Theoretical and experimental aspects of chaos control by time-delayed feedback.

PubMed

Just, Wolfram; Benner, Hartmut; Reibold, Ekkehard

2003-03-01

We review recent developments for the control of chaos by time-delayed feedback methods. While such methods are easily applied even in quite complex experimental context the theoretical analysis yields infinite-dimensional differential-difference systems which are hard to tackle. The essential ideas for a general theoretical approach are sketched and the results are compared to electronic circuits and to high power ferromagnetic resonance experiments. Our results show that the control performance can be understood on the basis of experimentally accessible quantities without resort to any model for the internal dynamics.

Continuous control of chaos based on the stability criterion.

PubMed

Yu, Hong Jie; Liu, Yan Zhu; Peng, Jian Hua

2004-06-01

A method of chaos control based on stability criterion is proposed in the present paper. This method can stabilize chaotic systems onto a desired periodic orbit by a small time-continuous perturbation nonlinear feedback. This method does not require linearization of the system around the stabilized orbit and only an approximate location of the desired periodic orbit is required which can be automatically detected in the control process. The control can be started at any moment by choosing appropriate perturbation restriction condition. It seems that more flexibility and convenience are the main advantages of this method. The discussions on control of attitude motion of a spacecraft, Rössler system, and two coupled Duffing oscillators are given as numerical examples.

Effortful control and school adjustment: The moderating role of classroom chaos.

PubMed

Berger, Rebecca H; Valiente, Carlos; Eisenberg, Nancy; Hernandez, Maciel M; Thompson, Marilyn; Spinrad, Tracy; VanSchyndel, Sarah; Silva, Kassondra; Southworth, Jody

2017-11-01

Guided by the person by environment framework, the primary goal of this study was to determine whether classroom chaos moderated the relation between effortful control and kindergarteners' school adjustment. Classroom observers reported on children's ( N = 301) effortful control in the fall. In the spring, teachers reported on classroom chaos and school adjustment outcomes (teacher-student relationship closeness and conflict, and school liking and avoidance). Cross-level interactions between effortful control and classroom chaos predicting school adjustment outcomes were assessed. A consistent pattern of interactions between effortful control and classroom chaos indicated that the relations between effortful control and the school adjustment outcomes were strongest in high chaos classrooms. Post-hoc analyses indicated that classroom chaos was associated with poor school adjustment when effortful control was low, suggesting that the combination of high chaos and low effortful control was associated with the poorest school outcomes.

Expectation-Based Control of Noise and Chaos

NASA Technical Reports Server (NTRS)

Zak, Michael

2006-01-01

A proposed approach to control of noise and chaos in dynamic systems would supplement conventional methods. The approach is based on fictitious forces composed of expectations governed by Fokker-Planck or Liouville equations that describe the evolution of the probability densities of the controlled parameters. These forces would be utilized as feedback control forces that would suppress the undesired diffusion of the controlled parameters. Examples of dynamic systems in which the approach is expected to prove beneficial include spacecraft, electronic systems, and coupled lasers.

Is case-chaos methodology an appropriate alternative to conventional case-control studies for investigating outbreaks?

PubMed

Edelstein, Michael; Wallensten, Anders; Kühlmann-Berenzon, Sharon

2014-08-15

Case-chaos methodology is a proposed alternative to case-control studies that simulates controls by randomly reshuffling the exposures of cases. We evaluated the method using data on outbreaks in Sweden. We identified 5 case-control studies from foodborne illness outbreaks that occurred between 2005 and 2012. Using case-chaos methodology, we calculated odds ratios 1,000 times for each exposure. We used the median as the point estimate and the 2.5th and 97.5th percentiles as the confidence interval. We compared case-chaos matched odds ratios with their respective case-control odds ratios in terms of statistical significance. Using Spearman's correlation, we estimated the correlation between matched odds ratios and the proportion of cases exposed to each exposure and quantified the relationship between the 2 using a normal linear mixed model. Each case-control study identified an outbreak vehicle (odds ratios = 4.9-45). Case-chaos methodology identified the outbreak vehicle 3 out of 5 times. It identified significant associations in 22 of 113 exposures that were not associated with outcome and 5 of 18 exposures that were significantly associated with outcome. Log matched odds ratios correlated with their respective proportion of cases exposed (Spearman ρ = 0.91) and increased significantly with the proportion of cases exposed (b = 0.054). Case-chaos methodology missed the outbreak source 2 of 5 times and identified spurious associations between a number of exposures and outcome. Measures of association correlated with the proportion of cases exposed. We recommended against using case-chaos analysis during outbreak investigations. © The Author 2014. Published by Oxford University Press on behalf of the Johns Hopkins Bloomberg School of Public Health. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com.

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.

Chaos as the hub of systems dynamics. The part I-The attitude control of spacecraft by involving in the heteroclinic chaos

NASA Astrophysics Data System (ADS)

Doroshin, Anton V.

2018-06-01

In this work the chaos in dynamical systems is considered as a positive aspect of dynamical behavior which can be applied to change systems dynamical parameters and, moreover, to change systems qualitative properties. From this point of view, the chaos can be characterized as a hub for the system dynamical regimes, because it allows to interconnect separated zones of the phase space of the system, and to fulfill the jump into the desirable phase space zone. The concretized aim of this part of the research is to focus on developing the attitude control method for magnetized gyrostat-satellites, which uses the passage through the intentionally generated heteroclinic chaos. The attitude dynamics of the satellite/spacecraft in this case represents the series of transitions from the initial dynamical regime into the chaotic heteroclinic regime with the subsequent exit to the final target dynamical regime with desirable parameters of the attitude dynamics.

Conduct Problems, IQ, and Household Chaos: A Longitudinal Multi-Informant Study

ERIC Educational Resources Information Center

Deater-Deckard, Kirby; Mullineaux, Paula Y.; Beekman, Charles; Petrill, Stephen A.; Schatschneider, Chris; Thompson, Lee A.

2009-01-01

Background: We tested the hypothesis that household chaos would be associated with lower child IQ and more child conduct problems concurrently and longitudinally over two years while controlling for housing conditions, parent education/IQ, literacy environment, parental warmth/negativity, and stressful events. Methods: The sample included 302…

Controlling chaos faster.

PubMed

Bick, Christian; Kolodziejski, Christoph; Timme, Marc

2014-09-01

Predictive feedback control is an easy-to-implement method to stabilize unknown unstable periodic orbits in chaotic dynamical systems. Predictive feedback control is severely limited because asymptotic convergence speed decreases with stronger instabilities which in turn are typical for larger target periods, rendering it harder to effectively stabilize periodic orbits of large period. Here, we study stalled chaos control, where the application of control is stalled to make use of the chaotic, uncontrolled dynamics, and introduce an adaptation paradigm to overcome this limitation and speed up convergence. This modified control scheme is not only capable of stabilizing more periodic orbits than the original predictive feedback control but also speeds up convergence for typical chaotic maps, as illustrated in both theory and application. The proposed adaptation scheme provides a way to tune parameters online, yielding a broadly applicable, fast chaos control that converges reliably, even for periodic orbits of large period.

Chaos in the fractional order logistic delay system: Circuit realization and synchronization

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

Baskonus, Haci Mehmet; Hammouch, Zakia; Mekkaoui, Toufik

2016-06-08

In this paper, we present a numerical study and a circuit design to prove existence of chaos in the fractional order Logistic delay system. In addition, we investigate an active control synchronization scheme in this system. Numerical and cicruit simulations show the effectiveness and feasibility of this method.

Price game and chaos control among three oligarchs with different rationalities in property insurance market.

PubMed

Ma, Junhai; Zhang, Junling

2012-12-01

Combining with the actual competition in Chinese property insurance market and assuming that the property insurance companies take the marginal utility maximization as the basis of decision-making when they play price games, we first established the price game model with three oligarchs who have different rationalities. Then, we discussed the existence and stability of equilibrium points. Third, we studied the theoretical value of Lyapunov exponent at Nash equilibrium point and its change process with the main parameters' changes though having numerical simulation for the system such as the bifurcation, chaos attractors, and so on. Finally, we analyzed the influences which the changes of different parameters have on the profits and utilities of oligarchs and their corresponding competition advantage. Based on this, we used the variable feedback control method to control the chaos of the system and stabilized the chaos state to Nash equilibrium point again. The results have significant theoretical and practical application value.

Price game and chaos control among three oligarchs with different rationalities in property insurance market

NASA Astrophysics Data System (ADS)

Ma, Junhai; Zhang, Junling

2012-12-01

Combining with the actual competition in Chinese property insurance market and assuming that the property insurance companies take the marginal utility maximization as the basis of decision-making when they play price games, we first established the price game model with three oligarchs who have different rationalities. Then, we discussed the existence and stability of equilibrium points. Third, we studied the theoretical value of Lyapunov exponent at Nash equilibrium point and its change process with the main parameters' changes though having numerical simulation for the system such as the bifurcation, chaos attractors, and so on. Finally, we analyzed the influences which the changes of different parameters have on the profits and utilities of oligarchs and their corresponding competition advantage. Based on this, we used the variable feedback control method to control the chaos of the system and stabilized the chaos state to Nash equilibrium point again. The results have significant theoretical and practical application value.

Generating chaos for discrete time-delayed systems via impulsive control.

PubMed

Guan, Zhi-Hong; Liu, Na

2010-03-01

Generating chaos for a class of discrete time-delayed systems via impulsive control is investigated in this paper. With the augmented matrix method, the time-delay impulsive systems can be transformed into a new class of linear discrete impulsive systems. Based on the largest Lyapunov exponent and the boundedness of the systems, some theoretical results about the chaotification for the discrete impulsive systems with time delay are derived and an example is given to visualize the satisfactory control performance.

Anticontrol of chaos in continuous-time systems via time-delay feedback.

PubMed

Wang, Xiao Fan; Chen, Guanrong; Yu, Xinghuo

2000-12-01

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.

Chaos Theory as a Model for Life Transitions Counseling: Nonlinear Dynamics and Life's Changes

ERIC Educational Resources Information Center

Bussolari, Cori J.; Goodell, Judith A.

2009-01-01

Chaos theory is presented for counselors working with clients experiencing life transitions. It is proposed as a model that considers disorder, unpredictability, and lack of control as normal parts of transition processes. Nonlinear constructs from physics are adapted for use in counseling. The model provides a method clients can use to…

Applied Chaos Level Test for Validation of Signal Conditions Underlying Optimal Performance of Voice Classification Methods.

