship between optimization capability of CE algorithm and distribution characteristic of chaotic system is conducted and analysed. From evaluation result, we find that distribution of chaotic system is an essential factor to influence optimization performance of CE algorithm. We propose a new interactive EC (IEC) algorithm, interactive chaotic evolution (ICE) that replaces fitness function with a real human in CE algorithm framework. There is a paired comparison-based mechanism behind CE search scheme in nature. A simulation experimental evaluation is conducted with a pseudo-IEC user to evaluate our proposed ICE algorithm. The evaluation result indicates that ICE algorithm can obtain a significant better performance than or the same performance as interactive DE. Some open topics on CE, ICE, fusion of these optimization techniques, algorithmic notation, and others are presented and discussed.

On the conservation of the Jacobi integral in the post-Newtonian circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Dubeibe, F. L.; Lora-Clavijo, F. D.; González, Guillermo A.

2017-05-01

In the present paper, using the first-order approximation of the n-body Lagrangian (derived on the basis of the post-Newtonian gravitational theory of Einstein, Infeld, and Hoffman), we explicitly write down the equations of motion for the planar circular restricted three-body problem in the Solar system. Additionally, with some simplified assumptions, we obtain two formulas for estimating the values of the mass-distance and velocity-speed of light ratios appropriate for a given post-Newtonian approximation. We show that the formulas derived in the present study, lead to good numerical accuracy in the conservation of the Jacobi constant and almost allow for an equivalence between the Lagrangian and Hamiltonian approaches at the same post-Newtonian order. Accordingly, the dynamics of the system is analyzed in terms of the Poincaré sections method and Lyapunov exponents, finding that for specific values of the Jacobi constant the dynamics can be either chaotic or regular. Our results suggest that the chaoticity of the post-Newtonian system is slightly increased in comparison with its Newtonian counterpart.

Fractional dynamics of globally slow transcription and its impact on deterministic genetic oscillation.

PubMed

Wei, Kun; Gao, Shilong; Zhong, Suchuan; Ma, Hong

2012-01-01

In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models--the Goodwin oscillator and the Rössler oscillator. By constructing a "dual memory" oscillator--the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

Universal algorithm for identification of fractional Brownian motion. A case of telomere subdiffusion.

PubMed

Burnecki, Krzysztof; Kepten, Eldad; Janczura, Joanna; Bronshtein, Irena; Garini, Yuval; Weron, Aleksander

2012-11-07

We present a systematic statistical analysis of the recently measured individual trajectories of fluorescently labeled telomeres in the nucleus of living human cells. The experiments were performed in the U2OS cancer cell line. We propose an algorithm for identification of the telomere motion. By expanding the previously published data set, we are able to explore the dynamics in six time orders, a task not possible earlier. As a result, we establish a rigorous mathematical characterization of the stochastic process and identify the basic mathematical mechanisms behind the telomere motion. We find that the increments of the motion are stationary, Gaussian, ergodic, and even more chaotic--mixing. Moreover, the obtained memory parameter estimates, as well as the ensemble average mean square displacement reveal subdiffusive behavior at all time spans. All these findings statistically prove a fractional Brownian motion for the telomere trajectories, which is confirmed by a generalized p-variation test. Taking into account the biophysical nature of telomeres as monomers in the chromatin chain, we suggest polymer dynamics as a sufficient framework for their motion with no influence of other models. In addition, these results shed light on other studies of telomere motion and the alternative telomere lengthening mechanism. We hope that identification of these mechanisms will allow the development of a proper physical and biological model for telomere subdynamics. This array of tests can be easily implemented to other data sets to enable quick and accurate analysis of their statistical characteristics. Copyright © 2012 Biophysical Society. Published by Elsevier Inc. All rights reserved.

Information encoder/decoder using chaotic systems

DOEpatents

Miller, Samuel Lee; Miller, William Michael; McWhorter, Paul Jackson

1997-01-01

The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals.

Information encoder/decoder using chaotic systems

DOEpatents

Miller, S.L.; Miller, W.M.; McWhorter, P.J.

1997-10-21

The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system. Encoder input signals modify the dynamics of the chaotic system comprising the encoder. The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them. The encoder output signals are then capable of secure transmissions using conventional transmission techniques. A decoder receives the encoder output signals (i.e., decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals. 32 figs.

Reducing the Dynamical Degradation by Bi-Coupling Digital Chaotic Maps

NASA Astrophysics Data System (ADS)

Liu, Lingfeng; Liu, Bocheng; Hu, Hanping; Miao, Suoxia

A chaotic map which is realized on a computer will suffer dynamical degradation. Here, a coupled chaotic model is proposed to reduce the dynamical degradation. In this model, the state variable of one digital chaotic map is used to control the parameter of the other digital map. This coupled model is universal and can be used for all chaotic maps. In this paper, two coupled models (one is coupled by two logistic maps, the other is coupled by Chebyshev map and Baker map) are performed, and the numerical experiments show that the performances of these two coupled chaotic maps are greatly improved. Furthermore, a simple pseudorandom bit generator (PRBG) based on coupled digital logistic maps is proposed as an application for our method.

Scilab software package for the study of dynamical systems

NASA Astrophysics Data System (ADS)

Bordeianu, C. C.; Beşliu, C.; Jipa, Al.; Felea, D.; Grossu, I. V.

2008-05-01

This work presents a new software package for the study of chaotic flows and maps. The codes were written using Scilab, a software package for numerical computations providing a powerful open computing environment for engineering and scientific applications. It was found that Scilab provides various functions for ordinary differential equation solving, Fast Fourier Transform, autocorrelation, and excellent 2D and 3D graphical capabilities. The chaotic behaviors of the nonlinear dynamics systems were analyzed using phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropy. Various well known examples are implemented, with the capability of the users inserting their own ODE. Program summaryProgram title: Chaos Catalogue identifier: AEAP_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEAP_v1_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 885 No. of bytes in distributed program, including test data, etc.: 5925 Distribution format: tar.gz Programming language: Scilab 3.1.1 Computer: PC-compatible running Scilab on MS Windows or Linux Operating system: Windows XP, Linux RAM: below 100 Megabytes Classification: 6.2 Nature of problem: Any physical model containing linear or nonlinear ordinary differential equations (ODE). Solution method: Numerical solving of ordinary differential equations. The chaotic behavior of the nonlinear dynamical system is analyzed using Poincaré sections, phase-space maps, autocorrelation functions, power spectra, Lyapunov exponents and Kolmogorov-Sinai entropies. Restrictions: The package routines are normally able to handle ODE systems of high orders (up to order twelve and possibly higher), depending on the nature of the problem. Running time: 10 to 20 seconds for problems that do not involve Lyapunov exponents calculation; 60 to 1000 seconds for problems that involve high orders ODE and Lyapunov exponents calculation.

Synchronization transmission of laser pattern signal within uncertain switched network

NASA Astrophysics Data System (ADS)

Lü, Ling; Li, Chengren; Li, Gang; Sun, Ao; Yan, Zhe; Rong, Tingting; Gao, Yan

2017-06-01

We propose a new technology for synchronization transmission of laser pattern signal within uncertain network with controllable topology. In synchronization process, the connection of dynamic network can vary at all time according to different demands. Especially, we construct the Lyapunov function of network through designing a special semi-positive definite function, and the synchronization transmission of laser pattern signal within uncertain network with controllable topology can be realized perfectly, which effectively avoids the complicated calculation for solving the second largest eignvalue of the coupling matrix of the dynamic network in order to obtain the network synchronization condition. At the same time, the uncertain parameters in dynamic equations belonging to network nodes can also be identified accurately via designing the identification laws of uncertain parameters. In addition, there are not any limitations for the synchronization target of network in the new technology, in other words, the target can either be a state variable signal of an arbitrary node within the network or an exterior signal.

Bubble-Induced Color Doppler Feedback for Histotripsy Tissue Fractionation.

PubMed

Miller, Ryan M; Zhang, Xi; Maxwell, Adam D; Cain, Charles A; Xu, Zhen

2016-03-01

Histotripsy therapy produces cavitating bubble clouds to increasingly fractionate and eventually liquefy tissue using high-intensity ultrasound pulses. Following cavitation generated by each pulse, coherent motion of the cavitation residual nuclei can be detected using metrics formed from ultrasound color Doppler acquisitions. In this paper, three experiments were performed to investigate the characteristics of this motion as real-time feedback on histotripsy tissue fractionation. In the first experiment, bubble-induced color Doppler (BCD) and particle image velocimetry (PIV) analysis monitored the residual cavitation nuclei in the treatment region in an agarose tissue phantom treated with two-cycle histotripsy pulses at [Formula: see text] using a 500-kHz transducer. Both BCD and PIV results showed brief chaotic motion of the residual nuclei followed by coherent motion first moving away from the transducer and then rebounding back. Velocity measurements from both PIV and BCD agreed well, showing a monotonic increase in rebound time up to a saturation point for increased therapy dose. In a second experiment, a thin layer of red blood cells (RBC) was added to the phantom to allow quantification of the fractionation of the RBC layer to compare with BCD metrics. A strong linear correlation was observed between the fractionation level and the time to BCD peak rebound velocity over histotripsy treatment. Finally, the correlation between BCD feedback and histotripsy tissue fractionation was validated in ex vivo porcine liver evaluated histologically. BCD metrics showed strong linear correlation with fractionation progression, suggesting that BCD provides useful quantitative real-time feedback on histotripsy treatment progression.

Bubble-induced Color Doppler Feedback for Histotripsy Tissue Fractionation

PubMed Central

Miller, Ryan M.; Zhang, Xi; Maxwell, Adam; Cain, Charles; Xu, Zhen

2016-01-01

Histotripsy therapy produces cavitating bubble clouds to increasingly fractionate and eventually liquefy tissue using high intensity ultrasound pulses. Following cavitation generated by each pulse, coherent motion of the cavitation residual nuclei can be detected using metrics formed from ultrasound color Doppler acquisitions. In this paper, three experiments were performed to investigate the characteristics of this motion as real-time feedback on histotripsy tissue fractionation. In the first experiment, bubble-induced color Doppler (BCD) and particle image velocimetry (PIV) analysis monitored the residual cavitation nuclei in the treatment region in an agarose tissue phantom treated with 2-cycle histotripsy pulses at > 30 MPa using a 500 kHz transducer. Both BCD and PIV results showed brief chaotic motion of the residual nuclei followed by coherent motion first moving away from the transducer and then rebounding back. Velocity measurements from both PIV and BCD agreed well, showing a monotonic increase in rebound time up to a saturation point for increased therapy dose. In a second experiment, a thin layer of red blood cells (RBC) was added to the phantom to allow quantification of the fractionation of the RBC layer to compare with BCD metrics. A strong linear correlation was observed between the fractionation level and the time to BCD peak rebound velocity over histotripsy treatment. Finally, the correlation between BCD feedback and histotripsy tissue fractionation was validated in ex vivo porcine liver evaluated histologically. BCD metrics showed strong linear correlation with fractionation progression, suggesting that BCD provides useful quantitative real-time feedback on histotripsy treatment progression. PMID:26863659

Control of Initialized Fractional-Order Systems. Revised

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

2002-01-01

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex w-plane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex w-plane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Control of Initialized Fractional-Order Systems

NASA Technical Reports Server (NTRS)

Hartly, Tom T.; Lorenzo, Carl F.

2002-01-01

Due to the importance of historical effects in fractional-order systems, this paper presents a general fractional-order control theory that includes the time-varying initialization response. Previous studies have not properly accounted for these historical effects. The initialization response, along with the forced response, for fractional-order systems is determined. Stability properties of fractional-order systems are presented in the complex Airplane, which is a transformation of the s-plane. Time responses are discussed with respect to pole positions in the complex Airplane and frequency response behavior is included. A fractional-order vector space representation, which is a generalization of the state space concept, is presented including the initialization response. Control methods for vector representations of initialized fractional-order systems are shown. Nyquist, root-locus, and other input-output control methods are adapted to the control of fractional-order systems. Finally, the fractional-order differintegral is generalized to continuous order-distributions that have the possibility of including a continuum of fractional orders in a system element.

Quantum-chaotic cryptography

NASA Astrophysics Data System (ADS)

de Oliveira, G. L.; Ramos, R. V.

2018-03-01

In this work, it is presented an optical scheme for quantum key distribution employing two synchronized optoelectronic oscillators (OEO) working in the chaotic regime. The produced key depends on the chaotic dynamic, and the synchronization between Alice's and Bob's OEOs uses quantum states. An attack on the synchronization signals will disturb the synchronization of the chaotic systems increasing the error rate in the final key.

Synchronization transition in neuronal networks composed of chaotic or non-chaotic oscillators.

PubMed

Xu, Kesheng; Maidana, Jean Paul; Castro, Samy; Orio, Patricio

2018-05-30

Chaotic dynamics has been shown in the dynamics of neurons and neural networks, in experimental data and numerical simulations. Theoretical studies have proposed an underlying role of chaos in neural systems. Nevertheless, whether chaotic neural oscillators make a significant contribution to network behaviour and whether the dynamical richness of neural networks is sensitive to the dynamics of isolated neurons, still remain open questions. We investigated synchronization transitions in heterogeneous neural networks of neurons connected by electrical coupling in a small world topology. The nodes in our model are oscillatory neurons that - when isolated - can exhibit either chaotic or non-chaotic behaviour, depending on conductance parameters. We found that the heterogeneity of firing rates and firing patterns make a greater contribution than chaos to the steepness of the synchronization transition curve. We also show that chaotic dynamics of the isolated neurons do not always make a visible difference in the transition to full synchrony. Moreover, macroscopic chaos is observed regardless of the dynamics nature of the neurons. However, performing a Functional Connectivity Dynamics analysis, we show that chaotic nodes can promote what is known as multi-stable behaviour, where the network dynamically switches between a number of different semi-synchronized, metastable states.

Chimera states in coupled Kuramoto oscillators with inertia.

PubMed

Olmi, Simona

2015-12-01

The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaotic but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.

A New Method for Suppressing Periodic Narrowband Interference Based on the Chaotic van der Pol Oscillator

NASA Astrophysics Data System (ADS)

Lu, Jia; Zhang, Xiaoxing; Xiong, Hao

The chaotic van der Pol oscillator is a powerful tool for detecting defects in electric systems by using online partial discharge (PD) monitoring. This paper focuses on realizing weak PD signal detection in the strong periodic narrowband interference by using high sensitivity to the periodic narrowband interference signals and immunity to white noise and PD signals of chaotic systems. A new approach to removing the periodic narrowband interference by using a van der Pol chaotic oscillator is described by analyzing the motion characteristic of the chaotic oscillator on the basis of the van der Pol equation. Furthermore, the Floquet index for measuring the amplitude of periodic narrowband signals is redefined. The denoising signal processed by the chaotic van der Pol oscillators is further processed by wavelet analysis. Finally, the denoising results verify that the periodic narrowband and white noise interference can be removed efficiently by combining the theory of the chaotic van der Pol oscillator and wavelet analysis.

Analysis, synchronisation and circuit design of a new highly nonlinear chaotic system

NASA Astrophysics Data System (ADS)

Mobayen, Saleh; Kingni, Sifeu Takougang; Pham, Viet-Thanh; Nazarimehr, Fahimeh; Jafari, Sajad

2018-02-01

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behaviour of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicity, periodic oscillations and double-scroll chaotic attractor. Basin of attraction of the proposed system shows that the chaotic attractor is self-excited. Furthermore, feasibility of double-scroll chaotic attractor in the real word is investigated by using the OrCAD-PSpice software via an electronic implementation of the proposed system. A good qualitative agreement is illustrated between the numerical simulations and the OrCAD-PSpice results. Finally, a finite-time control method based on dynamic sliding surface for the synchronisation of master and slave chaotic systems in the presence of external disturbances is performed. Using the suggested control technique, the superior master-slave synchronisation is attained. Illustrative simulation results on the studied chaotic system are presented to indicate the effectiveness of the suggested scheme.

High-order fractional partial differential equation transform for molecular surface construction.

PubMed

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation.

Stability Analysis of Distributed Order Fractional Chen System

PubMed Central

Aminikhah, H.; Refahi Sheikhani, A.; Rezazadeh, H.

2013-01-01

We first investigate sufficient and necessary conditions of stability of nonlinear distributed order fractional system and then we generalize the integer-order Chen system into the distributed order fractional domain. Based on the asymptotic stability theory of nonlinear distributed order fractional systems, the stability of distributed order fractional Chen system is discussed. In addition, we have found that chaos exists in the double fractional order Chen system. Numerical solutions are used to verify the analytical results. PMID:24489508

Influence of additive laser manufacturing parameters on surface using density of partially melted particles

NASA Astrophysics Data System (ADS)

Rosa, Benoit; Brient, Antoine; Samper, Serge; Hascoët, Jean-Yves

2016-12-01

Mastering the additive laser manufacturing surface is a real challenge and would allow functional surfaces to be obtained without finishing. Direct Metal Deposition (DMD) surfaces are composed by directional and chaotic textures that are directly linked to the process principles. The aim of this work is to obtain surface topographies by mastering the operating process parameters. Based on experimental investigation, the influence of operating parameters on the surface finish has been modeled. Topography parameters and multi-scale analysis have been used in order to characterize the DMD obtained surfaces. This study also proposes a methodology to characterize DMD chaotic texture through topography filtering and 3D image treatment. In parallel, a new parameter is proposed: density of particles (D p). Finally, this study proposes a regression modeling between process parameters and density of particles parameter.

Analysis of Real Ship Rolling Dynamics under Wave Excitement Force Composed of Sums of Cosine Functions

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

Zhang, Y. S.; Cai, F.; Xu, W. M.

2011-09-28

The ship motion equation with a cosine wave excitement force describes the slip moments in regular waves. A new kind of wave excitement force model, with the form as sums of cosine functions was proposed to describe ship rolling in irregular waves. Ship rolling time series were obtained by solving the ship motion equation with the fourth-order-Runger-Kutta method. These rolling time series were synthetically analyzed with methods of phase-space track, power spectrum, primary component analysis, and the largest Lyapunove exponent. Simulation results show that ship rolling presents some chaotic characteristic when the wave excitement force was applied by sums ofmore » cosine functions. The result well explains the course of ship rolling's chaotic mechanism and is useful for ship hydrodynamic study.« less

State-space prediction model for chaotic time series

NASA Astrophysics Data System (ADS)

Alparslan, A. K.; Sayar, M.; Atilgan, A. R.

1998-08-01

A simple method for predicting the continuation of scalar chaotic time series ahead in time is proposed. The false nearest neighbors technique in connection with the time-delayed embedding is employed so as to reconstruct the state space. A local forecasting model based upon the time evolution of the topological neighboring in the reconstructed phase space is suggested. A moving root-mean-square error is utilized in order to monitor the error along the prediction horizon. The model is tested for the convection amplitude of the Lorenz model. The results indicate that for approximately 100 cycles of the training data, the prediction follows the actual continuation very closely about six cycles. The proposed model, like other state-space forecasting models, captures the long-term behavior of the system due to the use of spatial neighbors in the state space.

Dynamics and circuit of a chaotic system with a curve of equilibrium points

NASA Astrophysics Data System (ADS)

Pham, Viet-Thanh; Volos, Christos; Kapitaniak, Tomasz; Jafari, Sajad; Wang, Xiong

2018-03-01

Although chaotic systems have been intensively studied since the 1960s, new systems with mysterious features are still of interest. A novel chaotic system including hyperbolic functions is proposed in this work. Especially, the system has an infinite number of equilibrium points. Dynamics of the system are investigated by using non-linear tools such as phase portrait, bifurcation diagram, and Lyapunov exponent. It is interesting that the system can display coexisting chaotic attractors. An electronic circuit for realising the chaotic system has been implemented. Experimental results show a good agreement with theoretical ones.

Lattice Boltzmann Simulation of Kinetic Isotope Effect During Snow Crystal Formation

NASA Astrophysics Data System (ADS)

Lu, G.; Depaolo, D. J.; Kang, Q.; Zhang, D.

2007-12-01

The isotopic composition of precipitation, especially that of snow, plays a special role in the global hydrological cycle and in reconstruction of past climates using polar ice cores. The fractionation of the major water isotope species (HHO, HDO, HHO-18) during ice crystal formation is critical to understanding the global distribution of isotopes in precipitation. Ice crystal growth in clouds is traditionally treated with a spherically-symmetric steady state diffusion model, with semi-empirical modifications added to account for ventilation and for complex crystal morphology. Although it is known that crystal growth rate, which depends largely on the degree of vapor over- saturation, determines crystal morphology, there are no quantitative models that relate morphology to the vapor saturation factor. Since kinetic (vapor phase diffusion-controlled) isotopic fractionation also depends on growth rate, there should be direct relationships between vapor saturation, crystal morphology, and crystal isotopic composition. We use a 2D lattice Boltzmann model to simulate diffusion-controlled ice crystal growth from vapor- oversaturated air. In the model, crystals grow solely according to the diffusive fluxes just above the crystal surfaces, and hence crystal morphology arises from the initial and boundary conditions in the model and does not need to be specified a priori. Crystal growth patterns can be varied between random growth and deterministic growth (along the maximum concentration gradient for example). The input parameters needed are the isotope- dependent vapor deposition rate constant (k) and the water vapor diffusivity in air (D). The values of both k and D can be computed from kinetic theory, and there are also experimentally determined values of D. The deduced values of k are uncertain to the extent that the condensation coefficient for ice is uncertain. The ratio D/k is a length (order 1 micron) that determines the minimum scale of dendritic growth features and allows us to scale the numerical calculations to atmospheric conditions. Our calculations confirm that the crystal/vapor isotopic fractionation approaches the equilibrium value, and the crystals are compact (circular in 2D) as the saturation factor approaches unity (S= 1.0). However, few natural crystals form under such conditions. At higher oversaturation (e.g. S = 1.2), dendritic crystals of millimeter size develop on timescales appropriate to cloud processes, and kinetic effects control isotopic fractionation. Fractionation factors for dendritic crystals are similar to those predicted by the spherical diffusion model, but the model also gives estimates of crystal heterogeneity. Dendritic crystals are constrained to be relatively large, with dimension much greater than about 20D/k. The most difficult aspect of the modeling is to account for the large density difference between air and ice, which requires us to use a fictitious higher density for the vapor-oversaturated air and scale the crystal growth time accordingly. An approach using a larger scale simulation and the domain decomposition method can provide a vapor flux for a nested smaller scale calculation. The results clarify the controls on crystal growth, and the relationships between saturation state, growth rate, crystal morphology and isotopic fractionation.

Computations of Chaotic Flows in Micromixers

DTIC Science & Technology

2006-04-07

Naval Research Laboratory Washington, DC 20375-5320 NRL/MR/6410--06-8948 Computations of Chaotic Flows in Micromixers April 7, 2006 Approved for...PAGES 17. LIMITATION OF ABSTRACT Computations of Chaotic Flows in Micromixers Carolyn R. Kaplan, Junhui Liu, David R. Mott, and Elaine S. Oran NRL/MR...striations form in time 1 _______________ Manuscript approved December 8, 2005. COMPUTATIONS OF CHAOTIC FLOWS IN MICROMIXERS or distance. Sometimes it is

Performance of Multi-chaotic PSO on a shifted benchmark functions set

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

Pluhacek, Michal; Senkerik, Roman; Zelinka, Ivan

2015-03-10

In this paper the performance of Multi-chaotic PSO algorithm is investigated using two shifted benchmark functions. The purpose of shifted benchmark functions is to simulate the time-variant real-world problems. The results of chaotic PSO are compared with canonical version of the algorithm. It is concluded that using the multi-chaotic approach can lead to better results in optimization of shifted functions.

Foundational Skills and Dispositions for Learning: An Experience with Information Problem Solving on the Web

ERIC Educational Resources Information Center

Caviglia, Francesco; Delfino, Manuela

2016-01-01

Active participation in the information society requires the ability to find some order in the chaotic nature of the Web and not to get lost within the endemic presence of inaccurate, misleading, biased and false information. This article presents an approach to Information Problem Solving (IPS)--that is, finding, understanding and assessing…

Incoherent by Design: What You Should Know about Differences between Undergraduate and Graduate Training of Elementary Teachers

ERIC Educational Resources Information Center

Greenberg, Julie; Dugan, Natalie

2015-01-01

This brief quantifies the fundamentally chaotic nature of elementary teacher preparation for initial certification, which is by far the most popular choice of individuals who consider teaching. In order to understand the different approaches taken by programs housed on the same university campus, researchers examined 13 institutions that offer…

Dynamic interaction of monowheel inclined vehicle-vibration platform coupled system with quadratic and cubic nonlinearities

NASA Astrophysics Data System (ADS)

Zhou, Shihua; Song, Guiqiu; Sun, Maojun; Ren, Zhaohui; Wen, Bangchun

2018-01-01

In order to analyze the nonlinear dynamics and stability of a novel design for the monowheel inclined vehicle-vibration platform coupled system (MIV-VPCS) with intermediate nonlinearity support subjected to a harmonic excitation, a multi-degree of freedom lumped parameter dynamic model taking into account the dynamic interaction of the MIV-VPCS with quadratic and cubic nonlinearities is presented. The dynamical equations of the coupled system are derived by applying the displacement relationship, interaction force relationship at the contact position and Lagrange's equation, which are further discretized into a set of nonlinear ordinary differential equations with coupled terms by Galerkin's truncation. Based on the mathematical model, the coupled multi-body nonlinear dynamics of the vibration system is investigated by numerical method, and the parameters influences of excitation amplitude, mass ratio and inclined angle on the dynamic characteristics are precisely analyzed and discussed by bifurcation diagram, Largest Lyapunov exponent and 3-D frequency spectrum. Depending on different ranges of system parameters, the results show that the different motions and jump discontinuity appear, and the coupled system enters into chaotic behavior through different routes (period-doubling bifurcation, inverse period-doubling bifurcation, saddle-node bifurcation and Hopf bifurcation), which are strongly attributed to the dynamic interaction of the MIV-VPCS. The decreasing excitation amplitude and inclined angle could reduce the higher order bifurcations, and effectively control the complicated nonlinear dynamic behaviors under the perturbation of low rotational speed. The first bifurcation and chaotic motion occur at lower value of inclined angle, and the chaotic behavior lasts for larger intervals with higher rotational speed. The investigation results could provide a better understanding of the nonlinear dynamic behaviors for the dynamic interaction of the MIV-VPCS.

Open problems in active chaotic flows: Competition between chaos and order in granular materials.

PubMed

Ottino, J. M.; Khakhar, D. V.

2002-06-01

There are many systems where interaction among the elementary building blocks-no matter how well understood-does not even give a glimpse of the behavior of the global system itself. Characteristic for these systems is the ability to display structure without any external organizing principle being applied. They self-organize as a consequence of synthesis and collective phenomena and the behavior cannot be understood in terms of the systems' constitutive elements alone. A simple example is flowing granular materials, i.e., systems composed of particles or grains. How the grains interact with each other is reasonably well understood; as to how particles move, the governing law is Newton's second law. There are no surprises at this level. However, when the particles are many and the material is vibrated or tumbled, surprising behavior emerges. Systems self-organize in complex patterns that cannot be deduced from the behavior of the particles alone. Self-organization is often the result of competing effects; flowing granular matter displays both mixing and segregation. Small differences in either size or density lead to flow-induced segregation and order; similar to fluids, noncohesive granular materials can display chaotic mixing and disorder. Competition gives rise to a wealth of experimental outcomes. Equilibrium structures, obtained experimentally in quasi-two-dimensional systems, display organization in the presence of disorder, and are captured by a continuum flow model incorporating collisional diffusion and density-driven segregation. Several open issues remain to be addressed. These include analysis of segregating chaotic systems from a dynamical systems viewpoint, and understanding three-dimensional systems and wet granular systems (slurries). General aspects of the competition between chaos-enhanced mixing and properties-induced de-mixing go beyond granular materials and may offer a paradigm for other kinds of physical systems. (c) 2002 American Institute of Physics.

An Iterative Solver in the Presence and Absence of Multiplicity for Nonlinear Equations

PubMed Central

Özkum, Gülcan

2013-01-01

We develop a high-order fixed point type method to approximate a multiple root. By using three functional evaluations per full cycle, a new class of fourth-order methods for this purpose is suggested and established. The methods from the class require the knowledge of the multiplicity. We also present a method in the absence of multiplicity for nonlinear equations. In order to attest the efficiency of the obtained methods, we employ numerical comparisons alongside obtaining basins of attraction to compare them in the complex plane according to their convergence speed and chaotic behavior. PMID:24453914

Nonlinear optimal control for the synchronization of chaotic and hyperchaotic finance systems

NASA Astrophysics Data System (ADS)

Rigatos, G.; Siano, P.; Loia, V.; Ademi, S.; Ghosh, T.

2017-11-01

It is possible to make specific finance systems get synchronized to other finance systems exhibiting chaotic and hyperchaotic dynamics, by applying nonlinear optimal (H-infinity) control. This signifies that chaotic behavior can be generated in finance systems by exerting a suitable control input. Actually, a lead financial system is considered which exhibits inherently chaotic dynamics. Moreover, a follower finance system is introduced having parameters in its model that inherently prohibit the appearance of chaotic dynamics. Through the application of a suitable nonlinear optimal (H-infinity) control input it is proven that the follower finance system can replicate the chaotic dynamics of the lead finance system. By applying Lyapunov analysis it is proven that asymptotically the follower finance system gets synchronized with the lead system and that the tracking error between the state variables of the two systems vanishes.

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

NASA Technical Reports Server (NTRS)

Blonigan, Patrick J.; Wang, Qiqi; Nielsen, Eric J.; Diskin, Boris

2016-01-01

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

Denoising of chaotic signal using independent component analysis and empirical mode decomposition with circulate translating

NASA Astrophysics Data System (ADS)

Wen-Bo, Wang; Xiao-Dong, Zhang; Yuchan, Chang; Xiang-Li, Wang; Zhao, Wang; Xi, Chen; Lei, Zheng

2016-01-01

In this paper, a new method to reduce noises within chaotic signals based on ICA (independent component analysis) and EMD (empirical mode decomposition) is proposed. The basic idea is decomposing chaotic signals and constructing multidimensional input vectors, firstly, on the base of EMD and its translation invariance. Secondly, it makes the independent component analysis on the input vectors, which means that a self adapting denoising is carried out for the intrinsic mode functions (IMFs) of chaotic signals. Finally, all IMFs compose the new denoised chaotic signal. Experiments on the Lorenz chaotic signal composed of different Gaussian noises and the monthly observed chaotic sequence on sunspots were put into practice. The results proved that the method proposed in this paper is effective in denoising of chaotic signals. Moreover, it can correct the center point in the phase space effectively, which makes it approach the real track of the chaotic attractor. Project supported by the National Science and Technology, China (Grant No. 2012BAJ15B04), the National Natural Science Foundation of China (Grant Nos. 41071270 and 61473213), the Natural Science Foundation of Hubei Province, China (Grant No. 2015CFB424), the State Key Laboratory Foundation of Satellite Ocean Environment Dynamics, China (Grant No. SOED1405), the Hubei Provincial Key Laboratory Foundation of Metallurgical Industry Process System Science, China (Grant No. Z201303), and the Hubei Key Laboratory Foundation of Transportation Internet of Things, Wuhan University of Technology, China (Grant No.2015III015-B02).

Long-term influence of asteroids on planet longitudes and chaotic dynamics of the solar system

NASA Astrophysics Data System (ADS)

Woillez, E.; Bouchet, F.

2017-11-01

Over timescales much longer than an orbital period, the solar system exhibits large-scale chaotic behavior and can thus be viewed as a stochastic dynamical system. The aim of the present paper is to compare different sources of stochasticity in the solar system. More precisely we studied the importance of the long term influence of asteroids on the chaotic dynamics of the solar system. We show that the effects of asteroids on planets is similar to a white noise process, when those effects are considered on a timescale much larger than the correlation time τϕ ≃ 104 yr of asteroid trajectories. We computed the timescale τe after which the effects of the stochastic evolution of the asteroids lead to a loss of information for the initial conditions of the perturbed Laplace-Lagrange secular dynamics. The order of magnitude of this timescale is precisely determined by theoretical argument, and we find that τe ≃ 104 Myr. Although comparable to the full main-sequence lifetime of the sun, this timescale is considerably longer than the Lyapunov time τI ≃ 10 Myr of the solar system without asteroids. This shows that the external sources of chaos arise as a small perturbation in the stochastic secular behavior of the solar system, rather due to intrinsic chaos.

Giant Suppression of the Activation Rate in Dynamical Systems Exhibiting Chaotic Transitions

NASA Astrophysics Data System (ADS)

Gac, J. M.; Xafebrowski, J. J.

2008-05-01

The phenomenon of giant suppression of activation, when two or more correlated noise signals act on the system, was found a few years ago in dynamical bistable or metastable systems. When the correlation between these noise signals is strong enough and the amplitudes of the noise are chosen correctly --- the life time of the metastable state may be longer than in the case of the application of only a single noise even by many orders of magnitude. In this paper, we investigate similar phenomena in systems exhibiting several chaotic transitions: Pomeau--Manneville intermittency, boundary crisis and interior crisis induced intermittency. Our goal is to show that, in these systems the application of two noise components with the proper choice of the parameters in the case of intermittency can also lengthen the mean laminar phase length or, in the case of boundary crisis, lengthen the time the trajectory spends on the pre-crisis attractor. In systems with crisis induced intermittency, we introduce a new phenomenon we called quasi-deterministic giant suppression of activation in which the lengthening of the laminar phase lengths is caused not by the action of two correlated noise signals but by a single noise term which is correlated with one of the chaotic variables of the system.

Chaotic Particle Swarm Optimization with Mutation for Classification

PubMed Central

Assarzadeh, Zahra; Naghsh-Nilchi, Ahmad Reza

2015-01-01

In this paper, a chaotic particle swarm optimization with mutation-based classifier particle swarm optimization is proposed to classify patterns of different classes in the feature space. The introduced mutation operators and chaotic sequences allows us to overcome the problem of early convergence into a local minima associated with particle swarm optimization algorithms. That is, the mutation operator sharpens the convergence and it tunes the best possible solution. Furthermore, to remove the irrelevant data and reduce the dimensionality of medical datasets, a feature selection approach using binary version of the proposed particle swarm optimization is introduced. In order to demonstrate the effectiveness of our proposed classifier, mutation-based classifier particle swarm optimization, it is checked out with three sets of data classifications namely, Wisconsin diagnostic breast cancer, Wisconsin breast cancer and heart-statlog, with different feature vector dimensions. The proposed algorithm is compared with different classifier algorithms including k-nearest neighbor, as a conventional classifier, particle swarm-classifier, genetic algorithm, and Imperialist competitive algorithm-classifier, as more sophisticated ones. The performance of each classifier was evaluated by calculating the accuracy, sensitivity, specificity and Matthews's correlation coefficient. The experimental results show that the mutation-based classifier particle swarm optimization unequivocally performs better than all the compared algorithms. PMID:25709937

Fractional-order difference equations for physical lattices and some applications

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

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru

2015-10-15

Fractional-order operators for physical lattice models based on the Grünwald-Letnikov fractional differences are suggested. We use an approach based on the models of lattices with long-range particle interactions. The fractional-order operators of differentiation and integration on physical lattices are represented by kernels of lattice long-range interactions. In continuum limit, these discrete operators of non-integer orders give the fractional-order derivatives and integrals with respect to coordinates of the Grünwald-Letnikov types. As examples of the fractional-order difference equations for physical lattices, we give difference analogs of the fractional nonlocal Navier-Stokes equations and the fractional nonlocal Maxwell equations for lattices with long-range interactions.more » Continuum limits of these fractional-order difference equations are also suggested.« less

Trace metals in Bermuda rainwater

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

Jickells, T.D.; Knap, A.H.; Church, T.M.

1984-02-20

The concentration of Cd, Cu, Fe, Mn, Ni, Pb, and Zn have been measured in Bermuda rainwater. Factor analysis indicates that Fe, Mn, and Pb have similar to acidic components derived from North America. The other metals all behave simiarly but differently to the acides. Sea salt, even after allowances for fractionation, apparently contributes minor amounts of Cu, Pb, and Zn and uncertain amounts of Fe, Mn, and Cd to Atlantic Ocean precipitation. Wash out ratios, calculated from this data along with earlier measurements of atmospheric trace metal concentration on Bermuda, are of the same order as those reported frommore » other remote ocean areas. The wet depositional fluxes of Cu, Ni, Pb, and Zn to the western Atlantic Ocean are significant compared to measured oceanic flux rates. However, the wet depositional fluxes of Fe and Mn to this area are relatively small, suggesting additional inputs, while an excess wet depositional flux of Cd suggests large-scale atmospheric recycling of this element.« less

The equal combination synchronization of a class of chaotic systems with discontinuous output

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

Luo, Runzi; Zeng, Yanhui

This paper investigates the equal combination synchronization of a class of chaotic systems. The chaotic systems are assumed that only the output state variable is available and the output may be discontinuous state variable. By constructing proper observers, some novel criteria for the equal combination synchronization are proposed. The Lorenz chaotic system is taken as an example to demonstrate the efficiency of the proposed approach.

Modelling of long-wave chaotic radar system for anti-stealth applications

NASA Astrophysics Data System (ADS)

Al-Suhail, Ghaida A.; Tahir, Fadhil Rahma; Abd, Mariam Hussien; Pham, Viet-Thanh; Fortuna, Luigi

2018-04-01

Although the Very Low-Frequency (VLF) waveforms have limited practical applications in acoustics (sonar) and secure military communications with radars and submarines; to this end; this paper presents a new and simple analytical model of VLF monostatic direct chaotic radar system. The model hypothetically depends on the two identical coupled time-delayed feedback chaotic systems which can generate and recover a long-wave chaotic signal. To resist the influence of positive Lyapunov exponents of the time-delay chaotic systems, the complete replacement of Pecaro and Carroll (PC) synchronization is employed. It can faithfully recover the chaotic signal from the back-scattered (echo) signal from the target over a noisy channel. The system performance is characterized in terms of the time series of synchronization in addition to the peak of the cross-correlation. Simulation results are conducted for substantial sensitivities of the chaotic signal to the system parameters and initial conditions. As a result, it is found that an effective and robust chaotic radar (CRADAR) model can be obtained when the signal-to-noise ratio (SNR) highly degrades to 0 dB, but with clear peak in correlation performance for detecting the target. Then, the model can be considered as a state of the art towards counter stealth technology and might be developed for other acoustic secure applications.

A new chaotic oscillator with free control

NASA Astrophysics Data System (ADS)

Li, Chunbiao; Sprott, Julien Clinton; Akgul, Akif; Iu, Herbert H. C.; Zhao, Yibo

2017-08-01

A novel chaotic system is explored in which all terms are quadratic except for a linear function. The slope of the linear function rescales the amplitude and frequency of the variables linearly while its zero intercept allows offset boosting for one of the variables. Therefore, a free-controlled chaotic oscillation can be obtained with any desired amplitude, frequency, and offset by an easy modification of the linear function. When implemented as an electronic circuit, the corresponding chaotic signal can be controlled by two independent potentiometers, which is convenient for constructing a chaos-based application system. To the best of our knowledge, this class of chaotic oscillators has never been reported.

Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons

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

Barrio, Roberto, E-mail: rbarrio@unizar.es; Serrano, Sergio; Angeles Martínez, M.

2014-06-01

We study a plethora of chaotic phenomena in the Hindmarsh-Rose neuron model with the use of several computational techniques including the bifurcation parameter continuation, spike-quantification, and evaluation of Lyapunov exponents in bi-parameter diagrams. Such an aggregated approach allows for detecting regions of simple and chaotic dynamics, and demarcating borderlines—exact bifurcation curves. We demonstrate how the organizing centers—points corresponding to codimension-two homoclinic bifurcations—along with fold and period-doubling bifurcation curves structure the biparametric plane, thus forming macro-chaotic regions of onion bulb shapes and revealing spike-adding cascades that generate micro-chaotic structures due to the hysteresis.