PubMed

Liu, Boquan; Polce, Evan; Sprott, Julien C; Jiang, Jack J

2018-05-17

The purpose of this study is to introduce a chaos level test to evaluate linear and nonlinear voice type classification method performances under varying signal chaos conditions without subjective impression. Voice signals were constructed with differing degrees of noise to model signal chaos. Within each noise power, 100 Monte Carlo experiments were applied to analyze the output of jitter, shimmer, correlation dimension, and spectrum convergence ratio. The computational output of the 4 classifiers was then plotted against signal chaos level to investigate the performance of these acoustic analysis methods under varying degrees of signal chaos. A diffusive behavior detection-based chaos level test was used to investigate the performances of different voice classification methods. Voice signals were constructed by varying the signal-to-noise ratio to establish differing signal chaos conditions. Chaos level increased sigmoidally with increasing noise power. Jitter and shimmer performed optimally when the chaos level was less than or equal to 0.01, whereas correlation dimension was capable of analyzing signals with chaos levels of less than or equal to 0.0179. Spectrum convergence ratio demonstrated proficiency in analyzing voice signals with all chaos levels investigated in this study. The results of this study corroborate the performance relationships observed in previous studies and, therefore, demonstrate the validity of the validation test method. The presented chaos level validation test could be broadly utilized to evaluate acoustic analysis methods and establish the most appropriate methodology for objective voice analysis in clinical practice.

Method of phase space beam dilution utilizing bounded chaos generated by rf phase modulation

DOE PAGES

Pham, Alfonse N.; Lee, S. Y.; Ng, K. Y.

2015-12-10

This paper explores the physics of chaos in a localized phase-space region produced by rf phase modulation applied to a double rf system. The study can be exploited to produce rapid particle bunch broadening exhibiting longitudinal particle distribution uniformity. Hamiltonian models and particle-tracking simulations are introduced to understand the mechanism and applicability of controlled particle diffusion. When phase modulation is applied to the double rf system, regions of localized chaos are produced through the disruption and overlapping of parametric resonant islands and configured to be bounded by well-behaved invariant tori to prevent particle loss. The condition of chaoticity and themore » degree of particle dilution can be controlled by the rf parameters. As a result, the method has applications in alleviating adverse space-charge effects in high-intensity beams, particle bunch distribution uniformization, and industrial radiation-effects experiments.« less

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

Impulse-induced localized control of chaos in starlike networks.

PubMed

Chacón, Ricardo; Palmero, Faustino; Cuevas-Maraver, Jesús

2016-06-01

Locally decreasing the impulse transmitted by periodic pulses is shown to be a reliable method of taming chaos in starlike networks of dissipative nonlinear oscillators, leading to both synchronous periodic states and equilibria (oscillation death). Specifically, the paradigmatic model of damped kicked rotators is studied in which it is assumed that when the rotators are driven synchronously, i.e., all driving pulses transmit the same impulse, the networks display chaotic dynamics. It is found that the taming effect of decreasing the impulse transmitted by the pulses acting on particular nodes strongly depends on their number and degree of connectivity. A theoretical analysis is given explaining the basic physical mechanism as well as the main features of the chaos-control scenario.

Family CHAOS is associated with glycaemic control in children and adolescents with type 1 diabetes mellitus.

PubMed

Chae, M; Taylor, B J; Lawrence, J; Healey, D; Reith, D M; Gray, A; Wheeler, B J

2016-02-01

Despite advances in the medical management of type 1 diabetes mellitus (T1DM), for many, glycaemic control remains substandard. Other factors are clearly important in determining success, or lack thereof, with diabetes management. With this in mind, we have investigated whether family CHAOS may provide a novel tool to identify when environmental confusion could impact on diabetes management and subsequent glycaemic control. A case-control study of children and adolescents with established T1DM and age-/sex-matched controls was conducted. Demographic information, both maternal and paternal CHAOS scores, and HbA1c were collected. Statistical analysis was undertaken to explore associations between T1DM and CHAOS and between CHAOS and HbA1c. Data on 65 children with T1DM and 60 age-/sex-matched controls were obtained. There was no evidence of group differences for maternal CHAOS (p = 0.227), but paternal CHAOS scores were higher for the T1DM group (p = 0.041). Greater maternal and paternal CHAOS scores were both associated with higher HbA1c (p ≤ 0.027). The maternal association remained after controlling for diabetes duration, SMBG frequency, and insulin therapy. In children with T1DM, there appears to be a negative association between increased environmental confusion, as rated by CHAOS, and glycaemic control. In addition, when compared to controls, fathers of children and adolescents with T1DM appear to experience CHAOS differently to mothers. These findings contribute to the growing body of literature exploring psychosocial factors in T1DM. Continuing efforts are required to fully understand how the family and psychosocial environment interact with diabetes to impact on long-term health outcomes.

Control design and robustness analysis of a ball and plate system by using polynomial chaos

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

Colón, Diego; Balthazar, José M.; Reis, Célia A. dos

2014-12-10

In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinearmore » closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.« less

Control design and robustness analysis of a ball and plate system by using polynomial chaos

NASA Astrophysics Data System (ADS)

Colón, Diego; Balthazar, José M.; dos Reis, Célia A.; Bueno, Átila M.; Diniz, Ivando S.; de S. R. F. Rosa, Suelia

2014-12-01

In this paper, we present a mathematical model of a ball and plate system, a control law and analyze its robustness properties by using the polynomial chaos method. The ball rolls without slipping. There is an auxiliary robot vision system that determines the bodies' positions and velocities, and is used for control purposes. The actuators are to orthogonal DC motors, that changes the plate's angles with the ground. The model is a extension of the ball and beam system and is highly nonlinear. The system is decoupled in two independent equations for coordinates x and y. Finally, the resulting nonlinear closed loop systems are analyzed by the polynomial chaos methodology, which considers that some system parameters are random variables, and generates statistical data that can be used in the robustness analysis.

Impulsive control of stochastic systems with applications in chaos control, chaos synchronization, and neural networks.

PubMed

Li, Chunguang; Chen, Luonan; Aihara, Kazuyuki

2008-06-01

Real systems are often subject to both noise perturbations and impulsive effects. In this paper, we study the stability and stabilization of systems with both noise perturbations and impulsive effects. In other words, we generalize the impulsive control theory from the deterministic case to the stochastic case. The method is based on extending the comparison method to the stochastic case. The method presented in this paper is general and easy to apply. Theoretical results on both stability in the pth mean and stability with disturbance attenuation are derived. To show the effectiveness of the basic theory, we apply it to the impulsive control and synchronization of chaotic systems with noise perturbations, and to the stability of impulsive stochastic neural networks. Several numerical examples are also presented to verify the theoretical results.

Bioengineering Spin-Offs from Dynamical Systems Theory

NASA Astrophysics Data System (ADS)

Collins, J. J.

1997-03-01

Recently, there has been considerable interest in applying concepts and techniques from dynamical systems and statistical physics to physiological systems. In this talk, we present work dealing which two active topics in this area: stochastic resonance and (2) chaos control. Stochastic resonance is a phenomenon wherein the response of nonlinear system to a weak input signal is optimally enhanced by the presence of a particular level of noise. Here we demonstrate that noise-based techniques can be used to lower sensory detection thresholds in humans. We discuss how from a bioengineering and clinical standpoint, these developments may be particularly relevant for individuals with elevated sensory thresholds, such as older adults and patients with peripheral neuropathy. Chaos control techniques have been applied to a wide range of experimental systems, including biological preparations. The application of chaos control to biological systems has led to speculations that these methods may be clinically useful. Here we demonstrate that the principles of chaos control can be utilized to stabilize underlying unstable periodic orbits in non-chaotic biological systems. We discuss how from a bioengineering and clinical standpoint, these developments may be important for suppressing or eliminating certain types of cardiac arrhythmias.

Chaos control of Hastings-Powell model by combining chaotic motions.

PubMed

Danca, Marius-F; Chattopadhyay, Joydev

2016-04-01

In this paper, we propose a Parameter Switching (PS) algorithm as a new chaos control method for the Hastings-Powell (HP) system. The PS algorithm is a convergent scheme that switches the control parameter within a set of values while the controlled system is numerically integrated. The attractor obtained with the PS algorithm matches the attractor obtained by integrating the system with the parameter replaced by the averaged value of the switched parameter values. The switching rule can be applied periodically or randomly over a set of given values. In this way, every stable cycle of the HP system can be approximated if its underlying parameter value equalizes the average value of the switching values. Moreover, the PS algorithm can be viewed as a generalization of Parrondo's game, which is applied for the first time to the HP system, by showing that losing strategy can win: "losing + losing = winning." If "loosing" is replaced with "chaos" and, "winning" with "order" (as the opposite to "chaos"), then by switching the parameter value in the HP system within two values, which generate chaotic motions, the PS algorithm can approximate a stable cycle so that symbolically one can write "chaos + chaos = regular." Also, by considering a different parameter control, new complex dynamics of the HP model are revealed.

Investigation of chaos and its control in a Duffing-type nano beam model

NASA Astrophysics Data System (ADS)

Jha, Abhishek Kumar; Dasgupta, Sovan Sundar

2018-04-01

The prediction of chaos of a nano beam with harmonic excitation is investigated. Using the Galerkin method the nonlinear lumped model of a clamped-clamped nano beam with nonlinear cubic stiffness is obtained. This is a Duffing system with hardening type of nonlinearity. Based on the energy function and the phase portrait of the system, the resonator dynamics is categorized into four situations in which Using Malnikov function, an analytical criterion for homoclinic intersection in the form of inequality is written in terms of the system parameters. A numerical study including largest lyapunov exponent, Poincare diagram and phase portrait confirm the analytical prediction of chaos and effect of forcing amplitude. Subsequently, a linear velocity feedback controller is introduced into the system to successfully control the chaotic motion of the system at a faster rate at larger value of gain parameter.

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

Designing torus-doubling solutions to discrete time systems by hybrid projective synchronization

NASA Astrophysics Data System (ADS)

Xie, Hui; Wen, Guilin

2013-11-01

Doubling of torus occurs in high dimensional nonlinear systems, which is related to a certain kind of typical second bifurcations. It is a nontrivial task to create a torus-doubling solution with desired dynamical properties based on the classical bifurcation theories. In this paper, dead-beat hybrid projective synchronization is employed to build a novel method for designing stable torus-doubling solutions into discrete time systems with proper properties to achieve the purpose of utilizing bifurcation solutions as well as avoiding the possible conflict of physical meaning of the created solution. Although anti-controls of bifurcation and chaos synchronizations are two different topics in nonlinear dynamics and control, the results imply that it is possible to develop some new interdisciplinary methods between chaos synchronization and anti-controls of bifurcations.

Chaos control applied to cardiac rhythms represented by ECG signals

NASA Astrophysics Data System (ADS)

Borem Ferreira, Bianca; Amorim Savi, Marcelo; Souza de Paula, Aline

2014-10-01

The control of irregular or chaotic heartbeats is a key issue in cardiology. In this regard, chaos control techniques represent a good alternative since they suggest treatments different from those traditionally used. This paper deals with the application of the extended time-delayed feedback control method to stabilize pathological chaotic heart rhythms. Electrocardiogram (ECG) signals are employed to represent the cardiovascular behavior. A mathematical model is employed to generate ECG signals using three modified Van der Pol oscillators connected with time delay couplings. This model provides results that qualitatively capture the general behavior of the heart. Controlled ECG signals show the ability of the strategy either to control or to suppress the chaotic heart dynamics generating less-critical behaviors.

Specifying the Links Between Household Chaos and Preschool Children’s Development

PubMed Central

Martin, Anne; Razza, Rachel; Brooks-Gunn, Jeanne

2011-01-01

Household chaos has been linked to poorer cognitive, behavioral, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family instability, lack of routine, and television usually on. Chaos was measured at age 2; outcomes measured at age 5 tap receptive vocabulary, attention and behavior problems, and effortful control. Results show that controlling for all other measures of chaos, children with a lack of routine scored lower on receptive vocabulary and delayed gratification, while children whose television was generally on scored higher on aggression and attention problems. The provision of learning materials mediated a small part of the association between television and receptive vocabulary. Family instability, crowding, and noise did not predict any outcomes once other measures of chaos were controlled. PMID:22919120

Applied Chaos Level Test for Validation of Signal Conditions Underlying Optimal Performance of Voice Classification Methods

ERIC Educational Resources Information Center

Liu, Boquan; Polce, Evan; Sprott, Julien C.; Jiang, Jack J.

2018-01-01

Purpose: The purpose of this study is to introduce a chaos level test to evaluate linear and nonlinear voice type classification method performances under varying signal chaos conditions without subjective impression. Study Design: Voice signals were constructed with differing degrees of noise to model signal chaos. Within each noise power, 100…

Chaos control and synchronization in Bragg acousto-optic bistable systems driven by a separate chaotic system.

PubMed

Wang, Rong; Gao, Jin-Yue

2005-09-01

In this paper we propose a new scheme to achieve chaos control and synchronization in Bragg acousto-optic bistable systems. In the scheme, we use the output of one system to drive two identical chaotic systems. Using the maximal conditional Lyapunov exponent (MCLE) as the criterion, we analyze the conditions for realizing chaos synchronization. Numerical calculation shows that the two identical systems in chaos with negative MCLEs and driven by a chaotic system can go into chaotic synchronization whether or not they were in chaos initially. The two systems can go into different periodic states from chaos following an inverse period-doubling bifurcation route as well when driven by a periodic system.

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.

!CHAOS: A cloud of controls

NASA Astrophysics Data System (ADS)

Angius, S.; Bisegni, C.; Ciuffetti, P.; Di Pirro, G.; Foggetta, L. G.; Galletti, F.; Gargana, R.; Gioscio, E.; Maselli, D.; Mazzitelli, G.; Michelotti, A.; Orrù, R.; Pistoni, M.; Spagnoli, F.; Spigone, D.; Stecchi, A.; Tonto, T.; Tota, M. A.; Catani, L.; Di Giulio, C.; Salina, G.; Buzzi, P.; Checcucci, B.; Lubrano, P.; Piccini, M.; Fattibene, E.; Michelotto, M.; Cavallaro, S. R.; Diana, B. F.; Enrico, F.; Pulvirenti, S.

2016-01-01

The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of aaabstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.

Chaos based video encryption using maps and Ikeda time delay system

NASA Astrophysics Data System (ADS)

Valli, D.; Ganesan, K.

2017-12-01

Chaos based cryptosystems are an efficient method to deal with improved speed and highly secured multimedia encryption because of its elegant features, such as randomness, mixing, ergodicity, sensitivity to initial conditions and control parameters. In this paper, two chaos based cryptosystems are proposed: one is the higher-dimensional 12D chaotic map and the other is based on the Ikeda delay differential equation (DDE) suitable for designing a real-time secure symmetric video encryption scheme. These encryption schemes employ a substitution box (S-box) to diffuse the relationship between pixels of plain video and cipher video along with the diffusion of current input pixel with the previous cipher pixel, called cipher block chaining (CBC). The proposed method enhances the robustness against statistical, differential and chosen/known plain text attacks. Detailed analysis is carried out in this paper to demonstrate the security and uniqueness of the proposed scheme.

Robust pre-specified time synchronization of chaotic systems by employing time-varying switching surfaces in the sliding mode control scheme

NASA Astrophysics Data System (ADS)

Khanzadeh, Alireza; Pourgholi, Mahdi

2016-08-01

In the conventional chaos synchronization methods, the time at which two chaotic systems are synchronized, is usually unknown and depends on initial conditions. In this work based on Lyapunov stability theory a sliding mode controller with time-varying switching surfaces is proposed to achieve chaos synchronization at a pre-specified time for the first time. The proposed controller is able to synchronize chaotic systems precisely at any time when we want. Moreover, by choosing the time-varying switching surfaces in a way that the reaching phase is eliminated, the synchronization becomes robust to uncertainties and exogenous disturbances. Simulation results are presented to show the effectiveness of the proposed method of stabilizing and synchronizing chaotic systems with complete robustness to uncertainty and disturbances exactly at a pre-specified time.

Finding Order and Direction from Chaos: A Comparison of Chaos Career Counseling and Trait Matching Counseling

ERIC Educational Resources Information Center

McKay, Hannah; Bright, Jim E. H.; Pryor, Robert G. L.

2005-01-01

Chaos career counseling, based on the Chaos Theory of Careers (R. G. L. Pryor & J. E. H. Bright, 2003a, 2003b), was compared with trait matching career counseling and a wait list control. Sixty university students who attended the Careers Research and Assessment Service seeking career advice were randomly assigned to the chaos intervention, the…

Dynamic video encryption algorithm for H.264/AVC based on a spatiotemporal chaos system.

PubMed

Xu, Hui; Tong, Xiao-Jun; Zhang, Miao; Wang, Zhu; Li, Ling-Hao

2016-06-01

Video encryption schemes mostly employ the selective encryption method to encrypt parts of important and sensitive video information, aiming to ensure the real-time performance and encryption efficiency. The classic block cipher is not applicable to video encryption due to the high computational overhead. In this paper, we propose the encryption selection control module to encrypt video syntax elements dynamically which is controlled by the chaotic pseudorandom sequence. A novel spatiotemporal chaos system and binarization method is used to generate a key stream for encrypting the chosen syntax elements. The proposed scheme enhances the resistance against attacks through the dynamic encryption process and high-security stream cipher. Experimental results show that the proposed method exhibits high security and high efficiency with little effect on the compression ratio and time cost.

Quantitative Research Methods in Chaos and Complexity: From Probability to Post Hoc Regression Analyses

ERIC Educational Resources Information Center

Gilstrap, Donald L.

2013-01-01

In addition to qualitative methods presented in chaos and complexity theories in educational research, this article addresses quantitative methods that may show potential for future research studies. Although much in the social and behavioral sciences literature has focused on computer simulations, this article explores current chaos and…

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

Exploiting chaos for applications.

PubMed

Ditto, William L; Sinha, Sudeshna

2015-09-01

We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.

Phase Control in Nonlinear Systems

NASA Astrophysics Data System (ADS)

Zambrano, Samuel; Seoane, Jesús M.; Mariño, Inés P.; Sanjuán, Miguel A. F.; Meucci, Riccardo

The following sections are included: * Introduction * Phase Control of Chaos * Description of the model * Numerical exploration of phase control of chaos * Experimental evidence of phase control of chaos * Phase Control of Intermittency in Dynamical Systems * Crisis-induced intermittency and its control * Experimental setup and implementation of the phase control scheme * Phase control of the laser in the pre-crisis regime * Phase control of the intermittency after the crisis * Phase control of the intermittency in the quadratic map * Phase Control of Escapes in Open Dynamical Systems * Control of open dynamical systems * Model description * Numerical simulations and heuristic arguments * Experimental implementation in an electronic circuit * Conclusions and Discussions * Acknowledgments * References

Geometric method for forming periodic orbits in the Lorenz system

NASA Astrophysics Data System (ADS)

Nicholson, S. B.; Kim, Eun-jin

2016-04-01

Many systems in nature are out of equilibrium and irreversible. The non-detailed balance observable representation (NOR) provides a useful methodology for understanding the evolution of such non-equilibrium complex systems, by mapping out the correlation between two states to a metric space where a small distance represents a strong correlation [1]. In this paper, we present the first application of the NOR to a continuous system and demonstrate its utility in controlling chaos. Specifically, we consider the evolution of a continuous system governed by the Lorenz equation and calculate the NOR by following a sufficient number of trajectories. We then show how to control chaos by converting chaotic orbits to periodic orbits by utilizing the NOR. We further discuss the implications of our method for potential applications given the key advantage that this method makes no assumptions of the underlying equations of motion and is thus extremely general.

Household chaos and family sleep during infants' first year.

PubMed

Whitesell, Corey J; Crosby, Brian; Anders, Thomas F; Teti, Douglas M

2018-05-21

Household chaos has been linked with dysregulated family and individual processes. The present study investigated linkages between household chaos and infant and parent sleep, a self-regulated process impacted by individual, social, and environmental factors. Studies of relations between household chaos and child sleep have focused on older children and teenagers, with little attention given to infants or parent sleep. This study examines these relationships using objective measures of household chaos and sleep while controlling for, respectively, maternal emotional availability at bedtime and martial adjustment, in infant and parent sleep. Multilevel modeling examined mean and variability of sleep duration and fragmentation for infants, mothers, and fathers when infants were 1, 3, 6, 9, and 12 months (N = 167). Results indicated infants in higher chaos homes experienced delays in sleep consolidation patterns, with longer and more variable sleep duration, and greater fragmentation. Parent sleep was also associated with household chaos such that in higher chaos homes, mothers and fathers experienced greater variability in sleep duration, which paralleled infant findings. In lower chaos homes, parents' sleep fragmentation mirrored infants' decreasingly fragmented sleep across the first year and remained lower at all timepoints compared to parents and infants in high chaos homes. Collectively, these findings indicate that after controlling for maternal emotional availability and marital adjustment (respectively) household chaos has a dysregulatory impact on infant and parent sleep. Results are discussed in terms of the potential for chaos-induced poor sleep to dysregulate daytime functioning and, in turn, place parent-infant relationships at risk. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Observation and Control of Hamiltonian Chaos in Wave-particle Interaction

NASA Astrophysics Data System (ADS)

Doveil, F.; Elskens, Y.; Ruzzon, A.

2010-11-01

Wave-particle interactions are central in plasma physics. The paradigm beam-plasma system can be advantageously replaced by a traveling wave tube (TWT) to allow their study in a much less noisy environment. This led to detailed analysis of the self-consistent interaction between unstable waves and an either cold or warm electron beam. More recently a test cold beam has been used to observe its interaction with externally excited wave(s). This allowed observing the main features of Hamiltonian chaos and testing a new method to efficiently channel chaotic transport in phase space. To simulate accurately and efficiently the particle dynamics in the TWT and other 1D particle-wave systems, a new symplectic, symmetric, second order numerical algorithm is developed, using particle position as the independent variable, with a fixed spatial step. This contribution reviews : presentation of the TWT and its connection to plasma physics, resonant interaction of a charged particle in electrostatic waves, observation of particle trapping and transition to chaos, test of control of chaos, and description of the simulation algorithm. The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the 4m long helix of the TWT. The nonlinear synchronization of particles by a single wave, responsible for Landau damping, is observed. We explore the resonant velocity domain associated with a single wave as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a devil's staircase behavior when increasing the excitation level in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport in phase space as well as its robustness is successfully tested. The underlying concepts extend far beyond the field of electron devices and plasma physics.