Decisions with Uncertain Consequences—A Total Ordering on Loss-Distributions

PubMed Central

König, Sandra; Schauer, Stefan

2016-01-01

Decisions are often based on imprecise, uncertain or vague information. Likewise, the consequences of an action are often equally unpredictable, thus putting the decision maker into a twofold jeopardy. Assuming that the effects of an action can be modeled by a random variable, then the decision problem boils down to comparing different effects (random variables) by comparing their distribution functions. Although the full space of probability distributions cannot be ordered, a properly restricted subset of distributions can be totally ordered in a practically meaningful way. We call these loss-distributions, since they provide a substitute for the concept of loss-functions in decision theory. This article introduces the theory behind the necessary restrictions and the hereby constructible total ordering on random loss variables, which enables decisions under uncertainty of consequences. Using data obtained from simulations, we demonstrate the practical applicability of our approach. PMID:28030572

Chaotic behaviour of Zeeman machines at introductory course of mechanics

NASA Astrophysics Data System (ADS)

Nagy, Péter; Tasnádi, Péter

2016-05-01

Investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics into the basic course of mechanics taught to engineering students. In the present paper it will be demonstrated that Zeeman Machine can be a versatile and motivating tool for students to get introductory knowledge about chaotic motion via interactive simulations. It works in a relatively simple way and its properties can be understood very easily. Since the machine can be built easily and the simulation of its movement is also simple the experimental investigation and the theoretical description can be connected intuitively. Although Zeeman Machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also of interest with its typical chaotic features. By means of a periodically driven Zeeman Machine a wide range of chaotic properties of the simple systems can be demonstrated such as bifurcation diagrams, chaotic attractors, transient chaos and so on. The main goal of this paper is the presentation of an interactive learning material for teaching the basic features of the chaotic systems through the investigation of the Zeeman Machine.

High-order fractional partial differential equation transform for molecular surface construction

PubMed Central

Hu, Langhua; Chen, Duan; Wei, Guo-Wei

2013-01-01

Fractional derivative or fractional calculus plays a significant role in theoretical modeling of scientific and engineering problems. However, only relatively low order fractional derivatives are used at present. In general, it is not obvious what role a high fractional derivative can play and how to make use of arbitrarily high-order fractional derivatives. This work introduces arbitrarily high-order fractional partial differential equations (PDEs) to describe fractional hyperdiffusions. The fractional PDEs are constructed via fractional variational principle. A fast fractional Fourier transform (FFFT) is proposed to numerically integrate the high-order fractional PDEs so as to avoid stringent stability constraints in solving high-order evolution PDEs. The proposed high-order fractional PDEs are applied to the surface generation of proteins. We first validate the proposed method with a variety of test examples in two and three-dimensional settings. The impact of high-order fractional derivatives to surface analysis is examined. We also construct fractional PDE transform based on arbitrarily high-order fractional PDEs. We demonstrate that the use of arbitrarily high-order derivatives gives rise to time-frequency localization, the control of the spectral distribution, and the regulation of the spatial resolution in the fractional PDE transform. Consequently, the fractional PDE transform enables the mode decomposition of images, signals, and surfaces. The effect of the propagation time on the quality of resulting molecular surfaces is also studied. Computational efficiency of the present surface generation method is compared with the MSMS approach in Cartesian representation. We further validate the present method by examining some benchmark indicators of macromolecular surfaces, i.e., surface area, surface enclosed volume, surface electrostatic potential and solvation free energy. Extensive numerical experiments and comparison with an established surface model indicate that the proposed high-order fractional PDEs are robust, stable and efficient for biomolecular surface generation. PMID:24364020

The AGN Luminosity Fraction in Galaxy Mergers

NASA Astrophysics Data System (ADS)

Dietrich, Jeremy; Weiner, Aaron; Ashby, Matthew; Martinez-Galarza, Juan Rafael; Smith, Howard Alan

2017-01-01

Galaxy mergers are key events in galaxy evolution, generally triggering massive starbursts and AGNs. However, in these chaotic systems, it is not yet known what fraction each of these two mechanisms contributes to the total luminosity. Here we measure and model spectral energy distributions (SEDs) using the Code for Investigating Galaxy Emission (CIGALE) in up to 33 broad bands from the UV to the far-IR for 23 IR-luminous galaxies to estimate the fraction of the bolometric IR luminosity that can be attributed to the AGN. The galaxies are split nearly evenly into two subsamples: late-stage mergers, found in the IRAS Revised Bright Galaxy Sample or Faint Source Catalog, and early-stage mergers found in the Spitzer Interacting Galaxy Sample. We find that the AGN contribution to the total IR luminosity varies greatly from system to system, from 0% up to ~90%, but is substantially greater in the later-stage and brighter mergers. This is consistent with what is known about galaxy evolution and the triggering of AGNs.The SAO REU program is funded in part by the National Science Foundation REU and Department of Defense ASSURE programs under NSF Grant no. 1262851, and by the Smithsonian Institution.

A resilient domain decomposition polynomial chaos solver for uncertain elliptic PDEs

NASA Astrophysics Data System (ADS)

Mycek, Paul; Contreras, Andres; Le Maître, Olivier; Sargsyan, Khachik; Rizzi, Francesco; Morris, Karla; Safta, Cosmin; Debusschere, Bert; Knio, Omar

2017-07-01

A resilient method is developed for the solution of uncertain elliptic PDEs on extreme scale platforms. The method is based on a hybrid domain decomposition, polynomial chaos (PC) framework that is designed to address soft faults. Specifically, parallel and independent solves of multiple deterministic local problems are used to define PC representations of local Dirichlet boundary-to-boundary maps that are used to reconstruct the global solution. A LAD-lasso type regression is developed for this purpose. The performance of the resulting algorithm is tested on an elliptic equation with an uncertain diffusivity field. Different test cases are considered in order to analyze the impacts of correlation structure of the uncertain diffusivity field, the stochastic resolution, as well as the probability of soft faults. In particular, the computations demonstrate that, provided sufficiently many samples are generated, the method effectively overcomes the occurrence of soft faults.

A combination chaotic system and application in color image encryption

NASA Astrophysics Data System (ADS)

Parvaz, R.; Zarebnia, M.

2018-05-01

In this paper, by using Logistic, Sine and Tent systems we define a combination chaotic system. Some properties of the chaotic system are studied by using figures and numerical results. A color image encryption algorithm is introduced based on new chaotic system. Also this encryption algorithm can be used for gray scale or binary images. The experimental results of the encryption algorithm show that the encryption algorithm is secure and practical.

A noisy chaotic neural network for solving combinatorial optimization problems: stochastic chaotic simulated annealing.

PubMed

Wang, Lipo; Li, Sa; Tian, Fuyu; Fu, Xiuju

2004-10-01

Recently Chen and Aihara have demonstrated both experimentally and mathematically that their chaotic simulated annealing (CSA) has better search ability for solving combinatorial optimization problems compared to both the Hopfield-Tank approach and stochastic simulated annealing (SSA). However, CSA may not find a globally optimal solution no matter how slowly annealing is carried out, because the chaotic dynamics are completely deterministic. In contrast, SSA tends to settle down to a global optimum if the temperature is reduced sufficiently slowly. Here we combine the best features of both SSA and CSA, thereby proposing a new approach for solving optimization problems, i.e., stochastic chaotic simulated annealing, by using a noisy chaotic neural network. We show the effectiveness of this new approach with two difficult combinatorial optimization problems, i.e., a traveling salesman problem and a channel assignment problem for cellular mobile communications.

Synchronisation and Circuit Realisation of Chaotic Hartley System

NASA Astrophysics Data System (ADS)

Varan, Metin; Akgül, Akif; Güleryüz, Emre; Serbest, Kasım

2018-06-01

Hartley chaotic system is topologically the simplest, but its dynamical behaviours are very rich and its synchronisation has not been seen in literature. This paper aims to introduce a simple chaotic system which can be used as alternative to classical chaotic systems in synchronisation fields. Time series, phase portraits, and bifurcation diagrams reveal the dynamics of the mentioned system. Chaotic Hartley model is also supported with electronic circuit model simulations. Its exponential dynamics are hard to realise on circuit model; this paper is the first in literature that handles such a complex modelling problem. Modelling, synchronisation, and circuit realisation of the Hartley system are implemented respectively in MATLAB-Simulink and ORCAD environments. The effectiveness of the applied synchronisation method is revealed via numerical methods, and the results are discussed. Retrieved results show that this complex chaotic system can be used in secure communication fields.

Generating random numbers by means of nonlinear dynamic systems

NASA Astrophysics Data System (ADS)

Zang, Jiaqi; Hu, Haojie; Zhong, Juhua; Luo, Duanbin; Fang, Yi

2018-07-01

To introduce the randomness of a physical process to students, a chaotic pendulum experiment was opened in East China University of Science and Technology (ECUST) on the undergraduate level in the physics department. It was shown chaotic motion could be initiated through adjusting the operation of a chaotic pendulum. By using the data of the angular displacements of chaotic motion, random binary numerical arrays can be generated. To check the randomness of generated numerical arrays, the NIST Special Publication 800-20 method was adopted. As a result, it was found that all the random arrays which were generated by the chaotic motion could pass the validity criteria and some of them were even better than the quality of pseudo-random numbers generated by a computer. Through the experiments, it is demonstrated that chaotic pendulum can be used as an efficient mechanical facility in generating random numbers, and can be applied in teaching random motion to the students.

Almost output regulation of LFT systems via gain-scheduling control

NASA Astrophysics Data System (ADS)

Yuan, Chengzhi; Duan, Chang; Wu, Fen

2018-05-01

Output regulation of general uncertain systems is a meaningful yet challenging problem. In spite of the rich literature in the field, the problem has not yet been addressed adequately due to the lack of an effective design mechanism. In this paper, we propose a new design framework for almost output regulation of uncertain systems described in the general form of linear fractional transformation (LFT) with time-varying parametric uncertainties and unknown external perturbations. A novel semi-LFT gain-scheduling output regulator structure is proposed, such that the associated control synthesis conditions guaranteeing both output regulation and ? disturbance attenuation performance are formulated as a set of linear matrix inequalities (LMIs) plus parameter-dependent linear matrix equations, which can be solved separately. A numerical example has been used to demonstrate the effectiveness of the proposed approach.

Connectivity-Preserving Approach for Distributed Adaptive Synchronized Tracking of Networked Uncertain Nonholonomic Mobile Robots.

PubMed

Yoo, Sung Jin; Park, Bong Seok

2017-09-06

This paper addresses a distributed connectivity-preserving synchronized tracking problem of multiple uncertain nonholonomic mobile robots with limited communication ranges. The information of the time-varying leader robot is assumed to be accessible to only a small fraction of follower robots. The main contribution of this paper is to introduce a new distributed nonlinear error surface for dealing with both the synchronized tracking and the preservation of the initial connectivity patterns among nonholonomic robots. Based on this nonlinear error surface, the recursive design methodology is presented to construct the approximation-based local adaptive tracking scheme at the robot dynamic level. Furthermore, a technical lemma is established to analyze the stability and the connectivity preservation of the total closed-loop control system in the Lyapunov sense. An example is provided to illustrate the effectiveness of the proposed methodology.

Improved first-order uncertainty method for water-quality modeling

USGS Publications Warehouse

Melching, C.S.; Anmangandla, S.

1992-01-01

Uncertainties are unavoidable in water-quality modeling and subsequent management decisions. Monte Carlo simulation and first-order uncertainty analysis (involving linearization at central values of the uncertain variables) have been frequently used to estimate probability distributions for water-quality model output due to their simplicity. Each method has its drawbacks: Monte Carlo simulation's is mainly computational time; and first-order analysis are mainly questions of accuracy and representativeness, especially for nonlinear systems and extreme conditions. An improved (advanced) first-order method is presented, where the linearization point varies to match the output level whose exceedance probability is sought. The advanced first-order method is tested on the Streeter-Phelps equation to estimate the probability distribution of critical dissolved-oxygen deficit and critical dissolved oxygen using two hypothetical examples from the literature. The advanced first-order method provides a close approximation of the exceedance probability for the Streeter-Phelps model output estimated by Monte Carlo simulation using less computer time - by two orders of magnitude - regardless of the probability distributions assumed for the uncertain model parameters.

Long-term affects of a single P fertilization on Hedley P pools in a South Carolina loblolly pine plantation

Treesearch

Bradley W. Miller; Thomas R. Fox

2010-01-01

While phosphorus (P) fertilization increases plant available or “labile” P immediately after fertilization, it is uncertain how it influences P pools over the long term in forest soils. Phosphorus pools from a 22-year-old loblolly pine (Pinus taeda L.) fertilization study were quantified using the Hedley sequential fractionation procedure, Mehlich-1...

Analytical Studies on the Synchronization of a Network of Linearly-Coupled Simple Chaotic Systems

NASA Astrophysics Data System (ADS)

Sivaganesh, G.; Arulgnanam, A.; Seethalakshmi, A. N.; Selvaraj, S.

2018-05-01

We present explicit generalized analytical solutions for a network of linearly-coupled simple chaotic systems. Analytical solutions are obtained for the normalized state equations of a network of linearly-coupled systems driven by a common chaotic drive system. Two parameter bifurcation diagrams revealing the various hidden synchronization regions, such as complete, phase and phase-lag synchronization are identified using the analytical results. The synchronization dynamics and their stability are studied using phase portraits and the master stability function, respectively. Further, experimental results for linearly-coupled simple chaotic systems are presented to confirm the analytical results. The synchronization dynamics of a network of chaotic systems studied analytically is reported for the first time.

Fuzzy fractals, chaos, and noise

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

Zardecki, A.

1997-05-01

To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the conceptmore » of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.« less

A new 4D chaotic system with hidden attractor and its engineering applications: Analog circuit design and field programmable gate array implementation

NASA Astrophysics Data System (ADS)

Abdolmohammadi, Hamid Reza; Khalaf, Abdul Jalil M.; Panahi, Shirin; Rajagopal, Karthikeyan; Pham, Viet-Thanh; Jafari, Sajad

2018-06-01

Nowadays, designing chaotic systems with hidden attractor is one of the most interesting topics in nonlinear dynamics and chaos. In this paper, a new 4D chaotic system is proposed. This new chaotic system has no equilibria, and so it belongs to the category of systems with hidden attractors. Dynamical features of this system are investigated with the help of its state-space portraits, bifurcation diagram, Lyapunov exponents diagram, and basin of attraction. Also a hardware realisation of this system is proposed by using field programmable gate arrays (FPGA). In addition, an electronic circuit design for the chaotic system is introduced.

Chaotic ultra-wideband radio generator based on an optoelectronic oscillator with a built-in microwave photonic filter.

PubMed

Wang, Li Xian; Zhu, Ning Hua; Zheng, Jian Yu; Liu, Jian Guo; Li, Wei

2012-05-20

We induce a microwave photonic bandpass filter into an optoelectronic oscillator to generate a chaotic ultra-wideband signal in both the optical and electrical domain. The theoretical analysis and numerical simulation indicate that this system is capable of generating band-limited high-dimensional chaos. Experimental results coincide well with the theoretical prediction and show that the power spectrum of the generated chaotic signal basically meets the Federal Communications Commission indoor mask. The generated chaotic carrier is further intensity modulated by a 10 MHz square wave, and the waveform of the output ultra-wideband signal is measured for demonstrating the chaotic on-off keying modulation.

The chaotic saddle of a three degrees of freedom scattering system reconstructed from cross-section data

NASA Astrophysics Data System (ADS)

Drótos, G.; Jung, C.

2016-06-01

The topic of this paper is hyperbolic chaotic scattering in a three degrees of freedom system. We generalize how shadows in the domain of the doubly differential cross-section are found: they are traced out by the appropriately filtered unstable manifolds of the periodic trajectories in the chaotic saddle. These shadows are related to the rainbow singularities in the doubly differential cross-section. As a result of this relation, we discover a method of how to recognize in the cross section a smoothly deformed image of the chaotic saddle, allowing the reconstruction of the symbolic dynamics of the chaotic saddle, its topology and its scaling factors.

A new transiently chaotic flow with ellipsoid equilibria

NASA Astrophysics Data System (ADS)

Panahi, Shirin; Aram, Zainab; Jafari, Sajad; Pham, Viet-Thanh; Volos, Christos; Rajagopal, Karthikeyan

2018-03-01

In this article, a simple autonomous transiently chaotic flow with cubic nonlinearities is proposed. This system represents some unusual features such as having a surface of equilibria. We shall describe some dynamical properties and behaviours of this system in terms of eigenvalue structures, bifurcation diagrams, time series, and phase portraits. Various behaviours of this system such as periodic and transiently chaotic dynamics can be shown by setting special parameters in proper values. Our system belongs to a newly introduced category of transiently chaotic systems: systems with hidden attractors. Transiently chaotic behaviour of our proposed system has been implemented and tested by the OrCAD-PSpise software. We have found a proper qualitative similarity between circuit and simulation results.

Exponential Synchronization of Networked Chaotic Delayed Neural Network by a Hybrid Event Trigger Scheme.

PubMed

Fei, Zhongyang; Guan, Chaoxu; Gao, Huijun; Zhongyang Fei; Chaoxu Guan; Huijun Gao; Fei, Zhongyang; Guan, Chaoxu; Gao, Huijun

2018-06-01

This paper is concerned with the exponential synchronization for master-slave chaotic delayed neural network with event trigger control scheme. The model is established on a network control framework, where both external disturbance and network-induced delay are taken into consideration. The desired aim is to synchronize the master and slave systems with limited communication capacity and network bandwidth. In order to save the network resource, we adopt a hybrid event trigger approach, which not only reduces the data package sending out, but also gets rid of the Zeno phenomenon. By using an appropriate Lyapunov functional, a sufficient criterion for the stability is proposed for the error system with extended ( , , )-dissipativity performance index. Moreover, hybrid event trigger scheme and controller are codesigned for network-based delayed neural network to guarantee the exponential synchronization between the master and slave systems. The effectiveness and potential of the proposed results are demonstrated through a numerical example.

Chaotic Dynamical Ferromagnetic Phase Induced by Nonequilibrium Quantum Fluctuations

NASA Astrophysics Data System (ADS)

Lerose, Alessio; Marino, Jamir; Žunkovič, Bojan; Gambassi, Andrea; Silva, Alessandro

2018-03-01

We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbor spin interaction in one spatial dimension on the nonequilibrium dynamical phase diagram of the fully connected quantum Ising model. In particular, we focus on the transient dynamics after a quantum quench and study the prethermal state via a combination of analytic time-dependent spin wave theory and numerical methods based on matrix product states. We find that, upon increasing the strength of the quantum fluctuations, the dynamical critical point fans out into a chaotic dynamical phase within which the asymptotic ordering is characterized by strong sensitivity to the parameters and initial conditions. We argue that such a phenomenon is general, as it arises from the impact of quantum fluctuations on the mean-field out of equilibrium dynamics of any system which exhibits a broken discrete symmetry.

Data-driven forecasting of high-dimensional chaotic systems with long short-term memory networks.

PubMed

Vlachas, Pantelis R; Byeon, Wonmin; Wan, Zhong Y; Sapsis, Themistoklis P; Koumoutsakos, Petros

2018-05-01

We introduce a data-driven forecasting method for high-dimensional chaotic systems using long short-term memory (LSTM) recurrent neural networks. The proposed LSTM neural networks perform inference of high-dimensional dynamical systems in their reduced order space and are shown to be an effective set of nonlinear approximators of their attractor. We demonstrate the forecasting performance of the LSTM and compare it with Gaussian processes (GPs) in time series obtained from the Lorenz 96 system, the Kuramoto-Sivashinsky equation and a prototype climate model. The LSTM networks outperform the GPs in short-term forecasting accuracy in all applications considered. A hybrid architecture, extending the LSTM with a mean stochastic model (MSM-LSTM), is proposed to ensure convergence to the invariant measure. This novel hybrid method is fully data-driven and extends the forecasting capabilities of LSTM networks.

Complexity and network dynamics in physiological adaptation: an integrated view.

PubMed

Baffy, György; Loscalzo, Joseph

2014-05-28

Living organisms constantly interact with their surroundings and sustain internal stability against perturbations. This dynamic process follows three fundamental strategies (restore, explore, and abandon) articulated in historical concepts of physiological adaptation such as homeostasis, allostasis, and the general adaptation syndrome. These strategies correspond to elementary forms of behavior (ordered, chaotic, and static) in complex adaptive systems and invite a network-based analysis of the operational characteristics, allowing us to propose an integrated framework of physiological adaptation from a complex network perspective. Applicability of this concept is illustrated by analyzing molecular and cellular mechanisms of adaptation in response to the pervasive challenge of obesity, a chronic condition resulting from sustained nutrient excess that prompts chaotic exploration for system stability associated with tradeoffs and a risk of adverse outcomes such as diabetes, cardiovascular disease, and cancer. Deconstruction of this complexity holds the promise of gaining novel insights into physiological adaptation in health and disease. Published by Elsevier Inc.