Chaos control of the brushless direct current motor using adaptive dynamic surface control based on neural network with the minimum weights.

PubMed

Luo, Shaohua; Wu, Songli; Gao, Ruizhen

2015-07-01

This paper investigates chaos control for the brushless DC motor (BLDCM) system by adaptive dynamic surface approach based on neural network with the minimum weights. The BLDCM system contains parameter perturbation, chaotic behavior, and uncertainty. With the help of radial basis function (RBF) neural network to approximate the unknown nonlinear functions, the adaptive law is established to overcome uncertainty of the control gain. By introducing the RBF neural network and adaptive technology into the dynamic surface control design, a robust chaos control scheme is developed. It is proved that the proposed control approach can guarantee that all signals in the closed-loop system are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Simulation results are provided to show that the proposed approach works well in suppressing chaos and parameter perturbation.

Chaos control of the brushless direct current motor using adaptive dynamic surface control based on neural network with the minimum weights

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

Luo, Shaohua; Department of Mechanical Engineering, Chongqing Aerospace Polytechnic, Chongqing, 400021; Wu, Songli

2015-07-15

This paper investigates chaos control for the brushless DC motor (BLDCM) system by adaptive dynamic surface approach based on neural network with the minimum weights. The BLDCM system contains parameter perturbation, chaotic behavior, and uncertainty. With the help of radial basis function (RBF) neural network to approximate the unknown nonlinear functions, the adaptive law is established to overcome uncertainty of the control gain. By introducing the RBF neural network and adaptive technology into the dynamic surface control design, a robust chaos control scheme is developed. It is proved that the proposed control approach can guarantee that all signals in themore » closed-loop system are globally uniformly bounded, and the tracking error converges to a small neighborhood of the origin. Simulation results are provided to show that the proposed approach works well in suppressing chaos and parameter perturbation.« less

Detecting nonlinearity and chaos in epidemic data

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

Ellner, S.; Gallant, A.R.; Theiler, J.

1993-08-01

Historical data on recurrent epidemics have been central to the debate about the prevalence of chaos in biological population dynamics. Schaffer and Kot who first recognized that the abundance and accuracy of disease incidence data opened the door to applying a range of methods for detecting chaos that had been devised in the early 1980`s. Using attractor reconstruction, estimates of dynamical invariants, and comparisons between data and simulation of SEIR models, the ``case for chaos in childhood epidemics`` was made through a series of influential papers beginning in the mid 1980`s. The proposition that the precise timing and magnitude ofmore » epidemic outbreaks are deterministic but chaotic is appealing, since it raises the hope of finding determinism and simplicity beneath the apparently stochastic and complicated surface of the data. The initial enthusiasm for methods of detecting chaos in data has been followed by critical re-evaluations of their limitations. Early hopes of a ``one size fits all`` algorithm to diagnose chaos vs. noise in any data set have given way to a recognition that a variety of methods must be used, and interpretation of results must take into account the limitations of each method and the imperfections of the data. Our goals here are to outline some newer methods for detecting nonlinearity and chaos that have a solid statistical basis and are suited to epidemic data, and to begin a re-evaluation of the claims for nonlinear dynamics and chaos in epidemics using these newer methods. We also identify features of epidemic data that create problems for the older, better known methods of detecting chaos. When we ask ``are epidemics nonlinear?``, we are not questioning the existence of global nonlinearities in epidemic dynamics, such as nonlinear transmission rates. Our question is whether the data`s deviations from an annual cyclic trend (which would reflect global nonlinearities) are described by a linear, noise-driven stochastic process.« less

Household Chaos--Links with Parenting and Child Behaviour

ERIC Educational Resources Information Center

Coldwell, Joanne; Pike, Alison; Dunn, Judy

2006-01-01

Background: The study aimed to confirm previous findings showing links between household chaos and parenting in addition to examining whether household chaos was predictive of children's behaviour over and above parenting. In addition, we investigated whether household chaos acts as a moderator between parenting and children's behaviour. Method:…

Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model

NASA Astrophysics Data System (ADS)

Ren, Jingli; Yu, Liping

2016-12-01

In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.

Comparison Between Terrestrial Explosion Crater Morphology in Floating Ice and Europan Chaos

NASA Technical Reports Server (NTRS)

Billings, S. E.; Kattenhorn, S. A.

2003-01-01

Craters created by explosives have been found to serve as valuable analogs to impact craters, within limits. Explosion craters have been created in floating terrestrial ice in experiments related to clearing ice from waterways. Features called chaos occur on the surface of Europa s floating ice shell. Chaos is defined as a region in which the background plains have been disrupted. Common features of chaos include rafted blocks of pre-existing terrain suspended in a matrix of smooth or hummocky material; low surface albedo; and structural control on chaos outline shape by pre-existing lineaments. All published models of chaos formation call on endogenic processes whereby chaos forms through thermal processes. Nonetheless, we note morphological similarities between terrestrial explosion craters and Europan chaos at a range of scales and consider whether some chaos may have formed by impact. We explore these similarities through geologic and morphologic mapping.

Chaos minimization in DC-DC boost converter using circuit parameter optimization

NASA Astrophysics Data System (ADS)

Sudhakar, N.; Natarajan, Rajasekar; Gourav, Kumar; Padmavathi, P.

2017-11-01

DC-DC converters are prone to several types of nonlinear phenomena including bifurcation, quasi periodicity, intermittency and chaos. These undesirable effects must be controlled for periodic operation of the converter to ensure the stability. In this paper an effective solution to control of chaos in solar fed DC-DC boost converter is proposed. Controlling of chaos is significantly achieved using optimal circuit parameters obtained through Bacterial Foraging Optimization Algorithm. The optimization renders the suitable parameters in minimum computational time. The obtained results are compared with the operation of traditional boost converter. Further the obtained results with BFA optimized parameter ensures the operations of the converter are within the controllable region. To elaborate the study of bifurcation analysis with optimized and unoptimized parameters are also presented.

Complexity and chaos control in a discrete-time prey-predator model

NASA Astrophysics Data System (ADS)

Din, Qamar

2017-08-01

We investigate the complex behavior and chaos control in a discrete-time prey-predator model. Taking into account the Leslie-Gower prey-predator model, we propose a discrete-time prey-predator system with predator partially dependent on prey and investigate the boundedness, existence and uniqueness of positive equilibrium and bifurcation analysis of the system by using center manifold theorem and bifurcation theory. Various feedback control strategies are implemented for controlling the bifurcation and chaos in the system. Numerical simulations are provided to illustrate theoretical discussion.

Chaotic dynamics in nonlinear duopoly Stackelberg game with heterogeneous players

NASA Astrophysics Data System (ADS)

Xiao, Yue; Peng, Yu; Lu, Qian; Wu, Xue

2018-02-01

In this paper, a nonlinear duopoly Stackelberg game of competition on output is concerned. In consideration of the effects of difference between plan products and actual products, the two heterogeneous players always adopt suitable strategies which can improve their benefits most. In general, status of each firm is unequal. As the firms take strategies sequentially and produce simultaneously, complex behaviors are brought about. Numerical simulation presents period doubling bifurcation, maximal Lyapunov exponent and chaos. Moreover, an appropriate method of chaos controlling is applied and fractal dimension is analyzed as well.

Planning in Higher Education and Chaos Theory: A Model, a Method.

ERIC Educational Resources Information Center

Cutright, Marc

This paper proposes a model, based on chaos theory, that explores strategic planning in higher education. It notes that chaos theory was first developed in the physical sciences to explain how apparently random activity was, in fact, complexity patterned. The paper goes on to describe how chaos theory has subsequently been applied to the social…

Stochastic Estimation via Polynomial Chaos

DTIC Science & Technology

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Control of collective network chaos.

PubMed

Wagemakers, Alexandre; Barreto, Ernest; Sanjuán, Miguel A F; So, Paul

2014-06-01

Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of "reduced" ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity.

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

Luo, Shaohua; School of Automation, Chongqing University, Chongqing 400044; Sun, Quanping

This paper addresses chaos control of the micro-electro- mechanical resonator by using adaptive dynamic surface technology with extended state observer. To reveal the mechanism of the micro- electro-mechanical resonator, the phase diagrams and corresponding time histories are given to research the nonlinear dynamics and chaotic behavior, and Homoclinic and heteroclinic chaos which relate closely with the appearance of chaos are presented based on the potential function. To eliminate the effect of chaos, an adaptive dynamic surface control scheme with extended state observer is designed to convert random motion into regular motion without precise system model parameters and measured variables. Puttingmore » tracking differentiator into chaos controller solves the ‘explosion of complexity’ of backstepping and poor precision of the first-order filters. Meanwhile, to obtain high performance, a neural network with adaptive law is employed to approximate unknown nonlinear function in the process of controller design. The boundedness of all the signals of the closed-loop system is proved in theoretical analysis. Finally, numerical simulations are executed and extensive results illustrate effectiveness and robustness of the proposed scheme.« less

The design and research of anti-color-noise chaos M-ary communication system

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

Fu, Yongqing, E-mail: fuyongqing@hrbeu.edu.cn; Li, Xingyuan; Li, Yanan

Previously a novel chaos M-ary digital communication method based on spatiotemporal chaos Hamilton oscillator has been proposed. Without chaos synchronization circumstance, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-white-noise performance compared with traditional communication method. In this paper, the channel noise influence on chaotic modulation signals and the construction problem of anti-color-noise chaotic M-ary communication system are studied. The formula of zone partition demodulator’s boundary in additive white Gaussian noise is derived, besides, the problem about how to determine the boundary of zone partition demodulator in additive color noise is deeply studied; Then an approach on constructingmore » anti-color-noise chaos M-ary communication system is proposed, in which a pre-distortion filter is added after the chaos baseband modulator in the transmitter and whitening filter is added before zone partition demodulator in the receiver. Finally, the chaos M-ary communication system based on Hamilton oscillator is constructed and simulated in different channel noise. The result shows that the proposed method in this paper can improve the anti-color-noise performance of the whole communication system compared with the former system, and it has better anti-fading and resisting disturbance performance than Quadrature Phase Shift Keying system.« less

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 method for parameter estimation in nonlinear dynamical equations

NASA Astrophysics Data System (ADS)

Wang, Liu; He, Wen-Ping; Liao, Le-Jian; Wan, Shi-Quan; He, Tao

2015-01-01

Parameter estimation is an important scientific problem in various fields such as chaos control, chaos synchronization and other mathematical models. In this paper, a new method for parameter estimation in nonlinear dynamical equations is proposed based on evolutionary modelling (EM). This will be achieved by utilizing the following characteristics of EM which includes self-organizing, adaptive and self-learning features which are inspired by biological natural selection, and mutation and genetic inheritance. The performance of the new method is demonstrated by using various numerical tests on the classic chaos model—Lorenz equation (Lorenz 1963). The results indicate that the new method can be used for fast and effective parameter estimation irrespective of whether partial parameters or all parameters are unknown in the Lorenz equation. Moreover, the new method has a good convergence rate. Noises are inevitable in observational data. The influence of observational noises on the performance of the presented method has been investigated. The results indicate that the strong noises, such as signal noise ratio (SNR) of 10 dB, have a larger influence on parameter estimation than the relatively weak noises. However, it is found that the precision of the parameter estimation remains acceptable for the relatively weak noises, e.g. SNR is 20 or 30 dB. It indicates that the presented method also has some anti-noise performance.

Chaos control in delayed phase space constructed by the Takens embedding theory

NASA Astrophysics Data System (ADS)

Hajiloo, R.; Salarieh, H.; Alasty, A.

2018-01-01

In this paper, the problem of chaos control in discrete-time chaotic systems with unknown governing equations and limited measurable states is investigated. Using the time-series of only one measurable state, an algorithm is proposed to stabilize unstable fixed points. The approach consists of three steps: first, using Takens embedding theory, a delayed phase space preserving the topological characteristics of the unknown system is reconstructed. Second, a dynamic model is identified by recursive least squares method to estimate the time-series data in the delayed phase space. Finally, based on the reconstructed model, an appropriate linear delayed feedback controller is obtained for stabilizing unstable fixed points of the system. Controller gains are computed using a systematic approach. The effectiveness of the proposed algorithm is examined by applying it to the generalized hyperchaotic Henon system, prey-predator population map, and the discrete-time Lorenz system.

Collision analysis of one kind of chaos-based hash function

NASA Astrophysics Data System (ADS)

Xiao, Di; Peng, Wenbing; Liao, Xiaofeng; Xiang, Tao

2010-02-01

In the last decade, various chaos-based hash functions have been proposed. Nevertheless, the corresponding analyses of them lag far behind. In this Letter, we firstly take a chaos-based hash function proposed very recently in Amin, Faragallah and Abd El-Latif (2009) [11] as a sample to analyze its computational collision problem, and then generalize the construction method of one kind of chaos-based hash function and summarize some attentions to avoid the collision problem. It is beneficial to the hash function design based on chaos in the future.

Multiple period-doubling bifurcation route to chaos in periodically pulsed Murali-Lakshmanan-Chua circuit-controlling and synchronization of chaos.

PubMed

Parthasarathy, S; Manikandakumar, K

2007-12-01

We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system.

Chaos control by electric current in an enzymatic reaction.

PubMed

Lekebusch, A; Förster, A; Schneider, F W

1996-09-01

We apply the continuous delayed feedback method of Pyragas to control chaos in the enzymatic Peroxidase-Oxidase (PO) reaction, using the electric current as the control parameter. At each data point in the time series, a time delayed feedback function applies a small amplitude perturbation to inert platinum electrodes, which causes redox processes on the surface of the electrodes. These perturbations are calculated as the difference between the previous (time delayed) signal and the actual signal. Unstable periodic P1, 1(1), and 1(2) orbits (UPOs) were stabilized in the CSTR (continuous stirred tank reactor) experiments. The stabilization is demonstrated by at least three conditions: A minimum in the experimental dispersion function, the equality of the delay time with the period of the stabilized attractor and the embedment of the stabilized periodic attractor in the chaotic attractor.

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.

Melnikov's criteria, parametric control of chaos, and stationary chaos occurrence in systems with asymmetric potential subjected to multiscale type excitation.

PubMed

Kwuimy, C A Kitio; Nataraj, C; Litak, G

2011-12-01

We consider the problems of chaos and parametric control in nonlinear systems under an asymmetric potential subjected to a multiscale type excitation. The lower bound line for horseshoes chaos is analyzed using the Melnikov's criterion for a transition to permanent or transient nonperiodic motions, complement by the fractal or regular shape of the basin of attraction. Numerical simulations based on the basins of attraction, bifurcation diagrams, Poincaré sections, Lyapunov exponents, and phase portraits are used to show how stationary dissipative chaos occurs in the system. Our attention is focussed on the effects of the asymmetric potential term and the driven frequency. It is shown that the threshold amplitude ∣γ(c)∣ of the excitation decreases for small values of the driven frequency ω and increases for large values of ω. This threshold value decreases with the asymmetric parameter α and becomes constant for sufficiently large values of α. γ(c) has its maximum value for asymmetric load in comparison with the symmetric load. Finally, we apply the Melnikov theorem to the controlled system to explore the gain control parameter dependencies.

Structural stability and chaotic solutions of perturbed Benjamin-Ono equations

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

Birnir, B.; Morrison, P.J.

1986-11-01

A method for proving chaos in partial differential equations is discussed and applied to the Benjamin-Ono equation subject to perturbations. The perturbations are of two types: one that corresponds to viscous dissipation, the so-called Burger's term, and one that involves the Hilbert transform and has been used to model Landau damping. The method proves chaos in the PDE by proving temporal chaos in its pole solutions. The spatial structure of the pole solutions remains intact, but their positions are chaotic in time. Melnikov's method is invoked to show this temporal chaos. It is discovered that the pole behavior is verymore » sensitive to the Burger's perturbation, but is quite insensitive to the perturbation involving the Hilbert transform.« less

Control of Chaos: New Perspectives in Experimental and Theoretical Science. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. Theme Issue. Part 1. Volume 8, Number 8, August 1998.

DTIC Science & Technology

1998-08-01

de Matemdticas, Universidad de Murcia, Murcia, Spain RICARDO CHACON Departamento de Electr6nica e, Ingenieria Electromecdnica, Escuela, de... Ingenierias Industriales, Universidad de Extremadura, 06071, Badajoz, Spain MIGUEL ANGEL LOPEZ Departamento de Matemdticas, Aplicada, Escuela Universitaria de...World Scientific Publishing Company FUZZY CONTROL OF CHAOS OSCAR CALVO* CICpBA, L.E.L C.1, Departamento de Electrotecnia, Facultad de Ingenieria

Suppression of chaos via control of energy flow

NASA Astrophysics Data System (ADS)

Guo, Shengli; Ma, Jun; Alsaedi, Ahmed

2018-03-01

Continuous energy supply is critical and important to support oscillating behaviour; otherwise, the oscillator will die. For nonlinear and chaotic circuits, enough energy supply is also important to keep electric devices working. In this paper, Hamilton energy is calculated for dimensionless dynamical system (e.g., the chaotic Lorenz system) using Helmholtz's theorem. The Hamilton energy is considered as a new variable and then the dynamical system is controlled by using the scheme of energy feedback. It is found that chaos can be suppressed even when intermittent feedback scheme is applied. This scheme is effective to control chaos and to stabilise other dynamical systems.

Controlling Mackey-Glass chaos.

PubMed

Kiss, Gábor; Röst, Gergely

2017-11-01

The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

Controlling Mackey-Glass chaos

NASA Astrophysics Data System (ADS)

Kiss, Gábor; Röst, Gergely

2017-11-01

The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

Creation of a magnetic barrier at a noble q close to physical midpoint between two resonant surfaces in the ASDEX UG tokamak

NASA Astrophysics Data System (ADS)

Vazquez, Justin; Ali, Halima; Punjabi, Alkesh

2009-11-01

Ciraolo, Vittot and Chandre method of building invariant manifolds inside chaos in Hamiltonian systems [Ali H. and Punjabi A, Plasma Phys. Control. Fusion, 49, 1565--1582 (2007)] is used in the ASDEX UG tokamak. In this method, a second order perturbation is added to the perturbed Hamiltonian [op cit]. It creates an invariant torus inside the chaos, and reduces the plasma transport. The perturbation that is added to the equilibrium Hamiltonian is at least an order of magnitude smaller than the perturbation that causes chaos. This additional term has a finite, limited number of Fourier modes. Resonant magnetic perturbations (m,n) = (3,2)+(4,3) are added to the field line Hamiltonian for the ASDEX UG. An area-preserving map for the field line trajectories in the ASDEX UG is used. The common amplitude δ of these modes that gives complete chaos between the resonant surfaces ψ43 and ψ32 is determined. A magnetic barrier is built at a surface with noble q that is very nearly equals to the q at the physical midpoint between the two resonant surfaces. The maximum amplitude of magnetic perturbation for which this barrier can be sustained is determined. This work is supported by US Department of Energy grants DE-FG02-07ER54937, DE-FG02-01ER54624 and DE-FG02-04ER54793.

Direct generation of all-optical random numbers from optical pulse amplitude chaos.

PubMed

Li, Pu; Wang, Yun-Cai; Wang, An-Bang; Yang, Ling-Zhen; Zhang, Ming-Jiang; Zhang, Jian-Zhong

2012-02-13

We propose and theoretically demonstrate an all-optical method for directly generating all-optical random numbers from pulse amplitude chaos produced by a mode-locked fiber ring laser. Under an appropriate pump intensity, the mode-locked laser can experience a quasi-periodic route to chaos. Such a chaos consists of a stream of pulses with a fixed repetition frequency but random intensities. In this method, we do not require sampling procedure and external triggered clocks but directly quantize the chaotic pulses stream into random number sequence via an all-optical flip-flop. Moreover, our simulation results show that the pulse amplitude chaos has no periodicity and possesses a highly symmetric distribution of amplitude. Thus, in theory, the obtained random number sequence without post-processing has a high-quality randomness verified by industry-standard statistical tests.

Harnessing quantum transport by transient chaos.

PubMed

Yang, Rui; Huang, Liang; Lai, Ying-Cheng; Grebogi, Celso; Pecora, Louis M

2013-03-01

Chaos has long been recognized to be generally advantageous from the perspective of control. In particular, the infinite number of unstable periodic orbits embedded in a chaotic set and the intrinsically sensitive dependence on initial conditions imply that a chaotic system can be controlled to a desirable state by using small perturbations. Investigation of chaos control, however, was largely limited to nonlinear dynamical systems in the classical realm. In this paper, we show that chaos may be used to modulate or harness quantum mechanical systems. To be concrete, we focus on quantum transport through nanostructures, a problem of considerable interest in nanoscience, where a key feature is conductance fluctuations. We articulate and demonstrate that chaos, more specifically transient chaos, can be effective in modulating the conductance-fluctuation patterns. Experimentally, this can be achieved by applying an external gate voltage in a device of suitable geometry to generate classically inaccessible potential barriers. Adjusting the gate voltage allows the characteristics of the dynamical invariant set responsible for transient chaos to be varied in a desirable manner which, in turn, can induce continuous changes in the statistical characteristics of the quantum conductance-fluctuation pattern. To understand the physical mechanism of our scheme, we develop a theory based on analyzing the spectrum of the generalized non-Hermitian Hamiltonian that includes the effect of leads, or electronic waveguides, as self-energy terms. As the escape rate of the underlying non-attracting chaotic set is increased, the imaginary part of the complex eigenenergy becomes increasingly large so that pointer states are more difficult to form, making smoother the conductance-fluctuation pattern.

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.

A heuristic method for identifying chaos from frequency content.

PubMed

Wiebe, R; Virgin, L N

2012-03-01

The sign of the largest Lyapunov exponent is the fundamental indicator of chaos in a dynamical system. However, although the extraction of Lyapunov exponents can be accomplished with (necessarily noisy) the experimental data, this is still a relatively data-intensive and sensitive endeavor. This paper presents an alternative pragmatic approach to identifying chaos using response frequency characteristics and extending the concept of the spectrogram. The method is shown to work well on both experimental and simulated time series.