Chaotic Dynamical Ferromagnetic Phase Induced by Nonequilibrium Quantum Fluctuations.

PubMed

Lerose, Alessio; Marino, Jamir; Žunkovič, Bojan; Gambassi, Andrea; Silva, Alessandro

2018-03-30

We investigate the robustness of a dynamical phase transition against quantum fluctuations by studying the impact of a ferromagnetic nearest-neighbor spin interaction in one spatial dimension on the nonequilibrium dynamical phase diagram of the fully connected quantum Ising model. In particular, we focus on the transient dynamics after a quantum quench and study the prethermal state via a combination of analytic time-dependent spin wave theory and numerical methods based on matrix product states. We find that, upon increasing the strength of the quantum fluctuations, the dynamical critical point fans out into a chaotic dynamical phase within which the asymptotic ordering is characterized by strong sensitivity to the parameters and initial conditions. We argue that such a phenomenon is general, as it arises from the impact of quantum fluctuations on the mean-field out of equilibrium dynamics of any system which exhibits a broken discrete symmetry.

Efficient biometric authenticated key agreements based on extended chaotic maps for telecare medicine information systems.

PubMed

Lou, Der-Chyuan; Lee, Tian-Fu; Lin, Tsung-Hung

2015-05-01

Authenticated key agreements for telecare medicine information systems provide patients, doctors, nurses and health visitors with accessing medical information systems and getting remote services efficiently and conveniently through an open network. In order to have higher security, many authenticated key agreement schemes appended biometric keys to realize identification except for using passwords and smartcards. Due to too many transmissions and computational costs, these authenticated key agreement schemes are inefficient in communication and computation. This investigation develops two secure and efficient authenticated key agreement schemes for telecare medicine information systems by using biometric key and extended chaotic maps. One scheme is synchronization-based, while the other nonce-based. Compared to related approaches, the proposed schemes not only retain the same security properties with previous schemes, but also provide users with privacy protection and have fewer transmissions and lower computational cost.

Lossy chaotic electromagnetic reverberation chambers: Universal statistical behavior of the vectorial field

NASA Astrophysics Data System (ADS)

Gros, J.-B.; Kuhl, U.; Legrand, O.; Mortessagne, F.

2016-03-01

The effective Hamiltonian formalism is extended to vectorial electromagnetic waves in order to describe statistical properties of the field in reverberation chambers. The latter are commonly used in electromagnetic compatibility tests. As a first step, the distribution of wave intensities in chaotic systems with varying opening in the weak coupling limit for scalar quantum waves is derived by means of random matrix theory. In this limit the only parameters are the modal overlap and the number of open channels. Using the extended effective Hamiltonian, we describe the intensity statistics of the vectorial electromagnetic eigenmodes of lossy reverberation chambers. Finally, the typical quantity of interest in such chambers, namely, the distribution of the electromagnetic response, is discussed. By determining the distribution of the phase rigidity, describing the coupling to the environment, using random matrix numerical data, we find good agreement between the theoretical prediction and numerical calculations of the response.

Anti-control of chaos of single time-scale brushless DC motor.

PubMed

Ge, Zheng-Ming; Chang, Ching-Ming; Chen, Yen-Sheng

2006-09-15

Anti-control of chaos of single time-scale brushless DC motors is studied in this paper. In order to analyse a variety of periodic and chaotic phenomena, we employ several numerical techniques such as phase portraits, bifurcation diagrams and Lyapunov exponents. Anti-control of chaos can be achieved by adding an external constant term or an external periodic term.

Voice and Vision in Paul Zimmer's "The Great Bird of Love."

ERIC Educational Resources Information Center

Worsham, Fabian Clements

Paul Zimmer's latest poetry collection, "The Great Bird of Love," is serious and somber, fraught with the burden of evil, the indifference of God, and the certainty of death. The book is not humorless, however, as humor is central to both the chaotic evil and the ordered goodness of human life. It is in this collection that it is…

Characteristic coupling time between axial and transverse energy modes for anti-hydrogen in magnetostatic traps

NASA Astrophysics Data System (ADS)

Zhong, Mike; Fajans, Joel

2016-10-01

For upcoming ALPHA collaboration laser spectroscopy and gravity experiments, the nature of the chaotic trajectories of individual antihydrogen atoms trapped in the octupole Ioffe magnetic trap is of importance. Of particular interest for experimental design is the coupling time between the axial and transverse modes of energy for the antihydrogen atoms. Using Monte Carlo simulations of semiclassical dynamics of antihydrogen trajectories, we quantify this characteristic coupling time between axial and transverse modes of energy. There appear to be two classes of trajectories: for orbits whose axial energy is higher than 10% of the total energy, the axial energy varies chaotically on the order of 1-10 seconds, whereas for orbits whose axial energy is around 10% of the total energy, the axial energy remains nearly constant on the order of 1000 seconds or longer. Furthermore, we search through parameter -space to find parameters of the magnetic trap that minimize and maximize this characteristic coupling time. This work was supported by the UC Berkeley Summer Undergraduate Research Fellowship, the Berkeley Research Computing program, the Department of Energy contract DE-FG02-06ER54904, and the National Science Foundation Grant 1500538-PHY.

Chaotic Dynamics and Application of LCR Oscillators Sharing Common Nonlinearity

NASA Astrophysics Data System (ADS)

Jeevarekha, A.; Paul Asir, M.; Philominathan, P.

2016-06-01

This paper addresses the problem of sharing common nonlinearity among nonautonomous and autonomous oscillators. By choosing a suitable common nonlinear element with the driving point characteristics capable of bringing out chaotic motion in a combined system, we obtain identical chaotic states. The dynamics of the coupled system is explored through numerical and experimental studies. Employing the concept of common nonlinearity, a simple chaotic communication system is modeled and its performance is verified through Multisim simulation.

An in-depth assessment into simultaneous monitoring of dissolved reactive phosphorus (DRP) and low-molecular-weight organic phosphorus (LMWOP) in aquatic environments using diffusive gradients in thin films (DGT).

PubMed

Mohr, Christian Wilhelm; Vogt, Rolf David; Røyset, Oddvar; Andersen, Tom; Parekh, Neha Amit

2015-04-01

Long-term laborious and thus costly monitoring of phosphorus (P) fractions is required in order to provide reasonable estimates of the levels of bioavailable phosphorus for eutrophication studies. A practical solution to this problem is the application of passive samplers, known as Diffusive Gradient in Thin films (DGTs), providing time-average concentrations. DGT, with the phosphate adsorbent Fe-oxide based binding gel, is capable of collecting both orthophosphate and low molecular weight organic phosphorus (LMWOP) compounds, such as adenosine monophosphate (AMP) and myo-inositol hexakisphosphate (IP6). The diffusion coefficient (D) is a key parameter relating the amount of analyte determined from the DGT to a time averaged ambient concentration. D at 20 °C for AMP and IP6 were experimentally determined to be 2.9 × 10(-6) cm(2) s(-1) and 1.0 × 10(-6) cm(2) s(-1), respectively. Estimations by conceptual models of LMWOP uptake by DGTs indicated that this fraction constituted more than 75% of the dissolved organic phosphorus (DOP) accumulated. Since there is no one D for LMWOP, a D range was estimated through assessment of D models. The models tested for estimating D for a variety of common LMWOP molecules proved to be still too uncertain for practical use. The experimentally determined D for AMP and IP6 were therefore used as upper and lower D, respectively, in order to estimate minimum and maximum ambient concentrations of LMWOP. Validation of the DGT data was performed by comparing concentrations of P fractions determined in natural water samples with concentration of P fractions determined using DGT. Stream water draining three catchments with different land-use (forest, mixed and agriculture) showed clear differences in relative and absolute concentrations of dissolved reactive phosphorus (DRP) and dissolved organic P (DOP). There was no significant difference between water sample and DGT DRP (p > 0.05). Moreover, the upper and lower limit D for LMWOP proved reasonable as water sample determined DOP was found to lie in-between the limits of DGT LMWOP concentrations, indicating that on average DOP consists mainly of LMWOP. "Best fit" D was determined for each stream in order to practically use the DGTs for estimating time average DOP. Applying DGT in a eutrophic lake provided insight into P cycling in the water column.

High security chaotic multiple access scheme for visible light communication systems with advanced encryption standard interleaving

NASA Astrophysics Data System (ADS)

Qiu, Junchao; Zhang, Lin; Li, Diyang; Liu, Xingcheng

2016-06-01

Chaotic sequences can be applied to realize multiple user access and improve the system security for a visible light communication (VLC) system. However, since the map patterns of chaotic sequences are usually well known, eavesdroppers can possibly derive the key parameters of chaotic sequences and subsequently retrieve the information. We design an advanced encryption standard (AES) interleaving aided multiple user access scheme to enhance the security of a chaotic code division multiple access-based visible light communication (C-CDMA-VLC) system. We propose to spread the information with chaotic sequences, and then the spread information is interleaved by an AES algorithm and transmitted over VLC channels. Since the computation complexity of performing inverse operations to deinterleave the information is high, the eavesdroppers in a high speed VLC system cannot retrieve the information in real time; thus, the system security will be enhanced. Moreover, we build a mathematical model for the AES-aided VLC system and derive the theoretical information leakage to analyze the system security. The simulations are performed over VLC channels, and the results demonstrate the effectiveness and high security of our presented AES interleaving aided chaotic CDMA-VLC system.

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

Olmi, Simona, E-mail: simona.olmi@fi.isc.cnr.it; INFN Sez. Firenze, via Sansone, 1 - I-50019 Sesto Fiorentino

The dynamics of two symmetrically coupled populations of rotators is studied for different values of the inertia. The system is characterized by different types of solutions, which all coexist with the fully synchronized state. At small inertia, the system is no more chaotic and one observes mainly quasi-periodic chimeras, while the usual (stationary) chimera state is not anymore observable. At large inertia, one observes two different kind of chaotic solutions with broken symmetry: the intermittent chaotic chimera, characterized by a synchronized population and a population displaying a turbulent behaviour, and a second state where the two populations are both chaoticmore » but whose dynamics adhere to two different macroscopic attractors. The intermittent chaotic chimeras are characterized by a finite life-time, whose duration increases as a power-law with the system size and the inertia value. Moreover, the chaotic population exhibits clear intermittent behavior, displaying a laminar phase where the two populations tend to synchronize, and a turbulent phase where the macroscopic motion of one population is definitely erratic. In the thermodynamic limit, these states survive for infinite time and the laminar regimes tends to disappear, thus giving rise to stationary chaotic solutions with broken symmetry contrary to what observed for chaotic chimeras on a ring geometry.« less

Design and analysis of fractional order seismic transducer for displacement and acceleration measurements

NASA Astrophysics Data System (ADS)

Veeraian, Parthasarathi; Gandhi, Uma; Mangalanathan, Umapathy

2018-04-01

Seismic transducers are widely used for measurement of displacement, velocity, and acceleration. This paper presents the design of seismic transducer in the fractional domain for the measurement of displacement and acceleration. The fractional order transfer function for seismic displacement and acceleration transducer are derived using Grünwald-Letnikov derivative. Frequency response analysis of fractional order seismic displacement transducer (FOSDT) and fractional order seismic acceleration transducer (FOSAT) are carried out for different damping ratio with the different fractional order, and the maximum dynamic measurement range is identified. The results demonstrate that fractional order seismic transducer has increased dynamic measurement range and less phase distortion as compared to the conventional seismic transducer even with a lower damping ratio. Time response of FOSDT and FOSAT are derived analytically in terms of Mittag-Leffler function, the effect of fractional behavior in the time domain is evaluated from the impulse and step response. The fractional order system is found to have significantly reduced overshoot as compared to the conventional transducer. The fractional order seismic transducer design proposed in this paper is illustrated with a design example for FOSDT and FOSAT. Finally, an electrical equivalent of FOSDT and FOSAT is considered, and its frequency response is found to be in close agreement with the proposed fractional order seismic transducer.

Chaotic dynamics around cometary nuclei

NASA Astrophysics Data System (ADS)

Lages, José; Shevchenko, Ivan I.; Rollin, Guillaume

2018-06-01

We apply a generalized Kepler map theory to describe the qualitative chaotic dynamics around cometary nuclei, based on accessible observational data for five comets whose nuclei are well-documented to resemble dumb-bells. The sizes of chaotic zones around the nuclei and the Lyapunov times of the motion inside these zones are estimated. In the case of Comet 1P/Halley, the circumnuclear chaotic zone seems to engulf an essential part of the Hill sphere, at least for orbits of moderate to high eccentricity.

Synchronization of Chaotic Systems without Direct Connections Using Reinforcement Learning

NASA Astrophysics Data System (ADS)

Sato, Norihisa; Adachi, Masaharu

In this paper, we propose a control method for the synchronization of chaotic systems that does not require the systems to be connected, unlike existing methods such as that proposed by Pecora and Carroll in 1990. The method is based on the reinforcement learning algorithm. We apply our method to two discrete-time chaotic systems with mismatched parameters and achieve M step delay synchronization. Moreover, we extend the proposed method to the synchronization of continuous-time chaotic systems.

Robust finite-time chaos synchronization of uncertain permanent magnet synchronous motors.

PubMed

Chen, Qiang; Ren, Xuemei; Na, Jing

2015-09-01

In this paper, a robust finite-time chaos synchronization scheme is proposed for two uncertain third-order permanent magnet synchronous motors (PMSMs). The whole synchronization error system is divided into two cascaded subsystems: a first-order subsystem and a second-order subsystem. For the first subsystem, we design a finite-time controller based on the finite-time Lyapunov stability theory. Then, according to the backstepping idea and the adding a power integrator technique, a second finite-time controller is constructed recursively for the second subsystem. No exogenous forces are required in the controllers design but only the direct-axis (d-axis) and the quadrature-axis (q-axis) stator voltages are used as manipulated variables. Comparative simulations are provided to show the effectiveness and superior performance of the proposed method. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Optimal second order sliding mode control for linear uncertain systems.

PubMed

Das, Madhulika; Mahanta, Chitralekha

2014-11-01

In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

Experimental Chaos - Proceedings of the 3rd Conference

NASA Astrophysics Data System (ADS)

Harrison, Robert G.; Lu, Weiping; Ditto, William; Pecora, Lou; Spano, Mark; Vohra, Sandeep

1996-10-01

The Table of Contents for the full book PDF is as follows: * Preface * Spatiotemporal Chaos and Patterns * Scale Segregation via Formation of Domains in a Nonlinear Optical System * Laser Dynamics as Hydrodynamics * Spatiotemporal Dynamics of Human Epileptic Seizures * Experimental Transition to Chaos in a Quasi 1D Chain of Oscillators * Measuring Coupling in Spatiotemporal Dynamical Systems * Chaos in Vortex Breakdown * Dynamical Analysis * Radial Basis Function Modelling and Prediction of Time Series * Nonlinear Phenomena in Polyrhythmic Hand Movements * Using Models to Diagnose, Test and Control Chaotic Systems * New Real-Time Analysis of Time Series Data with Physical Wavelets * Control and Synchronization * Measuring and Controlling Chaotic Dynamics in a Slugging Fluidized Bed * Control of Chaos in a Laser with Feedback * Synchronization and Chaotic Diode Resonators * Control of Chaos by Continuous-time Feedback with Delay * A Framework for Communication using Chaos Sychronization * Control of Chaos in Switching Circuits * Astrophysics, Meteorology and Oceanography * Solar-Wind-Magnetospheric Dynamics via Satellite Data * Nonlinear Dynamics of the Solar Atmosphere * Fractal Dimension of Scalar and Vector Variables from Turbulence Measurements in the Atmospheric Surface Layer * Mechanics * Escape and Overturning: Subtle Transient Behavior in Nonlinear Mechanical Models * Organising Centres in the Dynamics of Parametrically Excited Double Pendulums * Intermittent Behaviour in a Heating System Driven by Phase Transitions * Hydrodynamics * Size Segregation in Couette Flow of Granular Material * Routes to Chaos in Rotational Taylor-Couette Flow * Experimental Study of the Laminar-Turbulent Transition in an Open Flow System * Chemistry * Order and Chaos in Excitable Media under External Forcing * A Chemical Wave Propagation with Accelerating Speed Accompanied by Hydrodynamic Flow * Optics * Instabilities in Semiconductor Lasers with Optical Injection * Spatio-Temporal Dynamics of a Bimode CO2 Laser with Saturable Absorber * Chaotic Homoclinic Phenomena in Opto-Thermal Devices * Observation and Characterisation of Low-Frequency Chaos in Semiconductor Lasers with External Feedback * Condensed Matter * The Application of Nonlinear Dynamics in the Study of Ferroelectric Materials * Cellular Convection in a Small Aspect Ratio Liquid Crystal Device * Driven Spin-Wave Dynamics in YIG Films * Quantum Chaology in Quartz * Small Signal Amplification Caused by Nonlinear Properties of Ferroelectrics * Composite Materials Evolved from Chaos * Electronics and Circuits * Controlling a Chaotic Array of Pulse-Coupled Fitzhugh-Nagumo Circuits * Experimental Observation of On-Off Intermittency * Phase Lock-In of Chaotic Relaxation Oscillators * Biology and Medicine * Singular Value Decomposition and Circuit Structure in Invertebrate Ganglia * Nonlinear Forecasting of Spike Trains from Neurons of a Mollusc * Ultradian Rhythm in the Sensitive Plants: Chaos or Coloured Noise? * Chaos and the Crayfish Sixth Ganglion * Hardware Coupled Nonlinear Oscillators as a Model of Retina

Topics in quantum chaos

NASA Astrophysics Data System (ADS)

Jordan, Andrew Noble

2002-09-01

In this dissertation, we study the quantum mechanics of classically chaotic dynamical systems. We begin by considering the decoherence effects a quantum chaotic system has on a simple quantum few state system. Typical time evolution of a quantum system whose classical limit is chaotic generates structures in phase space whose size is much smaller than Planck's constant. A naive application of Heisenberg's uncertainty principle indicates that these structures are not physically relevant. However, if we take the quantum chaotic system in question to be an environment which interacts with a simple two state quantum system (qubit), we show that these small phase-space structures cause the qubit to generically lose quantum coherence if and only if the environment has many degrees of freedom, such as a dilute gas. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence. Next, we turn to an analysis of statistical properties of time correlation functions and matrix elements of quantum chaotic systems. A semiclassical evaluation of matrix elements of an operator indicates that the dominant contribution will be related to a classical time correlation function over the energy surface. For a highly chaotic class of dynamics, these correlation functions may be decomposed into sums of Ruelle resonances, which control exponential decay to the ergodic distribution. The theory is illustrated both numerically and theoretically on the Baker map. For this system, we are able to isolate individual Ruelle modes. We further consider dynamical systems whose approach to ergodicity is given by a power law rather than an exponential in time. We propose a billiard with diffusive boundary conditions, whose classical solution may be calculated analytically. We go on to compare the exact solution with an approximation scheme, as well calculate asympotic corrections. Quantum spectral statistics are calculated assuming the validity of the Again, Altshuler and Andreev ansatz. We find singular behavior of the two point spectral correlator in the limit of small spacing. Finally, we analyse the effect that slow decay to ergodicity has on the structure of the quantum propagator, as well as wavefunction localization. We introduce a statistical quantum description of systems that are composed of both an orderly region and a random region. By averaging over the random region only, we find that measures of localization in momentum space semiclassically diverge with the dimension of the Hilbert space. We illustrate this numerically with quantum maps and suggest various other systems where this behavior should be important.

On the relationship between the Hurst exponent, the ratio of the mean square successive difference to the variance, and the number of turning points

NASA Astrophysics Data System (ADS)

Tarnopolski, Mariusz

2016-11-01

The long range dependence of the fractional Brownian motion (fBm), fractional Gaussian noise (fGn), and differentiated fGn (DfGn) is described by the Hurst exponent H. Considering the realizations of these three processes as time series, they might be described by their statistical features, such as half of the ratio of the mean square successive difference to the variance, A, and the number of turning points, T. This paper investigates the relationships between A and H, and between T and H. It is found numerically that the formulae A(H) = aebH in case of fBm, and A(H) = a + bHc for fGn and DfGn, describe well the A(H) relationship. When T(H) is considered, no simple formula is found, and it is empirically found that among polynomials, the fourth and second order description applies best. The most relevant finding is that when plotted in the space of (A , T) , the three process types form separate branches. Hence, it is examined whether A and T may serve as Hurst exponent indicators. Some real world data (stock market indices, sunspot numbers, chaotic time series) are analyzed for this purpose, and it is found that the H's estimated using the H(A) relations (expressed as inverted A(H) functions) are consistent with the H's extracted with the well known wavelet approach. This allows to efficiently estimate the Hurst exponent based on fast and easy to compute A and T, given that the process type: fBm, fGn or DfGn, is correctly classified beforehand. Finally, it is suggested that the A(H) relation for fGn and DfGn might be an exact (shifted) 3 / 2 power-law.