Controlling chaos-assisted directed transport via quantum resonance.

PubMed

Tan, Jintao; Zou, Mingliang; Luo, Yunrong; Hai, Wenhua

2016-06-01

We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

Controlling chaos-assisted directed transport via quantum resonance

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

Tan, Jintao; Zou, Mingliang; Luo, Yunrong

2016-06-15

We report on the first demonstration of chaos-assisted directed transport of a quantum particle held in an amplitude-modulated and tilted optical lattice, through a resonance-induced double-mean displacement relating to the true classically chaotic orbits. The transport velocity is controlled by the driving amplitude and the sign of tilt, and also depends on the phase of the initial state. The chaos-assisted transport feature can be verified experimentally by using a source of single atoms to detect the double-mean displacement one by one, and can be extended to different scientific fields.

The Capabilities of Chaos and Complexity

PubMed Central

Abel, David L.

2009-01-01

To what degree could chaos and complexity have organized a Peptide or RNA World of crude yet necessarily integrated protometabolism? How far could such protolife evolve in the absence of a heritable linear digital symbol system that could mutate, instruct, regulate, optimize and maintain metabolic homeostasis? To address these questions, chaos, complexity, self-ordered states, and organization must all be carefully defined and distinguished. In addition their cause-and-effect relationships and mechanisms of action must be delineated. Are there any formal (non physical, abstract, conceptual, algorithmic) components to chaos, complexity, self-ordering and organization, or are they entirely physicodynamic (physical, mass/energy interaction alone)? Chaos and complexity can produce some fascinating self-ordered phenomena. But can spontaneous chaos and complexity steer events and processes toward pragmatic benefit, select function over non function, optimize algorithms, integrate circuits, produce computational halting, organize processes into formal systems, control and regulate existing systems toward greater efficiency? The question is pursued of whether there might be some yet-to-be discovered new law of biology that will elucidate the derivation of prescriptive information and control. “System” will be rigorously defined. Can a low-informational rapid succession of Prigogine’s dissipative structures self-order into bona fide organization? PMID:19333445

Adaptive sliding mode control for a class of chaotic systems

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

Farid, R.; Ibrahim, A.; Zalam, B., E-mail: ramy5475@yahoo.com

2015-03-30

Chaos control here means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, an Adaptive Sliding Mode Controller (ASMC) is presented based on Lyapunov stability theory. The well known Chua's circuit is chosen to be our case study in this paper. The study shows the effectiveness of the proposed adaptive sliding mode controller.

Spreading Chaos: The Role of Popularizations in the Diffusion of Scientific Ideas

ERIC Educational Resources Information Center

Paul, Danette

2004-01-01

Scientific popularizations are generally considered translations (often dubious ones) of scientific research for a lay audience. This study explores the role popularizations play within scientific discourse, specifically in the development of chaos theory. The methods included a review of the popular and the semipopular books on chaos theory from…

Investigation on imperfection sensitivity of composite cylindrical shells using the nonlinearity reduction technique and the polynomial chaos method

NASA Astrophysics Data System (ADS)

Liang, Ke; Sun, Qin; Liu, Xiaoran

2018-05-01

The theoretical buckling load of a perfect cylinder must be reduced by a knock-down factor to account for structural imperfections. The EU project DESICOS proposed a new robust design for imperfection-sensitive composite cylindrical shells using the combination of deterministic and stochastic simulations, however the high computational complexity seriously affects its wider application in aerospace structures design. In this paper, the nonlinearity reduction technique and the polynomial chaos method are implemented into the robust design process, to significantly lower computational costs. The modified Newton-type Koiter-Newton approach which largely reduces the number of degrees of freedom in the nonlinear finite element model, serves as the nonlinear buckling solver to trace the equilibrium paths of geometrically nonlinear structures efficiently. The non-intrusive polynomial chaos method provides the buckling load with an approximate chaos response surface with respect to imperfections and uses buckling solver codes as black boxes. A fast large-sample study can be applied using the approximate chaos response surface to achieve probability characteristics of buckling loads. The performance of the method in terms of reliability, accuracy and computational effort is demonstrated with an unstiffened CFRP cylinder.

Controlling Chaos Via Knowledge of Initial Condition for a Curved Structure

NASA Technical Reports Server (NTRS)

Maestrello, L.

2000-01-01

Nonlinear response of a flexible curved panel exhibiting bifurcation to fully developed chaos is demonstrated along with the sensitivity to small perturbation from the initial conditions. The response is determined from the measured time series at two fixed points. The panel is forced by an external nonharmonic multifrequency and monofrequency sound field. Using a low power time-continuous feedback control, carefully tuned at each initial condition, produces large long-term effects on the dynamics toward taming chaos. Without the knowledge of the initial conditions, control may be achieved by destructive interference. In this case, the control power is proportional to the loading power. Calculation of the correlation dimension and the estimation of positive Lyapunov exponents, in practice, are the proof of chaotic response.

Control of complex dynamics and chaos in distributed parameter systems

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

Chakravarti, S.; Marek, M.; Ray, W.H.

This paper discusses a methodology for controlling complex dynamics and chaos in distributed parameter systems. The reaction-diffusion system with Brusselator kinetics, where the torus-doubling or quasi-periodic (two characteristic incommensurate frequencies) route to chaos exists in a defined range of parameter values, is used as an example. Poincare maps are used for characterization of quasi-periodic and chaotic attractors. The dominant modes or topos, which are inherent properties of the system, are identified by means of the Singular Value Decomposition. Tested modal feedback control schemas based on identified dominant spatial modes confirm the possibility of stabilization of simple quasi-periodic trajectories in themore » complex quasi-periodic or chaotic spatiotemporal patterns.« less

A Green's function method for local and non-local parallel transport in general magnetic fields

NASA Astrophysics Data System (ADS)

Del-Castillo-Negrete, Diego; Chacón, Luis

2009-11-01

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion and astrophysics research. Three issues make this problem particularly challenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), χ, and the perpendicular, χ, conductivities (χ/χ may exceed 10^10 in fusion plasmas); (ii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates; and (iii) Nonlocal parallel transport in the limit of small collisionality. Motivated by these issues, we present a Lagrangian Green's function method to solve the local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields. The numerical implementation employs a volume-preserving field-line integrator [Finn and Chac'on, Phys. Plasmas, 12 (2005)] for an accurate representation of the magnetic field lines regardless of the level of stochasticity. The general formalism and its algorithmic properties are discussed along with illustrative analytical and numerical examples. Problems of particular interest include: the departures from the Rochester--Rosenbluth diffusive scaling in the weak magnetic chaos regime, the interplay between non-locality and chaos, and the robustness of transport barriers in reverse shear configurations.

The Use of Creative Drama with Acting-Out Sixth and Seventh Grade Boys and Girls

ERIC Educational Resources Information Center

Allan, John B.

1977-01-01

Describes development and use of creative drama with 30 children over a six month period. Over time, the dramas evolved through four stages: chaos, control and chaos; control; and flexibility. Certain developmental and psychological themes also emerged: narcissism, exhibitionism, activity, orality, dominance, morality, social themes, comedy and…

Applied Chaos: From Oxymoron to Reality.

NASA Astrophysics Data System (ADS)

Ditto, William

1996-11-01

The rapidly emerging field of chaotic dynamics has presented the applied scientist with intriguing new tools to understand and manipulate systems that behave chaotically. An overview will be presented which will answer the questions: What is Chaos? and What can you do with Chaos? Examples of recent applications of chaos theory to the physical and biological sciences will be presented covering applications that range from encryption in communications to control of chaotically beating human hearts. Part A of program listing

Sensitivity of Chaos Measures in Detecting Stress in the Focusing Control Mechanism of the Short-Sighted Eye.

PubMed

Hampson, Karen M; Cufflin, Matthew P; Mallen, Edward A H

2017-08-01

When fixating on a stationary object, the power of the eye's lens fluctuates. Studies have suggested that changes in these so-called microfluctuations in accommodation may be a factor in the onset and progression of short-sightedness. Like many physiological signals, the fluctuations in the power of the lens exhibit chaotic behaviour. A breakdown or reduction in chaos in physiological systems indicates stress to the system or pathology. The purpose of this study was to determine whether the chaos in fluctuations of the power of the lens changes with refractive error, i.e. how short-sighted a subject is, and/or accommodative demand, i.e. the effective distance of the object that is being viewed. Six emmetropes (EMMs, non-short-sighted), six early-onset myopes (EOMs, onset of short-sightedness before the age of 15), and six late-onset myopes (LOMs, onset of short-sightedness after the age of 15) took part in the study. Accommodative microfluctuations were measured at 22 Hz using an SRW-5000 autorefractor at accommodative demands of 1 D (dioptres), 2 D, and 3 D. Chaos theory analysis was used to determine the embedding lag, embedding dimension, limit of predictability, and Lyapunov exponent. Topological transitivity was also tested for. For comparison, the power spectrum and standard deviation were calculated for each time record. The EMMs had a statistically significant higher Lyapunov exponent than the LOMs ([Formula: see text] vs. [Formula: see text]) and a lower embedding dimension than the LOMs ([Formula: see text] vs. [Formula: see text]). There was insufficient evidence (non-significant p value) of a difference between EOMs and EMMs or EOMs and LOMs. The majority of time records were topologically transitive. There was insufficient evidence of accommodative demand having an effect. Power spectrum analysis and assessment of the standard deviation of the fluctuations failed to discern differences based on refractive error. Chaos differences in accommodation microfluctuations indicate that the control system for LOMs is under stress in comparison to EMMs. Chaos theory analysis is a more sensitive marker of changes in accommodation microfluctuations than traditional analysis methods.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

PubMed

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-10-17

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

PubMed Central

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418

Stochastic chaos induced by diffusion processes with identical spectral density but different probability density functions.

PubMed

Lei, Youming; Zheng, Fan

2016-12-01

Stochastic chaos induced by diffusion processes, with identical spectral density but different probability density functions (PDFs), is investigated in selected lightly damped Hamiltonian systems. The threshold amplitude of diffusion processes for the onset of chaos is derived by using the stochastic Melnikov method together with a mean-square criterion. Two quasi-Hamiltonian systems, namely, a damped single pendulum and damped Duffing oscillator perturbed by stochastic excitations, are used as illustrative examples. Four different cases of stochastic processes are taking as the driving excitations. It is shown that in such two systems the spectral density of diffusion processes completely determines the threshold amplitude for chaos, regardless of the shape of their PDFs, Gaussian or otherwise. Furthermore, the mean top Lyapunov exponent is employed to verify analytical results. The results obtained by numerical simulations are in accordance with the analytical results. This demonstrates that the stochastic Melnikov method is effective in predicting the onset of chaos in the quasi-Hamiltonian systems.