Radiotherapy Dose Fractionation under Parameter Uncertainty

NASA Astrophysics Data System (ADS)

Davison, Matt; Kim, Daero; Keller, Harald

2011-11-01

In radiotherapy, radiation is directed to damage a tumor while avoiding surrounding healthy tissue. Tradeoffs ensue because dose cannot be exactly shaped to the tumor. It is particularly important to ensure that sensitive biological structures near the tumor are not damaged more than a certain amount. Biological tissue is known to have a nonlinear response to incident radiation. The linear quadratic dose response model, which requires the specification of two clinically and experimentally observed response coefficients, is commonly used to model this effect. This model yields an optimization problem giving two different types of optimal dose sequences (fractionation schedules). Which fractionation schedule is preferred depends on the response coefficients. These coefficients are uncertainly known and may differ from patient to patient. Because of this not only the expected outcomes but also the uncertainty around these outcomes are important, and it might not be prudent to select the strategy with the best expected outcome.

The chaotic set and the cross section for chaotic scattering in three degrees of freedom

NASA Astrophysics Data System (ADS)

Jung, C.; Merlo, O.; Seligman, T. H.; Zapfe, W. P. K.

2010-10-01

This article treats chaotic scattering with three degrees of freedom, where one of them is open and the other two are closed, as a first step towards a more general understanding of chaotic scattering in higher dimensions. Despite the strong restrictions, it breaks the essential simplicity implicit in any two-dimensional time-independent scattering problem. Introducing the third degree of freedom by breaking a continuous symmetry, we first explore the topological structure of the homoclinic/heteroclinic tangle and the structures in the scattering functions. Then we work out the implications of these structures for the doubly differential cross section. The most prominent structures in the cross section are rainbow singularities. They form a fractal pattern that reflects the fractal structure of the chaotic invariant set. This allows us to determine structures in the cross section from the invariant set and, conversely, to obtain information about the topology of the invariant set from the cross section. The latter is a contribution to the inverse scattering problem for chaotic systems.

Synchronization of chaotic systems

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

Pecora, Louis M.; Carroll, Thomas L.

2015-09-15

We review some of the history and early work in the area of synchronization in chaotic systems. We start with our own discovery of the phenomenon, but go on to establish the historical timeline of this topic back to the earliest known paper. The topic of synchronization of chaotic systems has always been intriguing, since chaotic systems are known to resist synchronization because of their positive Lyapunov exponents. The convergence of the two systems to identical trajectories is a surprise. We show how people originally thought about this process and how the concept of synchronization changed over the years tomore » a more geometric view using synchronization manifolds. We also show that building synchronizing systems leads naturally to engineering more complex systems whose constituents are chaotic, but which can be tuned to output various chaotic signals. We finally end up at a topic that is still in very active exploration today and that is synchronization of dynamical systems in networks of oscillators.« less

Experimental analysis of chaotic neural network models for combinatorial optimization under a unifying framework.

PubMed

Kwok, T; Smith, K A

2000-09-01

The aim of this paper is to study both the theoretical and experimental properties of chaotic neural network (CNN) models for solving combinatorial optimization problems. Previously we have proposed a unifying framework which encompasses the three main model types, namely, Chen and Aihara's chaotic simulated annealing (CSA) with decaying self-coupling, Wang and Smith's CSA with decaying timestep, and the Hopfield network with chaotic noise. Each of these models can be represented as a special case under the framework for certain conditions. This paper combines the framework with experimental results to provide new insights into the effect of the chaotic neurodynamics of each model. By solving the N-queen problem of various sizes with computer simulations, the CNN models are compared in different parameter spaces, with optimization performance measured in terms of feasibility, efficiency, robustness and scalability. Furthermore, characteristic chaotic neurodynamics crucial to effective optimization are identified, together with a guide to choosing the corresponding model parameters.

A new chaotic communication scheme based on adaptive synchronization.

PubMed

Xiang-Jun, Wu

2006-12-01

A new chaotic communication scheme using adaptive synchronization technique of two unified chaotic systems is proposed. Different from the existing secure communication methods, the transmitted signal is modulated into the parameter of chaotic systems. The adaptive synchronization technique is used to synchronize two identical chaotic systems embedded in the transmitter and the receiver. It is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical unified chaotic systems with unknown system parameters asymptotically synchronized; thus the parameter of the receiver system is identified. Then the recovery of the original information signal in the receiver is successfully achieved on the basis of the estimated parameter. It is noticed that the time required for recovering the information signal and the accuracy of the recovered signal very sensitively depends on the frequency of the information signal. Numerical results have verified the effectiveness of the proposed scheme.

Chaotic carrier pulse position modulation communication system and method

DOEpatents

Abarbanel, Henry D. I.; Larson, Lawrence E.; Rulkov, Nikolai F.; Sushchik, Mikhail M.; Tsimring, Lev S.; Volkovskii, Alexander R.

2001-01-01

A chaotic carrier pulse position modulation communication system and method is disclosed. The system includes a transmitter and receiver having matched chaotic pulse regenerators. The chaotic pulse regenerator in the receiver produces a synchronized replica of a chaotic pulse train generated by the regenerator in the transmitter. The pulse train from the transmitter can therefore act as a carrier signal. Data is encoded by the transmitter through selectively altering the interpulse timing between pulses in the chaotic pulse train. The altered pulse train is transmitted as a pulse signal. The receiver can detect whether a particular interpulse interval in the pulse signal has been altered by reference to the synchronized replica it generates, and can therefore detect the data transmitted by the receiver. Preferably, the receiver predicts the earliest moment in time it can expect a next pulse after observation of at least two consecutive pulses. It then decodes the pulse signal beginning at a short time before expected arrival of a pulse.

New Operational Matrices for Solving Fractional Differential Equations on the Half-Line

PubMed Central

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques. PMID:25996369

New operational matrices for solving fractional differential equations on the half-line.

PubMed

Bhrawy, Ali H; Taha, Taha M; Alzahrani, Ebraheem O; Alzahrani, Ebrahim O; Baleanu, Dumitru; Alzahrani, Abdulrahim A

2015-01-01

In this paper, the fractional-order generalized Laguerre operational matrices (FGLOM) of fractional derivatives and fractional integration are derived. These operational matrices are used together with spectral tau method for solving linear fractional differential equations (FDEs) of order ν (0 < ν < 1) on the half line. An upper bound of the absolute errors is obtained for the approximate and exact solutions. Fractional-order generalized Laguerre pseudo-spectral approximation is investigated for solving nonlinear initial value problem of fractional order ν. The extension of the fractional-order generalized Laguerre pseudo-spectral method is given to solve systems of FDEs. We present the advantages of using the spectral schemes based on fractional-order generalized Laguerre functions and compare them with other methods. Several numerical examples are implemented for FDEs and systems of FDEs including linear and nonlinear terms. We demonstrate the high accuracy and the efficiency of the proposed techniques.

Experiences with Probabilistic Analysis Applied to Controlled Systems

NASA Technical Reports Server (NTRS)

Kenny, Sean P.; Giesy, Daniel P.

2004-01-01

This paper presents a semi-analytic method for computing frequency dependent means, variances, and failure probabilities for arbitrarily large-order closed-loop dynamical systems possessing a single uncertain parameter or with multiple highly correlated uncertain parameters. The approach will be shown to not suffer from the same computational challenges associated with computing failure probabilities using conventional FORM/SORM techniques. The approach is demonstrated by computing the probabilistic frequency domain performance of an optimal feed-forward disturbance rejection scheme.

A Qualitative Study of Affordability: Virginia and San Antonio Class Programs

DTIC Science & Technology

2014-06-04

uncertain aspects of the life- cycle cost estimates, ensuring that actual costs and operational tempos resemble original assumptions is the most...total inventory, a typical variation for ships from the acquisition standard of 10%. Even though the Virginia-class has incurred only a fraction of the...Policy - 119 - Naval Postgraduate School REFERENCES 10 U.S.C. § 181 (1997). Birkler, J., Schank, J., Smith, G., Timson, F., Chiesa, J., Goldberg

Generalized modeling of the fractional-order memcapacitor and its character analysis

NASA Astrophysics Data System (ADS)

Guo, Zhang; Si, Gangquan; Diao, Lijie; Jia, Lixin; Zhang, Yanbin

2018-06-01

Memcapacitor is a new type of memory device generalized from the memristor. This paper proposes a generalized fractional-order memcapacitor model by introducing the fractional calculus into the model. The generalized formulas are studied and the two fractional-order parameter α, β are introduced where α mostly affects the fractional calculus value of charge q within the generalized Ohm's law and β generalizes the state equation which simulates the physical mechanism of a memcapacitor into the fractional sense. This model will be reduced to the conventional memcapacitor as α = 1 , β = 0 and to the conventional memristor as α = 0 , β = 1 . Then the numerical analysis of the fractional-order memcapacitor is studied. And the characteristics and output behaviors of the fractional-order memcapacitor applied with sinusoidal charge are derived. The analysis results have shown that there are four basic v - q and v - i curve patterns when the fractional order α, β respectively equal to 0 or 1, moreover all v - q and v - i curves of the other fractional-order models are transition curves between the four basic patterns.

Horseshoes in a Chaotic System with Only One Stable Equilibrium

NASA Astrophysics Data System (ADS)

Huan, Songmei; Li, Qingdu; Yang, Xiao-Song

To confirm the numerically demonstrated chaotic behavior in a chaotic system with only one stable equilibrium reported by Wang and Chen, we resort to Poincaré map technique and present a rigorous computer-assisted verification of horseshoe chaos by virtue of topological horseshoes theory.

The Six Fundamental Characteristics of Chaos and Their Clinical Relevance to Psychiatry: a New Hypothesis for the Origin of Psychosis

NASA Astrophysics Data System (ADS)

Schmid, Gary Bruno

Underlying idea: A new hypothesis about how the mental state of psychosis may arise in the brain as a "linear" information processing pathology is briefly introduced. This hypothesis is proposed in the context of a complementary approach to psychiatry founded in the logical paradigm of chaos theory. To best understand the relation between chaos theory and psychiatry, the semantic structure of chaos theory is analyzed with the help of six general, and six specific, fundamental characteristics which can be directly inferred from empirical observations on chaotic systems. This enables a mathematically and physically stringent perspective on psychological phenomena which until now could only be grasped intuitively: Chaotic systems are in a general sense dynamic, intrinsically coherent, deterministic, recursive, reactive and structured: in a specific sense, self-organizing, unpredictable, nonreproducible, triadic, unstable and self-similar. To a great extent, certain concepts of chaos theory can be associated with corresponding concepts in psychiatry, psychology and psychotherapy, thus enabling an understanding of the human psyche in general as a (fractal) chaotic system and an explanation of certain mental developments, such as the course of schizophrenia, the course of psychosis and psychotherapy as chaotic processes. General overview: A short comparison and contrast of classical and chaotic physical theory leads to four postulates and one hypothesis motivating a new, dynamic, nonlinear approach to classical, causal psychiatry: Process-Oriented PSYchiatry or "POPSY", for short. Four aspects of the relationship between chaos theory and POPSY are discussed: (1) The first of these, namely, Identification of Chaos / Picture of Illness involves a definition of Chaos / Psychosis and a discussion of the 6 logical characteristics of each. This leads to the concept of dynamical disease (definition, characteristics and examples) and to the idea of "psychological disturbance as dynamical illness". On the one hand, it is argued that the developmental course of psychosis is chaotic. On the other hand, we propose the hypothesis that the mental state of psychosis may be a linear information processing pathology. (2) The second aspect under discussion is the Assessment of Chaos / Diagnosis of Illness. In order to better understand how POPSY research treats this aspect, we take a look at the 3 different classes of (non-quantum) motion as models of 3 different possible courses of illness and outline present-day methods available for the quantitative assessment of chaotic (fractal) motion. (3) The third aspect, namely. Prediction of Chaos / Prognosis of Illness considers how each of these 3 classes of motion implies a different way of looking into the future: linear-causal, statistical and nonlinear-fractal, respectively (4) The fourth aspect of the relationship between chaos theory and POPSY, Control of Chaos / Treatment of Illness, is shown to have certain implications to complementary medicine. This paper completes with a short summary, conclusion and a closing remark.

Fractional viscoelasticity in fractal and non-fractal media: Theory, experimental validation, and uncertainty analysis

NASA Astrophysics Data System (ADS)

Mashayekhi, Somayeh; Miles, Paul; Hussaini, M. Yousuff; Oates, William S.

2018-02-01

In this paper, fractional and non-fractional viscoelastic models for elastomeric materials are derived and analyzed in comparison to experimental results. The viscoelastic models are derived by expanding thermodynamic balance equations for both fractal and non-fractal media. The order of the fractional time derivative is shown to strongly affect the accuracy of the viscoelastic constitutive predictions. Model validation uses experimental data describing viscoelasticity of the dielectric elastomer Very High Bond (VHB) 4910. Since these materials are known for their broad applications in smart structures, it is important to characterize and accurately predict their behavior across a large range of time scales. Whereas integer order viscoelastic models can yield reasonable agreement with data, the model parameters often lack robustness in prediction at different deformation rates. Alternatively, fractional order models of viscoelasticity provide an alternative framework to more accurately quantify complex rate-dependent behavior. Prior research that has considered fractional order viscoelasticity lacks experimental validation and contains limited links between viscoelastic theory and fractional order derivatives. To address these issues, we use fractional order operators to experimentally validate fractional and non-fractional viscoelastic models in elastomeric solids using Bayesian uncertainty quantification. The fractional order model is found to be advantageous as predictions are significantly more accurate than integer order viscoelastic models for deformation rates spanning four orders of magnitude.

Resonant responses and chaotic dynamics of composite laminated circular cylindrical shell with membranes

NASA Astrophysics Data System (ADS)

Zhang, W.; Liu, T.; Xi, A.; Wang, Y. N.

2018-06-01

This paper is focused on the resonant responses and chaotic dynamics of a composite laminated circular cylindrical shell with radially pre-stretched membranes at both ends and clamped along a generatrix. Based on the two-degree-of-freedom non-autonomous nonlinear equations of this system, the method of multiple scales is employed to obtain the four-dimensional nonlinear averaged equation. The resonant case considered here is the primary parametric resonance-1/2 subharmonic resonance and 1:1 internal resonance. Corresponding to several selected parameters, the frequency-response curves are obtained. From the numerical results, we find that the hardening-spring-type behaviors and jump phenomena are exhibited. The jump phenomena also occur in the amplitude curves of the temperature parameter excitation. Moreover, it is found that the temperature parameter excitation, the coupling degree of two order modes and the detuning parameters can effect the nonlinear oscillations of this system. The periodic and chaotic motions of the composite laminated circular cylindrical shell clamped along a generatrix are demonstrated by the bifurcation diagrams, the maximum Lyapunov exponents, the phase portraits, the waveforms, the power spectrums and the Poincaré map. The temperature parameter excitation shows that the Pomeau-Manneville type intermittent chaos occur under the certain initial conditions. It is also found that there exist the twin phenomena between the Pomeau-Manneville type intermittent chaos and the period-doubling bifurcation.

Parameter-dependent behaviour of periodic channels in a locus of boundary crisis

NASA Astrophysics Data System (ADS)

Rankin, James; Osinga, Hinke M.

2017-06-01

A boundary crisis occurs when a chaotic attractor outgrows its basin of attraction and suddenly disappears. As previously reported, the locus of a boundary crisis is organised by homo- or heteroclinic tangencies between the stable and unstable manifolds of saddle periodic orbits. In two parameters, such tangencies lead to curves, but the locus of boundary crisis along those curves exhibits gaps or channels, in which other non-chaotic attractors persist. These attractors are stable periodic orbits which themselves can undergo a cascade of period-doubling bifurcations culminating in multi-component chaotic attractors. The canonical diffeomorphic two-dimensional Hénon map exhibits such periodic channels, which are structured in a particular ordered way: each channel is bounded on one side by a saddle-node bifurcation and on the other by a period-doubling cascade to chaos; furthermore, all channels seem to have the same orientation, with the saddle-node bifurcation always on the same side. We investigate the locus of boundary crisis in the Ikeda map, which models the dynamics of energy levels in a laser ring cavity. We find that the Ikeda map features periodic channels with a richer and more general organisation than for the Hénon map. Using numerical continuation, we investigate how the periodic channels depend on a third parameter and characterise how they split into multiple channels with different properties.

Restoration and recovery of damaged eco-epidemiological systems: application to the Salton Sea, California, USA.

PubMed

Upadhyay, Ranjit Kumar; Raw, S N; Roy, P; Rai, Vikas

2013-04-01

In this paper, we have proposed and analysed a mathematical model to figure out possible ways to rescue a damaged eco-epidemiological system. Our strategy of rescue is based on the realization of the fact that chaotic dynamics often associated with excursions of system dynamics to extinction-sized densities. Chaotic dynamics of the model is depicted by 2D scans, bifurcation analysis, largest Lyapunov exponent and basin boundary calculations. 2D scan results show that μ, the total death rate of infected prey should be brought down in order to avoid chaotic dynamics. We have carried out linear and nonlinear stability analysis and obtained Hopf-bifurcation and persistence criteria of the proposed model system. The other outcome of this study is a suggestion which involves removal of infected fishes at regular interval of time. The estimation of timing and periodicity of the removal exercises would be decided by the nature of infection more than anything else. If this suggestion is carefully worked out and implemented, it would be most effective in restoring the health of the ecosystem which has immense ecological, economic and aesthetic potential. We discuss the implications of this result to Salton Sea, California, USA. The restoration of the Salton Sea provides a perspective for conservation and management strategy. Copyright © 2013 Elsevier Inc. All rights reserved.

Parameter estimation for chaotic systems using a hybrid adaptive cuckoo search with simulated annealing algorithm

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

Sheng, Zheng, E-mail: 19994035@sina.com; Wang, Jun; Zhou, Bihua

2014-03-15

This paper introduces a novel hybrid optimization algorithm to establish the parameters of chaotic systems. In order to deal with the weaknesses of the traditional cuckoo search algorithm, the proposed adaptive cuckoo search with simulated annealing algorithm is presented, which incorporates the adaptive parameters adjusting operation and the simulated annealing operation in the cuckoo search algorithm. Normally, the parameters of the cuckoo search algorithm are kept constant that may result in decreasing the efficiency of the algorithm. For the purpose of balancing and enhancing the accuracy and convergence rate of the cuckoo search algorithm, the adaptive operation is presented tomore » tune the parameters properly. Besides, the local search capability of cuckoo search algorithm is relatively weak that may decrease the quality of optimization. So the simulated annealing operation is merged into the cuckoo search algorithm to enhance the local search ability and improve the accuracy and reliability of the results. The functionality of the proposed hybrid algorithm is investigated through the Lorenz chaotic system under the noiseless and noise condition, respectively. The numerical results demonstrate that the method can estimate parameters efficiently and accurately in the noiseless and noise condition. Finally, the results are compared with the traditional cuckoo search algorithm, genetic algorithm, and particle swarm optimization algorithm. Simulation results demonstrate the effectiveness and superior performance of the proposed algorithm.« less

From Fault-Diagnosis and Performance Recovery of a Controlled System to Chaotic Secure Communication

NASA Astrophysics Data System (ADS)

Hsu, Wen-Teng; Tsai, Jason Sheng-Hong; Guo, Fang-Cheng; Guo, Shu-Mei; Shieh, Leang-San

Chaotic systems are often applied to encryption on secure communication, but they may not provide high-degree security. In order to improve the security of communication, chaotic systems may need to add other secure signals, but this may cause the system to diverge. In this paper, we redesign a communication scheme that could create secure communication with additional secure signals, and the proposed scheme could keep system convergence. First, we introduce the universal state-space adaptive observer-based fault diagnosis/estimator and the high-performance tracker for the sampled-data linear time-varying system with unanticipated decay factors in actuators/system states. Besides, robustness, convergence in the mean, and tracking ability are given in this paper. A residual generation scheme and a mechanism for auto-tuning switched gain is also presented, so that the introduced methodology is applicable for the fault detection and diagnosis (FDD) for actuator and state faults to yield a high tracking performance recovery. The evolutionary programming-based adaptive observer is then applied to the problem of secure communication. Whenever the tracker induces a large control input which might not conform to the input constraint of some physical systems, the proposed modified linear quadratic optimal tracker (LQT) can effectively restrict the control input within the specified constraint interval, under the acceptable tracking performance. The effectiveness of the proposed design methodology is illustrated through tracking control simulation examples.

The grief map

NASA Astrophysics Data System (ADS)

Monteiro, L. H. A.

2014-12-01

Grieving is a natural human reaction to a significant loss. According to a psychiatric model, this process is characterized by a typical sequence of psychological changes. Here, I propose a discrete-time dynamical system, called the grief map, in order to represent the grieving process. The corresponding bifurcation diagram, which exhibits stationary, periodic, and chaotic behavior, is related to the stages of this sorrowful journey occurring during about 12 months post-loss.

Scaling laws and reduced-order models for mixing and reactive-transport in heterogeneous anisotropic porous media

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Karra, S.; Nakshatrala, K. B.

2016-12-01

Fundamental to enhancement and control of the macroscopic spreading, mixing, and dilution of solute plumes in porous media structures is the topology of flow field and underlying heterogeneity and anisotropy contrast of porous media. Traditionally, in literature, the main focus was limited to the shearing effects of flow field (i.e., flow has zero helical density, meaning that flow is always perpendicular to vorticity vector) on scalar mixing [2]. However, the combined effect of anisotropy of the porous media and the helical structure (or chaotic nature) of the flow field on the species reactive-transport and mixing has been rarely studied. Recently, it has been experimentally shown that there is an irrefutable evidence that chaotic advection and helical flows are inherent in porous media flows [1,2]. In this poster presentation, we present a non-intrusive physics-based model-order reduction framework to quantify the effects of species mixing in-terms of reduced-order models (ROMs) and scaling laws. The ROM framework is constructed based on the recent advancements in non-negative formulations for reactive-transport in heterogeneous anisotropic porous media [3] and non-intrusive ROM methods [4]. The objective is to generate computationally efficient and accurate ROMs for species mixing for different values of input data and reactive-transport model parameters. This is achieved by using multiple ROMs, which is a way to determine the robustness of the proposed framework. Sensitivity analysis is performed to identify the important parameters. Representative numerical examples from reactive-transport are presented to illustrate the importance of the proposed ROMs to accurately describe mixing process in porous media. [1] Lester, Metcalfe, and Trefry, "Is chaotic advection inherent to porous media flow?," PRL, 2013. [2] Ye, Chiogna, Cirpka, Grathwohl, and Rolle, "Experimental evidence of helical flow in porous media," PRL, 2015. [3] Mudunuru, and Nakshatrala, "On enforcing maximum principles and achieving element-wise species balance for advection-diffusion-reaction equations under the finite element method," JCP, 2016. [4] Quarteroni, Manzoni, and Negri. "Reduced Basis Methods for Partial Differential Equations: An Introduction," Springer, 2016.

Computations of Chaotic Flows in Micromixers

DTIC Science & Technology

2005-01-01

2005 2. REPORT TYPE 3. DATES COVERED 00-00-2005 to 00-00-2005 4. TITLE AND SUBTITLE Computations of Chaotic Flows in Micromixers 5a. CONTRACT...Std Z39-18 215simulation, computing, and modeling 2005 NRL Review Computations of Chaotic Flows In Micromixers FIGURE 6 Schematic of staggered

Chaos in Atomic Force Microscopy

NASA Astrophysics Data System (ADS)

Hu, Shuiqing; Raman, Arvind

2006-01-01

Chaotic oscillations of microcantilever tips in dynamic atomic force microscopy (AFM) are reported and characterized. Systematic experiments performed using a variety of microcantilevers under a wide range of operating conditions indicate that softer AFM microcantilevers bifurcate from periodic to chaotic oscillations near the transition from the noncontact to the tapping regimes. Careful Lyapunov exponent and noise titration calculations of the tip oscillation data confirm their chaotic nature. AFM images taken by scanning the chaotically oscillating tips over the sample show small, but significant metrology errors at the nanoscale due to this “deterministic” uncertainty.

Experimental realization of a highly secure chaos communication under strong channel noise

NASA Astrophysics Data System (ADS)

Ye, Weiping; Dai, Qionglin; Wang, Shihong; Lu, Huaping; Kuang, Jinyu; Zhao, Zhenfeng; Zhu, Xiangqing; Tang, Guoning; Huang, Ronghuai; Hu, Gang

2004-09-01

A one-way coupled spatiotemporally chaotic map lattice is used to construct cryptosystem. With the combinatorial applications of both chaotic computations and conventional algebraic operations, our system has optimal cryptographic properties much better than the separative applications of known chaotic and conventional methods. We have realized experiments to practice duplex voice secure communications in realistic Wired Public Switched Telephone Network by applying our chaotic system and the system of Advanced Encryption Standard (AES), respectively, for cryptography. Our system can work stably against strong channel noise when AES fails to work.

Chaos enhancing tunneling in a coupled Bose-Einstein condensate with a double driving.

PubMed

Rong, Shiguang; Hai, Wenhua; Xie, Qiongtao; Zhu, Qianquan

2009-09-01

We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.

Identical synchronization of chaotic secure communication systems with channel induced coherence resonance

NASA Astrophysics Data System (ADS)

Sepantaie, Marc M.; Namazi, Nader M.; Sepantaie, Amir M.

2016-05-01

This paper is devoted to addressing the synchronization, and detection of random binary data exposed to inherent channel variations existing in Free Space Optical (FSO) communication systems. This task is achieved by utilizing the identical synchronization methodology of Lorenz chaotic communication system, and its synergetic interaction in adversities imposed by the FSO channel. Moreover, the Lorenz system has been analyzed, and revealed to induce Stochastic Resonance (SR) once exposed to Additive White Gaussian Noise (AWGN). In particular, the resiliency of the Lorenz chaotic system, in light of channel adversities, has been attributed to the success of the proposed communication system. Furthermore, this paper advocates the use of Haar wavelet transform for enhanced detection capability of the proposed chaotic communication system, which utilizes Chaotic Parameter Modulation (CPM) technique for means of transmission.

Wavelet threshold method of resolving noise interference in periodic short-impulse signals chaotic detection

NASA Astrophysics Data System (ADS)

Deng, Ke; Zhang, Lu; Luo, Mao-Kang

2010-03-01

The chaotic oscillator has already been considered as a powerful method to detect weak signals, even weak signals accompanied with noises. However, many examples, analyses and simulations indicate that chaotic oscillator detection system cannot guarantee the immunity to noises (even white noise). In fact the randomness of noises has a serious or even a destructive effect on the detection results in many cases. To solve this problem, we present a new detecting method based on wavelet threshold processing that can detect the chaotic weak signal accompanied with noise. All theoretical analyses and simulation experiments indicate that the new method reduces the noise interferences to detection significantly, thereby making the corresponding chaotic oscillator that detects the weak signals accompanied with noises more stable and reliable.

Multiple shooting shadowing for sensitivity analysis of chaotic dynamical systems

NASA Astrophysics Data System (ADS)

Blonigan, Patrick J.; Wang, Qiqi

2018-02-01

Sensitivity analysis methods are important tools for research and design with simulations. Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent fluid flow simulations. Unfortunately, conventional sensitivity analysis methods are unable to compute useful gradient information for long-time-averaged quantities in chaotic dynamical systems. Sensitivity analysis with least squares shadowing (LSS) can compute useful gradient information for a number of chaotic systems, including simulations of chaotic vortex shedding and homogeneous isotropic turbulence. However, this gradient information comes at a very high computational cost. This paper presents multiple shooting shadowing (MSS), a more computationally efficient shadowing approach than the original LSS approach. Through an analysis of the convergence rate of MSS, it is shown that MSS can have lower memory usage and run time than LSS.

Chaos in the brain: imaging via chaoticity of EEG/MEG signals

NASA Astrophysics Data System (ADS)

Kowalik, Zbigniew J.; Elbert, Thomas; Rockstroh, Brigitte; Hoke, Manfried

1995-03-01

Brain electro- (EEG) or magnetoencephalogram (MEG) can be analyzed by using methods of the nonlinear system theory. We show that even for very short and nonstationary time series it is possible to functionally differentiate various brain activities. Usually the analysis assumes that the analyzed signals are both long and stationary, so that the classic spectral methods can be used. Even more convincing results can be obtained under these circumstances when the dimensional analysis or estimation of the Kolmogorov entropy or the Lyapunov exponent are performed. When measuring the spontaneous activity of a human brain the assumption of stationarity is questionable and `static' methods (correlation dimension, entropy, etc.) are then not adequate. In this case `dynamic' methods like pointwise-D2 dimension or chaoticity measures should be applied. Predictability measures in the form of local Lyapunov exponents are capable of revealing directly the chaoticity of a given process, and can practically be applied for functional differentiation of brain activity. We exemplify these in cases of apallic syndrome, tinnitus and schizophrenia. We show that: the average chaoticity in apallic syndrome differentiates brain states both in space and time, chaoticity changes temporally in case of schizophrenia (critical jumps of chaoticity), chaoticity changes locally in space, i.e., in the cortex plane in case of tinnitus.

Chaotic diffusion in the Gliese-876 planetary system

NASA Astrophysics Data System (ADS)

Martí, J. G.; Cincotta, P. M.; Beaugé, C.

2016-07-01

Chaotic diffusion is supposed to be responsible for orbital instabilities in planetary systems after the dissipation of the protoplanetary disc, and a natural consequence of irregular motion. In this paper, we show that resonant multiplanetary systems, despite being highly chaotic, not necessarily exhibit significant diffusion in phase space, and may still survive virtually unchanged over time-scales comparable to their age. Using the GJ-876 system as an example, we analyse the chaotic diffusion of the outermost (and less massive) planet. We construct a set of stability maps in the surrounding regions of the Laplace resonance. We numerically integrate ensembles of close initial conditions, compute Poincaré maps and estimate the chaotic diffusion present in this system. Our results show that, the Laplace resonance contains two different regions: an inner domain characterized by low chaoticity and slow diffusion, and an outer one displaying larger values of dynamical indicators. In the outer resonant domain, the stochastic borders of the Laplace resonance seem to prevent the complete destruction of the system. We characterize the diffusion for small ensembles along the parameters of the outermost planet. Finally, we perform a stability analysis of the inherent chaotic, albeit stable Laplace resonance, by linking the behaviour of the resonant variables of the configurations to the different sub-structures inside the three-body resonance.

Synthesis of a fully-integrated digital signal source for communications from chaotic dynamics-based oscillations

NASA Astrophysics Data System (ADS)

Glenn, Chance Michael, Sr.

This work is the conceptualization, derivation, analysis, and fabrication of a fully practical digital signal source designed from a chaotic oscillator. In it we show how a simple electronic circuit based upon the Colpitts oscillator, can be made to produce highly complex signals capable of carrying digital information. We show a direct relationship between the continuous-time chaotic oscillations produced by the circuit and the logistic map, which is discrete-time, one-dimensional map that is a fundamental paradigm for the study of chaotic systems. We demonstrate the direct encoding of binary information into the oscillations of the chaotic circuit. We demonstrate a new concept in power amplification, called syncrodyne amplification , which uses fundamental properties of chaotic oscillators to provide high-efficiency, high gain amplification of standard communication waveforms as well as typical chaotic oscillations. We show modeling results of this system providing nearly 60-dB power gain and 80% PAE for communications waveforms conforming to GMSK modulation. Finally we show results from a fabricated syncrodyne amplifier circuit operating at 2 MHz, providing over 40-dB power gain and 72% PAE, and propose design criteria for an 824--850 MHz circuit utilizing heterojunction bipolar transistors (HBTs), providing the basis for microwave frequency realization.

Robust cooperation of connected vehicle systems with eigenvalue-bounded interaction topologies in the presence of uncertain dynamics

NASA Astrophysics Data System (ADS)

Li, Keqiang; Gao, Feng; Li, Shengbo Eben; Zheng, Yang; Gao, Hongbo

2017-12-01

This study presents a distributed H-infinity control method for uncertain platoons with dimensionally and structurally unknown interaction topologies provided that the associated topological eigenvalues are bounded by a predesigned range.With an inverse model to compensate for nonlinear powertrain dynamics, vehicles in a platoon are modeled by third-order uncertain systems with bounded disturbances. On the basis of the eigenvalue decomposition of topological matrices, we convert the platoon system to a norm-bounded uncertain part and a diagonally structured certain part by applying linear transformation. We then use a common Lyapunov method to design a distributed H-infinity controller. Numerically, two linear matrix inequalities corresponding to the minimum and maximum eigenvalues should be solved. The resulting controller can tolerate interaction topologies with eigenvalues located in a certain range. The proposed method can also ensure robustness performance and disturbance attenuation ability for the closed-loop platoon system. Hardware-in-the-loop tests are performed to validate the effectiveness of our method.

Homogenization-based interval analysis for structural-acoustic problem involving periodical composites and multi-scale uncertain-but-bounded parameters.

PubMed

Chen, Ning; Yu, Dejie; Xia, Baizhan; Liu, Jian; Ma, Zhengdong

2017-04-01

This paper presents a homogenization-based interval analysis method for the prediction of coupled structural-acoustic systems involving periodical composites and multi-scale uncertain-but-bounded parameters. In the structural-acoustic system, the macro plate structure is assumed to be composed of a periodically uniform microstructure. The equivalent macro material properties of the microstructure are computed using the homogenization method. By integrating the first-order Taylor expansion interval analysis method with the homogenization-based finite element method, a homogenization-based interval finite element method (HIFEM) is developed to solve a periodical composite structural-acoustic system with multi-scale uncertain-but-bounded parameters. The corresponding formulations of the HIFEM are deduced. A subinterval technique is also introduced into the HIFEM for higher accuracy. Numerical examples of a hexahedral box and an automobile passenger compartment are given to demonstrate the efficiency of the presented method for a periodical composite structural-acoustic system with multi-scale uncertain-but-bounded parameters.

Control of Initialized Fractional-Order Systems

NASA Technical Reports Server (NTRS)

Hartley, Tom T.; Lorenzo, Carl F.

2004-01-01

Fractional-Order systems, or systems containing fractional derivatives and integrals, have been studied by many in the engineering area. Additionally, very readable discussions, devoted specifically to the subject, are presented by Oldham and Spanier, Miller and Ross, and Pudlubny (1999a). It should be noted that there are a growing number of physical systems whose behavior can be compactly described using fractional system theory. Of specific interest to electrical engineers are long lines, electrochemical processes, dielectric polarization, colored noise, viscoelastic materials, and chaos. With the growing number of applications, it is important to establish a theory of control for these fractional-order systems, and for the potential use of fractional-order systems as feedback compensators. This topic is addressed in this paper. The first section discusses the control of fractional-order systems using a vector space representation, where initialization is included in the discussion. It should be noted that Bagley and Calico and Padovan and Sawicki both present a fractional state-space representation, which do not include the important historic effects. Incorporation of these effects based on the initialized fractional calculus is presented . The control methods presented in this paper are based on the initialized fractional order system theory. The second section presents an input-output approach. Some of the problems encountered in these sections are: a) the need to introduce a new complex plane to study the dynamics of fractional-order systems, b) the need to properly define the Laplace transform of the fractional derivative, and c) the proper inclusion of the initialization response in the system and control formulation. Following this, the next section generalizes the proportional-plus-integral-control (PI-control) and PID-control (PI-plus- derivative) concepts using fractional integrals. This is then further generalized using general fractional- order compensators. Finally the compensator concept is generalized by the use of a continuum of fractions in the compensator via the concept of order-distributions. The last section introduces fractional feedback in discrete-time.

Numerical explorations of R. M. Goodwin's business cycle model.

PubMed

Jakimowicz, Aleksander

2010-01-01

Goodwin's model, which was formulated in , still attracts economists' attention. The model possesses numerous interesting properties that have been discovered only recently due to the development of the chaos theory and the complexity theory. The first numerical explorations of the model were conducted in the early s by Strotz, McAnulty and Naines (1953). They discovered the coexistence of attractors that are well-known today, two properties of chaotic systems: the sensitive dependence on the initial conditions and the sensitive dependence on parameters. The occurrence of periodic and chaotic attractors is dependent on the value of parameters in a system. In case of certain parametric values fractal basin boundaries exist which results in enormous system sensitivity to external noise. If periodic attractors are placed in the neighborhood of the fractal basin boundaries, then even a low external noise can move the trajectory into the region in which the basin's structure is tangled. This leads to a kind of movement that resembles a chaotic movement on a strange attractor. In Goodwin's model, apart from typical chaotic behavior, there exists yet another kind of complex movements - transient chaotic behavior that is caused by the occurrence of invariant chaotic sets that are not attracting. Such sets are represented by chaotic saddles. Some of the latest observation methods of trajectories lying on invariant chaotic sets that are not attracting are straddle methods. This article provides examples of the basin boundary straddle trajectory and the saddle straddle trajectory. These cases were studied by Lorenz and Nusse (2002). I supplement the results they acquired with calculations of capacity dimension and correlation dimension.

Detection of chaotic dynamics in human gait signals from mobile devices

NASA Astrophysics Data System (ADS)

DelMarco, Stephen; Deng, Yunbin

2017-05-01

The ubiquity of mobile devices offers the opportunity to exploit device-generated signal data for biometric identification, health monitoring, and activity recognition. In particular, mobile devices contain an Inertial Measurement Unit (IMU) that produces acceleration and rotational rate information from the IMU accelerometers and gyros. These signals reflect motion properties of the human carrier. It is well-known that the complexity of bio-dynamical systems gives rise to chaotic dynamics. Knowledge of chaotic properties of these systems has shown utility, for example, in detecting abnormal medical conditions and neurological disorders. Chaotic dynamics has been found, in the lab, in bio-dynamical systems data such as electrocardiogram (heart), electroencephalogram (brain), and gait data. In this paper, we investigate the following question: can we detect chaotic dynamics in human gait as measured by IMU acceleration and gyro data from mobile phones? To detect chaotic dynamics, we perform recurrence analysis on real gyro and accelerometer signal data obtained from mobile devices. We apply the delay coordinate embedding approach from Takens' theorem to reconstruct the phase space trajectory of the multi-dimensional gait dynamical system. We use mutual information properties of the signal to estimate the appropriate delay value, and the false nearest neighbor approach to determine the phase space embedding dimension. We use a correlation dimension-based approach together with estimation of the largest Lyapunov exponent to make the chaotic dynamics detection decision. We investigate the ability to detect chaotic dynamics for the different one-dimensional IMU signals, across human subject and walking modes, and as a function of different phone locations on the human carrier.

Global asymptotical ω-periodicity of a fractional-order non-autonomous neural networks.

PubMed

Chen, Boshan; Chen, Jiejie

2015-08-01

We study the global asymptotic ω-periodicity for a fractional-order non-autonomous neural networks. Firstly, based on the Caputo fractional-order derivative it is shown that ω-periodic or autonomous fractional-order neural networks cannot generate exactly ω-periodic signals. Next, by using the contraction mapping principle we discuss the existence and uniqueness of S-asymptotically ω-periodic solution for a class of fractional-order non-autonomous neural networks. Then by using a fractional-order differential and integral inequality technique, we study global Mittag-Leffler stability and global asymptotical periodicity of the fractional-order non-autonomous neural networks, which shows that all paths of the networks, starting from arbitrary points and responding to persistent, nonconstant ω-periodic external inputs, asymptotically converge to the same nonconstant ω-periodic function that may be not a solution. Copyright © 2015 Elsevier Ltd. All rights reserved.

Diffusion control for a tempered anomalous diffusion system using fractional-order PI controllers.