Supervised chaos genetic algorithm based state of charge determination for LiFePO4 batteries in electric vehicles

NASA Astrophysics Data System (ADS)

Shen, Yanqing

2018-04-01

LiFePO4 battery is developed rapidly in electric vehicle, whose safety and functional capabilities are influenced greatly by the evaluation of available cell capacity. Added with adaptive switch mechanism, this paper advances a supervised chaos genetic algorithm based state of charge determination method, where a combined state space model is employed to simulate battery dynamics. The method is validated by the experiment data collected from battery test system. Results indicate that the supervised chaos genetic algorithm based state of charge determination method shows great performance with less computation complexity and is little influenced by the unknown initial cell state.

Chaos as a Social Determinant of Child Health: Reciprocal Associations?

PubMed Central

Schmeer, Kammi K.; Taylor, Miles

2013-01-01

This study informs the social determinants of child health by exploring an understudied aspect of children’s social contexts: chaos. Chaos has been conceptualized as crowded, noisy, disorganized, unpredictable settings for child development (Evans et al., 2010). We measure chaos at two levels of children’s ecological environment - the microsystem (household) and the mesosystem (work-family-child care nexus) – and at two points in early childhood (ages 3 and 5). Using data from the Fragile Families and Child Wellbeing Study (N=3288), a study of predominantly low-income women and their partners in large US cities, we develop structural equation models that assess how maternal-rated child health (also assessed at ages 3 and 5) is associated with latent constructs of chaos, and whether there are important reciprocal effects. Autoregressive crosslagged path analysis suggest that increasing chaos (at both the household and maternal work levels) is associated with worse child health, controlling for key confounders like household economic status, family structure, and maternal health status. Child health has little effect on chaos, providing further support for the hypothesis that chaos is an important social determinant of child health in this sample of relatively disadvantaged children. This suggests child health may be improved by supporting families in ways that reduce chaos in their home and work/family environments, and that as researchers move beyond SES, race, and family structure to explore other sources of health inequalities, chaos and its proximate determinants may be a promising avenue for future research. PMID:23541250

Local polynomial chaos expansion for linear differential equations with high dimensional random inputs

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

Chen, Yi; Jakeman, John; Gittelson, Claude

2015-01-08

In this paper we present a localized polynomial chaos expansion for partial differential equations (PDE) with random inputs. In particular, we focus on time independent linear stochastic problems with high dimensional random inputs, where the traditional polynomial chaos methods, and most of the existing methods, incur prohibitively high simulation cost. Furthermore, the local polynomial chaos method employs a domain decomposition technique to approximate the stochastic solution locally. In each subdomain, a subdomain problem is solved independently and, more importantly, in a much lower dimensional random space. In a postprocesing stage, accurate samples of the original stochastic problems are obtained frommore » the samples of the local solutions by enforcing the correct stochastic structure of the random inputs and the coupling conditions at the interfaces of the subdomains. Overall, the method is able to solve stochastic PDEs in very large dimensions by solving a collection of low dimensional local problems and can be highly efficient. In our paper we present the general mathematical framework of the methodology and use numerical examples to demonstrate the properties of the method.« less

Transient chaos in the Lorenz-type map with periodic forcing.

PubMed

Maslennikov, Oleg V; Nekorkin, Vladimir I; Kurths, Jürgen

2018-03-01

We consider a case study of perturbing a system with a boundary crisis of a chaotic attractor by periodic forcing. In the static case, the system exhibits persistent chaos below the critical value of the control parameter but transient chaos above the critical value. We discuss what happens to the system and particularly to the transient chaotic dynamics if the control parameter periodically oscillates. We find a non-exponential decaying behavior of the survival probability function, study the impact of the forcing frequency and amplitude on the escape rate, analyze the phase-space image of the observed dynamics, and investigate the influence of initial conditions.

Transient chaos in the Lorenz-type map with periodic forcing

NASA Astrophysics Data System (ADS)

Maslennikov, Oleg V.; Nekorkin, Vladimir I.; Kurths, Jürgen

2018-03-01

We consider a case study of perturbing a system with a boundary crisis of a chaotic attractor by periodic forcing. In the static case, the system exhibits persistent chaos below the critical value of the control parameter but transient chaos above the critical value. We discuss what happens to the system and particularly to the transient chaotic dynamics if the control parameter periodically oscillates. We find a non-exponential decaying behavior of the survival probability function, study the impact of the forcing frequency and amplitude on the escape rate, analyze the phase-space image of the observed dynamics, and investigate the influence of initial conditions.

Topographic variations in chaos on Europa: Implications for diapiric formation

NASA Technical Reports Server (NTRS)

Schenk, Paul M.; Pappalardo, Robert T.

2004-01-01

Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Cam et al., 1998; Greenberg et al., 19991, or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 20001. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.

Topographic variations in chaos on Europa: Implications for diapiric formation

NASA Astrophysics Data System (ADS)

Schenk, Paul M.; Pappalardo, Robert T.

2004-08-01

Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Carr et al., 1998; Greenberg et al., 1999], or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 2000]. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.

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.

Bifurcations, chaos and adaptive backstepping sliding mode control of a power system with excitation limitation

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

Min, Fuhong, E-mail: minfuhong@njnu.edu.cn; Wang, Yaoda; Peng, Guangya

2016-08-15

The bifurcation and Lyapunov exponent for a single-machine-infinite bus system with excitation model are carried out by varying the mechanical power, generator damping factor and the exciter gain, from which periodic motions, chaos and the divergence of system are observed respectively. From given parameters and different initial conditions, the coexisting motions are developed in power system. The dynamic behaviors in power system may switch freely between the coexisting motions, which will bring huge security menace to protection operation. Especially, the angle divergences due to the break of stable chaotic oscillation are found which causes the instability of power system. Finally,more » a new adaptive backstepping sliding mode controller is designed which aims to eliminate the angle divergences and make the power system run in stable orbits. Numerical simulations are illustrated to verify the effectivity of the proposed method.« less

Reliability of unstable periodic orbit based control strategies in biological systems.

PubMed

Mishra, Nagender; Hasse, Maria; Biswal, B; Singh, Harinder P

2015-04-01

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.

Reliability of unstable periodic orbit based control strategies in biological systems

NASA Astrophysics Data System (ADS)

Mishra, Nagender; Hasse, Maria; Biswal, B.; Singh, Harinder P.

2015-04-01

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.

Fuzzy chaos control for vehicle lateral dynamics based on active suspension system

NASA Astrophysics Data System (ADS)

Huang, Chen; Chen, Long; Jiang, Haobin; Yuan, Chaochun; Xia, Tian

2014-07-01

The existing research of the active suspension system (ASS) mainly focuses on the different evaluation indexes and control strategies. Among the different components, the nonlinear characteristics of practical systems and control are usually not considered for vehicle lateral dynamics. But the vehicle model has some shortages on tyre model with side-slip angle, road adhesion coefficient, vertical load and velocity. In this paper, the nonlinear dynamic model of lateral system is considered and also the adaptive neural network of tire is introduced. By nonlinear analysis methods, such as the bifurcation diagram and Lyapunov exponent, it has shown that the lateral dynamics exhibits complicated motions with the forward speed. Then, a fuzzy control method is applied to the lateral system aiming to convert chaos into periodic motion using the linear-state feedback of an available lateral force with changing tire load. Finally, the rapid control prototyping is built to conduct the real vehicle test. By comparison of time response diagram, phase portraits and Lyapunov exponents at different work conditions, the results on step input and S-shaped road indicate that the slip angle and yaw velocity of lateral dynamics enter into stable domain and the results of test are consistent to the simulation and verified the correctness of simulation. And the Lyapunov exponents of the closed-loop system are becoming from positive to negative. This research proposes a fuzzy control method which has sufficient suppress chaotic motions as an effective active suspension system.

Study the complexity and control of the recycling-supply chain of China's color TVs market based on the government subsidy

NASA Astrophysics Data System (ADS)

Xie, Lei; Ma, Junhai

2016-09-01

In these days, as the recycling of household appliances becomes increasingly popular, the recycling network tends to be perfect in television industry. This paper focuses on the game among two recyclers and a processor in a Duopoly market of color TV recycling. We find that if the adjustment coefficients of the decision variables are changed abruptly, the system will fall into chaotic state. In order to avoid hazard of falling into a chaotic state, we adopt the method of delay control, providing the manufacturers with effective measures about chaos control. This paper analyzes the system's reactions to government decision, finding that when the parameters become beneficial for manufacturers, consumers and the environment, the system will fall into chaos and system's regional stability will reduce. Resulting from our analysis, this paper gives advice on the improvement of the environment and enhance in social welfare. Tested through the data we collected, this study is practical in both its theory and its applicability.

Via generalized function projective synchronization in nonlinear Schrödinger equation for secure communication

NASA Astrophysics Data System (ADS)

Zhao, L. W.; Du, J. G.; Yin, J. L.

2018-05-01

This paper proposes a novel secured communication scheme in a chaotic system by applying generalized function projective synchronization of the nonlinear Schrödinger equation. This phenomenal approach guarantees a secured and convenient communication. Our study applied the Melnikov theorem with an active control strategy to suppress chaos in the system. The transmitted information signal is modulated into the parameter of the nonlinear Schrödinger equation in the transmitter and it is assumed that the parameter of the receiver system is unknown. Based on the Lyapunov stability theory and the adaptive control technique, the controllers are designed to make two identical nonlinear Schrödinger equation with the unknown parameter asymptotically synchronized. The numerical simulation results of our study confirmed the validity, effectiveness and the feasibility of the proposed novel synchronization method and error estimate for a secure communication. The Chaos masking signals of the information communication scheme, further guaranteed a safer and secured information communicated via this approach.

Living in Chaos and Striving for Control: How Adults with Attention Deficit Hyperactivity Disorder Deal with Their Disorder

ERIC Educational Resources Information Center

Toner, Michele; O'Donoghue, Thomas; Houghton, Stephen

2006-01-01

This article reports a Grounded Theory of "Living in Chaos and Striving for Control" developed in response to the central research question of how adults diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) deal with their disorder. Semi-structured interviews were conducted with 10 males diagnosed with ADHD in adulthood.…

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.

Preface to the Focus Issue: chaos detection methods and predictability.

PubMed

Gottwald, Georg A; Skokos, Charalampos

2014-06-01

This Focus Issue presents a collection of papers originating from the workshop Methods of Chaos Detection and Predictability: Theory and Applications held at the Max Planck Institute for the Physics of Complex Systems in Dresden, June 17-21, 2013. The main aim of this interdisciplinary workshop was to review comprehensively the theory and numerical implementation of the existing methods of chaos detection and predictability, as well as to report recent applications of these techniques to different scientific fields. The collection of twelve papers in this Focus Issue represents the wide range of applications, spanning mathematics, physics, astronomy, particle accelerator physics, meteorology and medical research. This Preface surveys the papers of this Issue.