PubMed

Juan Chen; Zhuang, Bo; Chen, YangQuan; Cui, Baotong

2017-05-09

This paper is concerned with diffusion control problem of a tempered anomalous diffusion system based on fractional-order PI controllers. The contribution of this paper is to introduce fractional-order PI controllers into the tempered anomalous diffusion system for mobile actuators motion and spraying control. For the proposed control force, convergence analysis of the system described by mobile actuator dynamical equations is presented based on Lyapunov stability arguments. Moreover, a new Centroidal Voronoi Tessellation (CVT) algorithm based on fractional-order PI controllers, henceforth called FOPI-based CVT algorithm, is provided together with a modified simulation platform called Fractional-Order Diffusion Mobile Actuator-Sensor 2-Dimension Fractional-Order Proportional Integral (FO-Diff-MAS2D-FOPI). Finally, extensive numerical simulations for the tempered anomalous diffusion process are presented to verify the effectiveness of our proposed fractional-order PI controllers. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

On the adaptivity and complexity embedded into differential evolution

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

Senkerik, Roman; Pluhacek, Michal; Jasek, Roman

2016-06-08

This research deals with the comparison of the two modern approaches for evolutionary algorithms, which are the adaptivity and complex chaotic dynamics. This paper aims on the investigations on the chaos-driven Differential Evolution (DE) concept. This paper is aimed at the embedding of discrete dissipative chaotic systems in the form of chaotic pseudo random number generators for the DE and comparing the influence to the performance with the state of the art adaptive representative jDE. This research is focused mainly on the possible disadvantages and advantages of both compared approaches. Repeated simulations for Lozi map driving chaotic systems were performedmore » on the simple benchmark functions set, which are more close to the real optimization problems. Obtained results are compared with the canonical not-chaotic and not adaptive DE. Results show that with used simple test functions, the performance of ChaosDE is better in the most cases than jDE and Canonical DE, furthermore due to the unique sequencing in CPRNG given by the hidden chaotic dynamics, thus better and faster selection of unique individuals from population, ChaosDE is faster.« less

Projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks.

PubMed

Feng, Cun-Fang; Xu, Xin-Jian; Wang, Sheng-Jun; Wang, Ying-Hai

2008-06-01

We study projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random networks. We relax some limitations of previous work, where projective-anticipating and projective-lag synchronization can be achieved only on two coupled chaotic systems. In this paper, we realize projective-anticipating and projective-lag synchronization on complex dynamical networks composed of a large number of interconnected components. At the same time, although previous work studied projective synchronization on complex dynamical networks, the dynamics of the nodes are coupled partially linear chaotic systems. In this paper, the dynamics of the nodes of the complex networks are time-delayed chaotic systems without the limitation of the partial linearity. Based on the Lyapunov stability theory, we suggest a generic method to achieve the projective-anticipating, projective, and projective-lag synchronization of time-delayed chaotic systems on random dynamical networks, and we find both its existence and sufficient stability conditions. The validity of the proposed method is demonstrated and verified by examining specific examples using Ikeda and Mackey-Glass systems on Erdos-Renyi networks.

Experimental distinction between chaotic and strange nonchaotic attractors on the basis of consistency.

PubMed

Uenohara, Seiji; Mitsui, Takahito; Hirata, Yoshito; Morie, Takashi; Horio, Yoshihiko; Aihara, Kazuyuki

2013-06-01

We experimentally study strange nonchaotic attractors (SNAs) and chaotic attractors by using a nonlinear integrated circuit driven by a quasiperiodic input signal. An SNA is a geometrically strange attractor for which typical orbits have nonpositive Lyapunov exponents. It is a difficult problem to distinguish between SNAs and chaotic attractors experimentally. If a system has an SNA as a unique attractor, the system produces an identical response to a repeated quasiperiodic signal, regardless of the initial conditions, after a certain transient time. Such reproducibility of response outputs is called consistency. On the other hand, if the attractor is chaotic, the consistency is low owing to the sensitive dependence on initial conditions. In this paper, we analyze the experimental data for distinguishing between SNAs and chaotic attractors on the basis of the consistency.

Chaotic Zones around Rotating Small Bodies

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

Lages, José; Shevchenko, Ivan I.; Shepelyansky, Dima L., E-mail: jose.lages@utinam.cnrs.fr

Small bodies of the solar system, like asteroids, trans-Neptunian objects, cometary nuclei, and planetary satellites, with diameters smaller than 1000 km usually have irregular shapes, often resembling dumb-bells or contact binaries. The spinning of such a gravitating dumb-bell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased; in particular, the zone swells more than twice if the rotation rate is decreased 10 times with respect to the “centrifugal breakup” threshold. We illustrate the properties of the chaotic orbital zones in examples ofmore » the global orbital dynamics about asteroid 243 Ida (which has a moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143 Itokawa.« less

Literalism, perspectivism, chaotic fragmentalism and psychotherapy techniques.

PubMed

Leitner, L M

1982-12-01

Literalism and chaotic fragmentalism have been advanced as two concepts to explain psychopathology while perspectivism has been used to explain psychological health (Landfield, 1980 a). It is hypothesized that, to the extent that they are therapeutic, all therapies move clients toward perspectivism and away from literalism and chaotic fragmentalism. Eight major schools of psychotherapy are discussed in terms of the principles of technique which enable them to change literalism and chaotic fragmentalism. The advantages of a unifying theory permitting diversity of techniques are discussed in relation to the ability of the clinician to be flexible yet not confused. Further, the unifying concepts of literalism, perspectivism, and chaotic fragmentalism are used to understand systematically the strengths and weaknesses of many therapeutic techniques. Finally, the implications of the differences in therapeutic techniques for changing different types of literalisms are discussed.

Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale.

PubMed

Maslennikov, Oleg V; Nekorkin, Vladimir I

2016-07-01

In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.

Chaotic Experiences and Low-Income Children’s Social-Emotional Development

PubMed Central

Bobbitt, Kaeley C.; Gershoff, Elizabeth T.

2016-01-01

Development in early childhood is increasingly likely to take place in multiple contexts. Continuity and discontinuity in children’s experiences across multiple contexts have important implications for their development. This study examines the extent to which children experience chaos in their homes and in their preschool settings is linked with their social-emotional development over the course of the preschool year. Data from a large, representative sample of low-income preschool children attending Head Start was used to test a series of multi-level models. Children whose experiences of their homes were highly chaotic, regardless of the how chaotic their experiences of their classroom were, decreased in their social-emotional skills over the preschool year. Chaotic experiences in the home environment thus appear to have more influence on children’s development than do chaotic preschool experiences. PMID:28435178

640-Gbit/s fast physical random number generation using a broadband chaotic semiconductor laser

NASA Astrophysics Data System (ADS)

Zhang, Limeng; Pan, Biwei; Chen, Guangcan; Guo, Lu; Lu, Dan; Zhao, Lingjuan; Wang, Wei

2017-04-01

An ultra-fast physical random number generator is demonstrated utilizing a photonic integrated device based broadband chaotic source with a simple post data processing method. The compact chaotic source is implemented by using a monolithic integrated dual-mode amplified feedback laser (AFL) with self-injection, where a robust chaotic signal with RF frequency coverage of above 50 GHz and flatness of ±3.6 dB is generated. By using 4-least significant bits (LSBs) retaining from the 8-bit digitization of the chaotic waveform, random sequences with a bit-rate up to 640 Gbit/s (160 GS/s × 4 bits) are realized. The generated random bits have passed each of the fifteen NIST statistics tests (NIST SP800-22), indicating its randomness for practical applications.

Adaptive fractional order sliding mode control for Boost converter in the Battery/Supercapacitor HESS.

PubMed

Wang, Jianlin; Xu, Dan; Zhou, Huan; Zhou, Tao

2018-01-01

In this paper, an adaptive fractional order sliding mode control (AFSMC) scheme is designed for the current tracking control of the Boost-type converter in a Battery/Supercapacitor hybrid energy storage system (HESS). In order to stabilize the current, the adaptation rules based on state-observer and Lyapunov function are being designed. A fractional order sliding surface function is defined based on the tracking current error and adaptive rules. Furthermore, through fractional order analysis, the stability of the fractional order control system is proven, and the value of the fractional order (λ) is being investigated. In addition, the effectiveness of the proposed AFSMC strategy is being verified by numerical simulations. The advantages of good transient response and robustness to uncertainty are being indicated by this design, when compared with a conventional integer order sliding mode control system.

Membrane Capacitive Memory Alters Spiking in Neurons Described by the Fractional-Order Hodgkin-Huxley Model

PubMed Central

Weinberg, Seth H.

2015-01-01

Excitable cells and cell membranes are often modeled by the simple yet elegant parallel resistor-capacitor circuit. However, studies have shown that the passive properties of membranes may be more appropriately modeled with a non-ideal capacitor, in which the current-voltage relationship is given by a fractional-order derivative. Fractional-order membrane potential dynamics introduce capacitive memory effects, i.e., dynamics are influenced by a weighted sum of the membrane potential prior history. However, it is not clear to what extent fractional-order dynamics may alter the properties of active excitable cells. In this study, we investigate the spiking properties of the neuronal membrane patch, nerve axon, and neural networks described by the fractional-order Hodgkin-Huxley neuron model. We find that in the membrane patch model, as fractional-order decreases, i.e., a greater influence of membrane potential memory, peak sodium and potassium currents are altered, and spike frequency and amplitude are generally reduced. In the nerve axon, the velocity of spike propagation increases as fractional-order decreases, while in a neural network, electrical activity is more likely to cease for smaller fractional-order. Importantly, we demonstrate that the modulation of the peak ionic currents that occurs for reduced fractional-order alone fails to reproduce many of the key alterations in spiking properties, suggesting that membrane capacitive memory and fractional-order membrane potential dynamics are important and necessary to reproduce neuronal electrical activity. PMID:25970534

Tuning algorithms for fractional order internal model controllers for time delay processes

NASA Astrophysics Data System (ADS)

Muresan, Cristina I.; Dutta, Abhishek; Dulf, Eva H.; Pinar, Zehra; Maxim, Anca; Ionescu, Clara M.

2016-03-01

This paper presents two tuning algorithms for fractional-order internal model control (IMC) controllers for time delay processes. The two tuning algorithms are based on two specific closed-loop control configurations: the IMC control structure and the Smith predictor structure. In the latter, the equivalency between IMC and Smith predictor control structures is used to tune a fractional-order IMC controller as the primary controller of the Smith predictor structure. Fractional-order IMC controllers are designed in both cases in order to enhance the closed-loop performance and robustness of classical integer order IMC controllers. The tuning procedures are exemplified for both single-input-single-output as well as multivariable processes, described by first-order and second-order transfer functions with time delays. Different numerical examples are provided, including a general multivariable time delay process. Integer order IMC controllers are designed in each case, as well as fractional-order IMC controllers. The simulation results show that the proposed fractional-order IMC controller ensures an increased robustness to modelling uncertainties. Experimental results are also provided, for the design of a multivariable fractional-order IMC controller in a Smith predictor structure for a quadruple-tank system.

Quantitative Measures of Chaotic Charged Particle Dynamics in the Magnetotail

NASA Astrophysics Data System (ADS)

Holland, D. L.; Martin, R. F., Jr.; Burris, C.

2017-12-01

It has long been noted that the motion of charged particles in magnetotail-like magnetic fields is chaotic, however, efforts to quantify the degree of chaos have had conflicting conclusions. In this paper we re-examine the question by focusing on quantitative measures of chaos. We first examine the percentage of orbits that enter the chaotic region of phase space and the average trapping time of those particles. We then examine the average exponential divergence rate (AEDR) of the chaotic particles between their first and last crossing of the mid-plane. We show that at resonant energies where the underlying phase space has a high degree of symmetry, only a small number of particle enter the chaotic region, but they are trapped for long periods of time and the time asymptotic value of the AEDR is very close to the average value of the AEDR. At the off-resonant energies where the phase space is highly asymmetric, the majority of the particle enter the chaotic region for fairly short periods of time and the time asymptotic value of the AEDR is much smaller than the average value. The root cause is that in the resonant case, the longest-lived orbits tend interact with the current many times and sample the entire chaotic region, whereas in the non-resonant case the longest-lived orbits only interact with the current sheet a small number of times but have very long mirrorings where the motion is nearly regular. Additionally we use an ad-hoc model where we model the current sheet as a Lorentz scattering system with each interaction with the current sheet being considered as a "collision". We find that the average kick per collision is greatest at off-resonant energies. Finally, we propose a chaos parameter as the product of the AEDR times the average chaotic particle trapping time times the percentage of orbits that are chaotic. We find that this takes on peak values at the resonant energies.

Proceedings of the 2nd Experimental Chaos Conference

NASA Astrophysics Data System (ADS)

Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep

1995-02-01

The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud

Information's role in the estimation of chaotic signals

NASA Astrophysics Data System (ADS)

Drake, Daniel Fred

1998-11-01

Researchers have proposed several methods designed to recover chaotic signals from noise-corrupted observations. While the methods vary, their qualitative performance does not: in low levels of noise all methods effectively recover the underlying signal; in high levels of noise no method can recover the underlying signal to any meaningful degree of accuracy. Of the methods proposed to date, all represent sub-optimal estimators. So: Is the inability to recover the signal in high noise levels simply a consequence of estimator sub-optimality? Or is estimator failure actually a manifestation of some intrinsic property of chaos itself? These questions are answered by deriving an optimal estimator for a class of chaotic systems and noting that it, too, fails in high levels of noise. An exact, closed- form expression for the estimator is obtained for a class of chaotic systems whose signals are solutions to a set of linear (but noncausal) difference equations. The existence of this linear description circumvents the difficulties normally encountered when manipulating the nonlinear (but causal) expressions that govern. chaotic behavior. The reason why even the optimal estimator fails to recover underlying chaotic signals in high levels of noise has its roots in information theory. At such noise levels, the mutual information linking the corrupted observations to the underlying signal is essentially nil, reducing the estimator to a simple guessing strategy based solely on a priori statistics. Entropy, long the common bond between information theory and dynamical systems, is actually one aspect of a far more complete characterization of information sources: the rate distortion function. Determining the rate distortion function associated with the class of chaotic systems considered in this work provides bounds on estimator performance in high levels of noise. Finally, a slight modification of the linear description leads to a method of synthesizing on limited precision platforms ``pseudo-chaotic'' sequences that mimic true chaotic behavior to any finite degree of precision and duration. The use of such a technique in spread-spectrum communications is considered.

A new fractional-order sliding mode controller via a nonlinear disturbance observer for a class of dynamical systems with mismatched disturbances.

PubMed

Pashaei, Shabnam; Badamchizadeh, Mohammadali

2016-07-01

This paper investigates the stabilization and disturbance rejection for a class of fractional-order nonlinear dynamical systems with mismatched disturbances. To fulfill this purpose a new fractional-order sliding mode control (FOSMC) based on a nonlinear disturbance observer is proposed. In order to design the suitable fractional-order sliding mode controller, a proper switching surface is introduced. Afterward, by using the sliding mode theory and Lyapunov stability theory, a robust fractional-order control law via a nonlinear disturbance observer is proposed to assure the existence of the sliding motion in finite time. The proposed fractional-order sliding mode controller exposes better control performance, ensures fast and robust stability of the closed-loop system, eliminates the disturbances and diminishes the chattering problem. Finally, the effectiveness of the proposed fractional-order controller is depicted via numerical simulation results of practical example and is compared with some other controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

Chaotic optical time-domain reflectometry using a distributed feedback laser diode modulated by an improved Colpitts oscillator

NASA Astrophysics Data System (ADS)

Li, Jing Xia; Xu, Hang; Liu, Li; Su, Peng Cheng; Zhang, Jian Guo

2015-05-01

We report a chaotic optical time-domain reflectometry for fiber fault location, where a chaotic probe signal is generated by driving a distributed feedback laser diode with an improved Colpitts chaotic oscillator. The results show that the unterminated fiber end, the loose connector, and the mismatch connector can be precisely located. A measurement range of approximately 91 km and a range independent resolution of 6 cm are achieved. This implementation method is easy to integrate and is cost effective, which gives it great potential for commercial applications.

Chaos in a chemical system

NASA Astrophysics Data System (ADS)

Srivastava, R.; Srivastava, P. K.; Chattopadhyay, J.

2013-07-01

Chaotic oscillations have been observed experimentally in dual-frequency oscillator OAP - Ce+4-BrO- 3-H2SO4 in CSTR. The system shows variation of oscillating potential and frequencies when it moves from low frequency to high frequency region and vice-versa. It was observed that system bifurcate from low frequency to chaotic regime through periode-2 and period-3 on the other hand system bifurcate from chaotic regime to high frequency oscillation through period-2. It was established that the observed oscillations are chaotic in nature on the basis of next amplitude map and bifurcation sequences.

Regular transport dynamics produce chaotic travel times.

PubMed

Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F; Toledo, Benjamín; Valdivia, Juan Alejandro

2014-06-01

In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.

Separation of Trend and Chaotic Components of Time Series and Estimation of Their Characteristics by Linear Splines

NASA Astrophysics Data System (ADS)

Kryanev, A. V.; Ivanov, V. V.; Romanova, A. O.; Sevastyanov, L. A.; Udumyan, D. K.

2018-03-01

This paper considers the problem of separating the trend and the chaotic component of chaotic time series in the absence of information on the characteristics of the chaotic component. Such a problem arises in nuclear physics, biomedicine, and many other applied fields. The scheme has two stages. At the first stage, smoothing linear splines with different values of smoothing parameter are used to separate the "trend component." At the second stage, the method of least squares is used to find the unknown variance σ2 of the noise component.

Fast and secure encryption-decryption method based on chaotic dynamics

DOEpatents

Protopopescu, Vladimir A.; Santoro, Robert T.; Tolliver, Johnny S.

1995-01-01

A method and system for the secure encryption of information. The method comprises the steps of dividing a message of length L into its character components; generating m chaotic iterates from m independent chaotic maps; producing an "initial" value based upon the m chaotic iterates; transforming the "initial" value to create a pseudo-random integer; repeating the steps of generating, producing and transforming until a pseudo-random integer sequence of length L is created; and encrypting the message as ciphertext based upon the pseudo random integer sequence. A system for accomplishing the invention is also provided.

Dynamic analysis of a buckled asymmetric piezoelectric beam for energy harvesting

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

Van Blarigan, Louis, E-mail: louis01@umail.ucsb.edu; Moehlis, Jeff

2016-03-15

A model of a buckled beam energy harvester is analyzed to determine the phenomena behind the transition between high and low power output levels. It is shown that the presence of a chaotic attractor is a sufficient condition to predict high power output, though there are relatively small areas where high output is achieved without a chaotic attractor. The chaotic attractor appears as a product of a period doubling cascade or a boundary crisis. Bifurcation diagrams provide insight into the development of the chaotic region as the input power level is varied, as well as the intermixed periodic windows.

Bluetooth based chaos synchronization using particle swarm optimization and its applications to image encryption.

PubMed

Yau, Her-Terng; Hung, Tzu-Hsiang; Hsieh, Chia-Chun

2012-01-01

This study used the complex dynamic characteristics of chaotic systems and Bluetooth to explore the topic of wireless chaotic communication secrecy and develop a communication security system. The PID controller for chaos synchronization control was applied, and the optimum parameters of this PID controller were obtained using a Particle Swarm Optimization (PSO) algorithm. Bluetooth was used to realize wireless transmissions, and a chaotic wireless communication security system was developed in the design concept of a chaotic communication security system. The experimental results show that this scheme can be used successfully in image encryption.

Regular transport dynamics produce chaotic travel times

NASA Astrophysics Data System (ADS)

Villalobos, Jorge; Muñoz, Víctor; Rogan, José; Zarama, Roberto; Johnson, Neil F.; Toledo, Benjamín; Valdivia, Juan Alejandro

2014-06-01

In the hope of making passenger travel times shorter and more reliable, many cities are introducing dedicated bus lanes (e.g., Bogota, London, Miami). Here we show that chaotic travel times are actually a natural consequence of individual bus function, and hence of public transport systems more generally, i.e., chaotic dynamics emerge even when the route is empty and straight, stops and lights are equidistant and regular, and loading times are negligible. More generally, our findings provide a novel example of chaotic dynamics emerging from a single object following Newton's laws of motion in a regularized one-dimensional system.

Bistability and chaos in the Taylor-Green dynamo.

PubMed

Yadav, Rakesh K; Verma, Mahendra K; Wahi, Pankaj

2012-03-01

Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing.

The strongest magnetic barrier in the DIII-D tokamak and comparison with the ASDEX UG

NASA Astrophysics Data System (ADS)

Ali, Halima; Punjabi, Alkesh

2013-05-01

Magnetic perturbations in tokamaks lead to the formation of magnetic islands, chaotic field lines, and the destruction of flux surfaces. Controlling or reducing transport along chaotic field lines is a key challenge in magnetically confined fusion plasmas. A local control method was proposed by Chandre et al. [Nucl. Fusion 46, 33-45 (2006)] to build barriers to magnetic field line diffusion by addition of a small second-order control term localized in the phase space to the field line Hamiltonian. Formation and existence of such magnetic barriers in Ohmically heated tokamaks (OHT), ASDEX UG and piecewise analytic DIII-D [Luxon, J.L.; Davis, L.E., Fusion Technol. 8, 441 (1985)] plasma equilibria was predicted by the authors [Ali, H.; Punjabi, A., Plasma Phys. Control. Fusion 49, 1565-1582 (2007)]. Very recently, this prediction for the DIII-D has been corroborated [Volpe, F.A., et al., Nucl. Fusion 52, 054017 (2012)] by field-line tracing calculations, using experimentally constrained Equilibrium Fit (EFIT) [Lao, et al., Nucl. Fusion 25, 1611 (1985)] DIII-D equilibria perturbed to include the vacuum field from the internal coils utilized in the experiments. This second-order approach is applied to the DIII-D tokamak to build noble irrational magnetic barriers inside the chaos created by the locked resonant magnetic perturbations (RMPs) (m, n)=(3, 1)+(4, 1), with m and n the poloidal and toroidal mode numbers of the Fourier expansion of the magnetic perturbation with amplitude δ. A piecewise, analytic, accurate, axisymmetric generating function for the trajectories of magnetic field lines in the DIII-D is constructed in magnetic coordinates from the experimental EFIT Grad-Shafranov solver [Lao, L, et al., Fusion Sci. Technol. 48, 968 (2005)] for the shot 115,467 at 3000 ms in the DIII-D. A symplectic mathematical map is used to integrate field lines in the DIII-D. A numerical algorithm [Ali, H., et al., Radiat. Eff. Def. Solids Inc. Plasma Sc. Plasma Tech. 165, 83 (2010)] based on continued fraction decomposition of the rotational transform labeling the barriers for selecting and identifying the strongest noble irrational barrier is used. The results are compared and contrasted with our previous results on the ASDEX UG. About six times stronger a barrier can be built in the DIII-D than in the ASDEX UG. High magnetic shear near the separatrix in the DIII-D is inferred as the possible cause of this. Implications of this for the DIII-D and the International Thermonuclear Experimental Reactor (ITER) are discussed.

Generating Random Numbers by Means of Nonlinear Dynamic Systems

ERIC Educational Resources Information Center

Zang, Jiaqi; Hu, Haojie; Zhong, Juhua; Luo, Duanbin; Fang, Yi

2018-01-01

To introduce the randomness of a physical process to students, a chaotic pendulum experiment was opened in East China University of Science and Technology (ECUST) on the undergraduate level in the physics department. It was shown chaotic motion could be initiated through adjusting the operation of a chaotic pendulum. By using the data of the…

Few Fractional Order Derivatives and Their Computations

ERIC Educational Resources Information Center

Bhatta, D. D.

2007-01-01

This work presents an introductory development of fractional order derivatives and their computations. Historical development of fractional calculus is discussed. This paper presents how to obtain computational results of fractional order derivatives for some elementary functions. Computational results are illustrated in tabular and graphical…

Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models

NASA Astrophysics Data System (ADS)

Ahmed, E.; El-Sayed, A. M. A.; El-Saka, H. A. A.

2007-01-01

In this paper we are concerned with the fractional-order predator-prey model and the fractional-order rabies model. Existence and uniqueness of solutions are proved. The stability of equilibrium points are studied. Numerical solutions of these models are given. An example is given where the equilibrium point is a centre for the integer order system but locally asymptotically stable for its fractional-order counterpart.

Fractional order PIλ controller synthesis for steam turbine speed governing systems.

PubMed

Chen, Kai; Tang, Rongnian; Li, Chuang; Lu, Junguo

2018-06-01

The current state of the art of fractional order stability theory is hardly to build connection between the time domain analysis and frequency domain synthesis. The existing tuning methodologies for fractional order PI λ D μ are not always satisfy the given gain crossover frequency and phase margin simultaneously. To overcome the drawbacks in the existing synthesis of fractional order controller, the synthesis of optimal fractional order PI λ controller for higher-order process is proposed. According to the specified phase margin, the corresponding upper boundary of gain crossover frequency and stability surface in parameter space are obtained. Sweeping the order parameter over λ∈(0,2), the complete set of stabilizing controller which guarantees both pre-specifying phase frequency characteristic can be collected. Whereafter, the optimal fractional order PI λ controller is applied to the speed governing systems of steam turbine generation units. The numerical simulation and hardware-in-the-loop simulation demonstrate the effectiveness and satisfactory closed-loop performance of obtained fractional order PI λ controller. Copyright © 2018 ISA. Published by Elsevier Ltd. All rights reserved.

Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram.

PubMed

Dafilis, Mathew P; Frascoli, Federico; Cadusch, Peter J; Liley, David T J

2013-06-01

The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.

Model-order reduction of lumped parameter systems via fractional calculus

NASA Astrophysics Data System (ADS)

Hollkamp, John P.; Sen, Mihir; Semperlotti, Fabio

2018-04-01

This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach to the simulation of non-homogeneous systems dictates the use of numerical solutions and often imposes stringent compromises between accuracy and computational performance. Fractional calculus provides an alternative approach where complex dynamical systems can be modeled with compact fractional equations that not only can still guarantee analytical solutions, but can also enable high levels of order reduction without compromising on accuracy. Different approaches are explored in order to transform the integer order model into a reduced order fractional model able to match the dynamic response of the initial system. Analytical and numerical results show that, under certain conditions, an exact match is possible and the resulting fractional differential models have both a complex and frequency-dependent order of the differential operator. The implications of this type of approach for both model order reduction and model synthesis are discussed.

Adaptive fractional order sliding mode control for Boost converter in the Battery/Supercapacitor HESS

PubMed Central

Xu, Dan; Zhou, Huan; Zhou, Tao

2018-01-01

In this paper, an adaptive fractional order sliding mode control (AFSMC) scheme is designed for the current tracking control of the Boost-type converter in a Battery/Supercapacitor hybrid energy storage system (HESS). In order to stabilize the current, the adaptation rules based on state-observer and Lyapunov function are being designed. A fractional order sliding surface function is defined based on the tracking current error and adaptive rules. Furthermore, through fractional order analysis, the stability of the fractional order control system is proven, and the value of the fractional order (λ) is being investigated. In addition, the effectiveness of the proposed AFSMC strategy is being verified by numerical simulations. The advantages of good transient response and robustness to uncertainty are being indicated by this design, when compared with a conventional integer order sliding mode control system. PMID:29702696

Generalized Smooth Transition Map Between Tent and Logistic Maps

NASA Astrophysics Data System (ADS)

Sayed, Wafaa S.; Fahmy, Hossam A. H.; Rezk, Ahmed A.; Radwan, Ahmed G.

There is a continuous demand on novel chaotic generators to be employed in various modeling and pseudo-random number generation applications. This paper proposes a new chaotic map which is a general form for one-dimensional discrete-time maps employing the power function with the tent and logistic maps as special cases. The proposed map uses extra parameters to provide responses that fit multiple applications for which conventional maps were not enough. The proposed generalization covers also maps whose iterative relations are not based on polynomials, i.e. with fractional powers. We introduce a framework for analyzing the proposed map mathematically and predicting its behavior for various combinations of its parameters. In addition, we present and explain the transition map which results in intermediate responses as the parameters vary from their values corresponding to tent map to those corresponding to logistic map case. We study the properties of the proposed map including graph of the map equation, general bifurcation diagram and its key-points, output sequences, and maximum Lyapunov exponent. We present further explorations such as effects of scaling, system response with respect to the new parameters, and operating ranges other than transition region. Finally, a stream cipher system based on the generalized transition map validates its utility for image encryption applications. The system allows the construction of more efficient encryption keys which enhances its sensitivity and other cryptographic properties.

Orbital structure in oscillating galactic potentials

NASA Astrophysics Data System (ADS)

Terzić, Balša; Kandrup, Henry E.

2004-01-01

Subjecting a galactic potential to (possibly damped) nearly periodic, time-dependent variations can lead to large numbers of chaotic orbits experiencing systematic changes in energy, and the resulting chaotic phase mixing could play an important role in explaining such phenomena as violent relaxation. This paper focuses on the simplest case of spherically symmetric potentials subjected to strictly periodic driving with the aim of understanding precisely why orbits become chaotic and under what circumstances they will exhibit systematic changes in energy. Four unperturbed potentials V0(r) were considered, each subjected to a time dependence of the form V(r, t) =V0(r)(1 +m0 sinωt). In each case, the orbits divide clearly into regular and chaotic, distinctions which appear absolute. In particular, transitions from regularity to chaos are seemingly impossible. Over finite time intervals, chaotic orbits subdivide into what can be termed `sticky' chaotic orbits, which exhibit no large-scale secular changes in energy and remain trapped in the phase-space region where they started; and `wildly' chaotic orbits, which do exhibit systematic drifts in energy as the orbits diffuse to different phase-space regions. This latter distinction is not absolute, transitions corresponding apparently to orbits penetrating a `leaky' phase-space barrier. The three different orbit types can be identified simply in terms of the frequencies for which their Fourier spectra have the most power. An examination of the statistical properties of orbit ensembles as a function of driving frequency ω allows us to identify the specific resonances that determine orbital structure. Attention focuses also on how, for fixed amplitude m0, such quantities as the mean energy shift, the relative measure of chaotic orbits and the mean value of the largest Lyapunov exponent vary with driving frequency ω and how, for fixed ω, the same quantities depend on m0.

Period doubling cascades of limit cycles in cardiac action potential models as precursors to chaotic early Afterdepolarizations.

PubMed

Kügler, Philipp; Bulelzai, M A K; Erhardt, André H

2017-04-04

Early afterdepolarizations (EADs) are pathological voltage oscillations during the repolarization phase of cardiac action potentials (APs). EADs are caused by drugs, oxidative stress or ion channel disease, and they are considered as potential precursors to cardiac arrhythmias in recent attempts to redefine the cardiac drug safety paradigm. The irregular behaviour of EADs observed in experiments has been previously attributed to chaotic EAD dynamics under periodic pacing, made possible by a homoclinic bifurcation in the fast subsystem of the deterministic AP system of differential equations. In this article we demonstrate that a homoclinic bifurcation in the fast subsystem of the action potential model is neither a necessary nor a sufficient condition for the genesis of chaotic EADs. We rather argue that a cascade of period doubling (PD) bifurcations of limit cycles in the full AP system paves the way to chaotic EAD dynamics across a variety of models including a) periodically paced and spontaneously active cardiomyocytes, b) periodically paced and non-active cardiomyocytes as well as c) unpaced and spontaneously active cardiomyocytes. Furthermore, our bifurcation analysis reveals that chaotic EAD dynamics may coexist in a stable manner with fully regular AP dynamics, where only the initial conditions decide which type of dynamics is displayed. EADs are a potential source of cardiac arrhythmias and hence are of relevance both from the viewpoint of drug cardiotoxicity testing and the treatment of cardiomyopathies. The model-independent association of chaotic EADs with period doubling cascades of limit cycles introduced in this article opens novel opportunities to study chaotic EADs by means of bifurcation control theory and inverse bifurcation analysis. Furthermore, our results may shed new light on the synchronization and propagation of chaotic EADs in homogeneous and heterogeneous multicellular and cardiac tissue preparations.

Composing chaotic music from the letter m

NASA Astrophysics Data System (ADS)

Sotiropoulos, Anastasios D.

Chaotic music is composed from a proposed iterative map depicting the letter m, relating the pitch, duration and loudness of successive steps. Each of the two curves of the letter m is based on the classical logistic map. Thus, the generating map is xn+1 = r xn(1/2 - xn) for xn between 0 and 1/2 defining the first curve, and xn+1 = r (xn - 1/2)(1 - xn) for xn between 1/2 and 1 representing the second curve. The parameter r which determines the height(s) of the letter m varies from 2 to 16, the latter value ensuring fully developed chaotic solutions for the whole letter m; r = 8 yielding full chaotic solutions only for its first curve. The m-model yields fixed points, bifurcation points and chaotic regions for each separate curve, as well as values of the parameter r greater than 8 which produce inter-fixed points, inter-bifurcation points and inter-chaotic regions from the interplay of the two curves. Based on this, music is composed from mapping the m- recurrence model solutions onto actual notes. The resulting musical score strongly depends on the sequence of notes chosen by the composer to define the musical range corresponding to the range of the chaotic mathematical solutions x from 0 to 1. Here, two musical ranges are used; one is the middle chromatic scale and the other is the seven- octaves range. At the composer's will and, for aesthetics, within the same composition, notes can be the outcome of different values of r and/or shifted in any octave. Compositions with endings of non-repeating note patterns result from values of r in the m-model that do not produce bifurcations. Scores of chaotic music composed from the m-model and the classical logistic model are presented.

Correlation Plenoptic Imaging.

PubMed

D'Angelo, Milena; Pepe, Francesco V; Garuccio, Augusto; Scarcelli, Giuliano

2016-06-03

Plenoptic imaging is a promising optical modality that simultaneously captures the location and the propagation direction of light in order to enable three-dimensional imaging in a single shot. However, in standard plenoptic imaging systems, the maximum spatial and angular resolutions are fundamentally linked; thereby, the maximum achievable depth of field is inversely proportional to the spatial resolution. We propose to take advantage of the second-order correlation properties of light to overcome this fundamental limitation. In this Letter, we demonstrate that the correlation in both momentum and position of chaotic light leads to the enhanced refocusing power of correlation plenoptic imaging with respect to standard plenoptic imaging.

Correlation Plenoptic Imaging

NASA Astrophysics Data System (ADS)

D'Angelo, Milena; Pepe, Francesco V.; Garuccio, Augusto; Scarcelli, Giuliano

2016-06-01

Plenoptic imaging is a promising optical modality that simultaneously captures the location and the propagation direction of light in order to enable three-dimensional imaging in a single shot. However, in standard plenoptic imaging systems, the maximum spatial and angular resolutions are fundamentally linked; thereby, the maximum achievable depth of field is inversely proportional to the spatial resolution. We propose to take advantage of the second-order correlation properties of light to overcome this fundamental limitation. In this Letter, we demonstrate that the correlation in both momentum and position of chaotic light leads to the enhanced refocusing power of correlation plenoptic imaging with respect to standard plenoptic imaging.

Ordering-separation phase transitions in a Co3V alloy

NASA Astrophysics Data System (ADS)

Ustinovshchikov, Yu. I.

2017-01-01

The microstructure of the Co3V alloy formed by heat treatment at various temperatures is studied by transmission electron microscopy. Two ordering-separation phase transitions are revealed at temperatures of 400-450 and 800°C. At the high-temperature phase separation, the microstructure consists of bcc vanadium particles and an fcc solid solution; at the low-temperature phase separation, the microstructure is cellular. In the ordering range, the microstructure consists of chemical compound Co3V particles chaotically arranged in the solid solution. The structure of the Co3V alloy is shown not to correspond to the structures indicated in the Co-V phase diagram at any temperatures.

Out-of-time-order fluctuation-dissipation theorem

NASA Astrophysics Data System (ADS)

Tsuji, Naoto; Shitara, Tomohiro; Ueda, Masahito

2018-01-01

We prove a generalized fluctuation-dissipation theorem for a certain class of out-of-time-ordered correlators (OTOCs) with a modified statistical average, which we call bipartite OTOCs, for general quantum systems in thermal equilibrium. The difference between the bipartite and physical OTOCs defined by the usual statistical average is quantified by a measure of quantum fluctuations known as the Wigner-Yanase skew information. Within this difference, the theorem describes a universal relation between chaotic behavior in quantum systems and a nonlinear-response function that involves a time-reversed process. We show that the theorem can be generalized to higher-order n -partite OTOCs as well as in the form of generalized covariance.

Fractional Hopfield Neural Networks: Fractional Dynamic Associative Recurrent Neural Networks.

PubMed

Pu, Yi-Fei; Yi, Zhang; Zhou, Ji-Liu

2017-10-01

This paper mainly discusses a novel conceptual framework: fractional Hopfield neural networks (FHNN). As is commonly known, fractional calculus has been incorporated into artificial neural networks, mainly because of its long-term memory and nonlocality. Some researchers have made interesting attempts at fractional neural networks and gained competitive advantages over integer-order neural networks. Therefore, it is naturally makes one ponder how to generalize the first-order Hopfield neural networks to the fractional-order ones, and how to implement FHNN by means of fractional calculus. We propose to introduce a novel mathematical method: fractional calculus to implement FHNN. First, we implement fractor in the form of an analog circuit. Second, we implement FHNN by utilizing fractor and the fractional steepest descent approach, construct its Lyapunov function, and further analyze its attractors. Third, we perform experiments to analyze the stability and convergence of FHNN, and further discuss its applications to the defense against chip cloning attacks for anticounterfeiting. The main contribution of our work is to propose FHNN in the form of an analog circuit by utilizing a fractor and the fractional steepest descent approach, construct its Lyapunov function, prove its Lyapunov stability, analyze its attractors, and apply FHNN to the defense against chip cloning attacks for anticounterfeiting. A significant advantage of FHNN is that its attractors essentially relate to the neuron's fractional order. FHNN possesses the fractional-order-stability and fractional-order-sensitivity characteristics.

Fault detection technique for wavelength division multiplexing passive optical network using chaotic fiber laser

NASA Astrophysics Data System (ADS)

Xu, Naijun; Yang, Lingzhen; Zhang, Juan; Zhang, Xiangyuan; Wang, Juanfen; Zhang, Zhaoxia; Liu, Xianglian

2014-03-01

We propose a fault localization method for wavelength division multiplexing passive optical network (WDM-PON). A proof-of-concept experiment was demonstrated by utilizing the wavelength tunable chaotic laser generated from an erbium-doped fiber ring laser with a manual tunable fiber Bragg grating (TFBG) filter. The range of the chaotic lasing wavelength can cover the C-band. Basing on the TFBG filter, we can adjust the wavelength of the chaotic laser to match the WDM-PON channel with identical wavelength. We determined the fault location by calculating the cross-correlation between the reference and return signals. Analysis of the characteristics of the wavelength tunable chaotic laser showed that the breakpoint, the loose connector, and the mismatch connector could be precisely located. A dynamic range of approximately 23.8 dB and a spatial resolution of 4 cm, which was independent of the measuring range, were obtained.

A quasi-crisis

NASA Astrophysics Data System (ADS)

Wang, Ying-Mei; Wang, Wen-Xiu; Chen, He-Sheng; Zhang, Kai; Jiang, Yu-Mei; Wang, Xu-Ming; He, Da-Ren

2002-03-01

A system concatenated by two area-preserving maps may be addressed as "quasi- dissipative," since such a system can display dissipative behaviors^1. This is due to noninvertibility induced by discontinuity in the system function. In such a system, the image set of the discontinuous border forms a chaotic quasi-attractor. At a critical control parameter value the quasi-attractor suddenly vanishes. The chaotic iterations escape, via a leaking hole, to an emergent period-8 elliptic island. The hole is the intersection of the chaotic quasi-attractor and the period-8 island. The chaotic quasi-attractor thus changes to chaotic quasi-transients. The scaling behavior that drives the quasi-crisis has been investigated numerically. It reads: ∝ (p-p_c)^-ν , where is defined as the averaged length of quasi-transients. The scaling exponent ν=1.66 ± 0.04. The critical parameter value equals p_c=-1.0069799. ^1 J. Wang et al., Phys.Rev.E, 64(2001)026202.

On synchronisation of a class of complex chaotic systems with complex unknown parameters via integral sliding mode control

NASA Astrophysics Data System (ADS)

Tirandaz, Hamed; Karami-Mollaee, Ali

2018-06-01

Chaotic systems demonstrate complex behaviour in their state variables and their parameters, which generate some challenges and consequences. This paper presents a new synchronisation scheme based on integral sliding mode control (ISMC) method on a class of complex chaotic systems with complex unknown parameters. Synchronisation between corresponding states of a class of complex chaotic systems and also convergence of the errors of the system parameters to zero point are studied. The designed feedback control vector and complex unknown parameter vector are analytically achieved based on the Lyapunov stability theory. Moreover, the effectiveness of the proposed methodology is verified by synchronisation of the Chen complex system and the Lorenz complex systems as the leader and the follower chaotic systems, respectively. In conclusion, some numerical simulations related to the synchronisation methodology is given to illustrate the effectiveness of the theoretical discussions.