Chaos and multi-scroll attractors in RCL-shunted junction coupled Jerk circuit connected by memristor

PubMed Central

Zhou, Ping; Ahmad, Bashir; Ren, Guodong; Wang, Chunni

2018-01-01

In this paper, a new four-variable dynamical system is proposed to set chaotic circuit composed of memristor and Josephson junction, and the dependence of chaotic behaviors on nonlinearity is investigated. A magnetic flux-controlled memristor is used to couple with the RCL-shunted junction circuit, and the dynamical behaviors can be modulated by changing the coupling intensity between the memristor and the RCL-shunted junction. Bifurcation diagram and Lyapunov exponent are calculated to confirm the emergence of chaos in the improved dynamical system. The outputs and dynamical behaviors can be controlled by the initial setting and external stimulus as well. As a result, chaos can be suppressed and spiking occurs in the sampled outputs under negative feedback, while applying positive feedback type via memristor can be effective to trigger chaos. Furthermore, it is found that the number of multi-attractors in the Jerk circuit can be modulated when memristor coupling is applied on the circuit. These results indicate that memristor coupling can be effective to control chaotic circuits and it is also useful to reproduce dynamical behaviors for neuronal activities. PMID:29342178

Chaos and multi-scroll attractors in RCL-shunted junction coupled Jerk circuit connected by memristor.

PubMed

Ma, Jun; Zhou, Ping; Ahmad, Bashir; Ren, Guodong; Wang, Chunni

2018-01-01

In this paper, a new four-variable dynamical system is proposed to set chaotic circuit composed of memristor and Josephson junction, and the dependence of chaotic behaviors on nonlinearity is investigated. A magnetic flux-controlled memristor is used to couple with the RCL-shunted junction circuit, and the dynamical behaviors can be modulated by changing the coupling intensity between the memristor and the RCL-shunted junction. Bifurcation diagram and Lyapunov exponent are calculated to confirm the emergence of chaos in the improved dynamical system. The outputs and dynamical behaviors can be controlled by the initial setting and external stimulus as well. As a result, chaos can be suppressed and spiking occurs in the sampled outputs under negative feedback, while applying positive feedback type via memristor can be effective to trigger chaos. Furthermore, it is found that the number of multi-attractors in the Jerk circuit can be modulated when memristor coupling is applied on the circuit. These results indicate that memristor coupling can be effective to control chaotic circuits and it is also useful to reproduce dynamical behaviors for neuronal activities.

Free-Energy Fluctuations and Chaos in the Sherrington-Kirkpatrick Model

NASA Astrophysics Data System (ADS)

Aspelmeier, T.

2008-03-01

The sample-to-sample fluctuations ΔFN of the free-energy in the Sherrington-Kirkpatrick model are shown rigorously to be related to bond chaos. Via this connection, the fluctuations become analytically accessible by replica methods. The replica calculation for bond chaos shows that the exponent μ governing the growth of the fluctuations with system size N, ΔFN˜Nμ, is bounded by μ≤(1)/(4).

Effect of correction of aberration dynamics on chaos in human ocular accommodation.

PubMed

Hampson, Karen M; Cufflin, Matthew P; Mallen, Edward A H

2013-11-15

We used adaptive optics to determine the effect of monochromatic aberration dynamics on the level of chaos in the accommodation control system. Four participants viewed a stationary target while the dynamics of their aberrations were either left uncorrected, defocus was corrected, or all aberrations except defocus were corrected. Chaos theory analysis was used to discern changes in the accommodative microfluctuations. We found a statistically significant reduction in the chaotic nature of the accommodation microfluctuations during correction of defocus, but not when all aberrations except defocus were corrected. The Lyapunov exponent decreased from 0.71 ± 0.07 D/s (baseline) to 0.55 ± 0.03 D/s (correction of defocus fluctuations). As the reduction of chaos in physiological signals is indicative of stress to the system, the results indicate that for the participants included in this study, fluctuations in defocus have a more profound effect than those of the other aberrations. There were no changes in the power spectrum between experimental conditions. Hence chaos theory analysis is a more subtle marker of changes in the accommodation control system and will be of value in the study of myopia onset and progression.

Recent progress in econophysics: Chaos, leverage, and business cycles as revealed by agent-based modeling and human experiments

NASA Astrophysics Data System (ADS)

Xin, Chen; Huang, Ji-Ping

2017-12-01

Agent-based modeling and controlled human experiments serve as two fundamental research methods in the field of econophysics. Agent-based modeling has been in development for over 20 years, but how to design virtual agents with high levels of human-like "intelligence" remains a challenge. On the other hand, experimental econophysics is an emerging field; however, there is a lack of experience and paradigms related to the field. Here, we review some of the most recent research results obtained through the use of these two methods concerning financial problems such as chaos, leverage, and business cycles. We also review the principles behind assessments of agents' intelligence levels, and some relevant designs for human experiments. The main theme of this review is to show that by combining theory, agent-based modeling, and controlled human experiments, one can garner more reliable and credible results on account of a better verification of theory; accordingly, this way, a wider range of economic and financial problems and phenomena can be studied.

Chaotification of complex networks with impulsive control.

PubMed

Guan, Zhi-Hong; Liu, Feng; Li, Juan; Wang, Yan-Wu

2012-06-01

This paper investigates the chaotification problem of complex dynamical networks (CDN) with impulsive control. Both the discrete and continuous cases are studied. The method is presented to drive all states of every node in CDN to chaos. The proposed impulsive control strategy is effective for both the originally stable and unstable CDN. The upper bound of the impulse intervals for originally stable networks is derived. Finally, the effectiveness of the theoretical results is verified by numerical examples.

Geometric and dynamic perspectives on phase-coherent and noncoherent chaos.

PubMed

Zou, Yong; Donner, Reik V; Kurths, Jürgen

2012-03-01

Statistically distinguishing between phase-coherent and noncoherent chaotic dynamics from time series is a contemporary problem in nonlinear sciences. In this work, we propose different measures based on recurrence properties of recorded trajectories, which characterize the underlying systems from both geometric and dynamic viewpoints. The potentials of the individual measures for discriminating phase-coherent and noncoherent chaotic oscillations are discussed. A detailed numerical analysis is performed for the chaotic Rössler system, which displays both types of chaos as one control parameter is varied, and the Mackey-Glass system as an example of a time-delay system with noncoherent chaos. Our results demonstrate that especially geometric measures from recurrence network analysis are well suited for tracing transitions between spiral- and screw-type chaos, a common route from phase-coherent to noncoherent chaos also found in other nonlinear oscillators. A detailed explanation of the observed behavior in terms of attractor geometry is given.

Extension of spatiotemporal chaos in glow discharge-semiconductor systems

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

Akhmet, Marat, E-mail: marat@metu.edu.tr; Fen, Mehmet Onur; Rafatov, Ismail

2014-12-15

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528–4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases themore » potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].« less

Extension of spatiotemporal chaos in glow discharge-semiconductor systems.

PubMed

Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur

2014-12-01

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].

Quasiperiodicity route to chaos in cardiac conduction model

NASA Astrophysics Data System (ADS)

Quiroz-Juárez, M. A.; Vázquez-Medina, R.; Ryzhii, E.; Ryzhii, M.; Aragón, J. L.

2017-01-01

It has been suggested that cardiac arrhythmias are instances of chaos. In particular that the ventricular fibrillation is a form of spatio-temporal chaos that arises from normal rhythm through a quasi-periodicity or Ruelle-Takens-Newhouse route to chaos. In this work, we modify the heterogeneous oscillator model of cardiac conduction system proposed in Ref. [Ryzhii E, Ryzhii M. A heterogeneous coupled oscillator model for simulation of ECG signals. Comput Meth Prog Bio 2014;117(1):40-49. doi:10.1016/j.cmpb.2014.04.009.], by including an ectopic pacemaker that stimulates the ventricular muscle to model arrhythmias. With this modification, the transition from normal rhythm to ventricular fibrillation is controlled by a single parameter. We show that this transition follows the so-called torus of quasi-periodic route to chaos, as verified by using numerical tools such as power spectrum and largest Lyapunov exponent.

Confirmatory Factor Analysis of the Malay Version of the Confusion, Hubbub and Order Scale (CHAOS-6) among Myocardial Infarction Survivors in a Malaysian Cardiac Healthcare Facility

PubMed Central

Ganasegeran, Kurubaran; Selvaraj, Kamaraj; Rashid, Abdul

2017-01-01

Background The six item Confusion, Hubbub and Order Scale (CHAOS-6) has been validated as a reliable tool to measure levels of household disorder. We aimed to investigate the goodness of fit and reliability of a new Malay version of the CHAOS-6. Methods The original English version of the CHAOS-6 underwent forward-backward translation into the Malay language. The finalised Malay version was administered to 105 myocardial infarction survivors in a Malaysian cardiac health facility. We performed confirmatory factor analyses (CFAs) using structural equation modelling. A path diagram and fit statistics were yielded to determine the Malay version’s validity. Composite reliability was tested to determine the scale’s reliability. Results All 105 myocardial infarction survivors participated in the study. The CFA yielded a six-item, one-factor model with excellent fit statistics. Composite reliability for the single factor CHAOS-6 was 0.65, confirming that the scale is reliable for Malay speakers. Conclusion The Malay version of the CHAOS-6 was reliable and showed the best fit statistics for our study sample. We thus offer a simple, brief, validated, reliable and novel instrument to measure chaos, the Skala Kecelaruan, Keriuhan & Tertib Terubahsuai (CHAOS-6), for the Malaysian population. PMID:28951688

Nonlinear dynamics and chaotic motions in feedback-controlled two- and three-degree-of-freedom robots

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

Ravishankar, A.S. Ghosal, A.

1999-01-01

The dynamics of a feedback-controlled rigid robot is most commonly described by a set of nonlinear ordinary differential equations. In this paper, the authors analyze these equations, representing the feedback-controlled motion of two- and three-degrees-of-freedom rigid robots with revolute (R) and prismatic (P) joints in the absence of compliance, friction, and potential energy, for the possibility of chaotic motions. The authors first study the unforced or inertial motions of the robots, and show that when the Gaussian or Riemannian curvature of the configuration space of a robot is negative, the robot equations can exhibit chaos. If the curvature is zeromore » or positive, then the robot equations cannot exhibit chaos. The authors show that among the two-degrees-of-freedom robots, the PP and the PR robot have zero Gaussian curvature while the RP and RR robots have negative Gaussian curvatures. For the three-degrees-of-freedom robots, they analyze the two well-known RRP and RRR configurations of the Stanford arm and the PUMA manipulator, respectively, and derive the conditions for negative curvature and possible chaotic motions. The criteria of negative curvature cannot be used for the forced or feedback-controlled motions. For the forced motion, the authors resort to the well-known numerical techniques and compute chaos maps, Poincare maps, and bifurcation diagrams. Numerical results are presented for the two-degrees-of-freedom RP and RR robots, and the authors show that these robot equations can exhibit chaos for low controller gains and for large underestimated models. From the bifurcation diagrams, the route to chaos appears to be through period doubling.« less

Introduction to the focus issue: fifty years of chaos: applied and theoretical.

PubMed

Hikihara, Takashi; Holmes, Philip; Kambe, Tsutomu; Rega, Giuseppe

2012-12-01

The discovery of deterministic chaos in the late nineteenth century, its subsequent study, and the development of mathematical and computational methods for its analysis have substantially influenced the sciences. Chaos is, however, only one phenomenon in the larger area of dynamical systems theory. This Focus Issue collects 13 papers, from authors and research groups representing the mathematical, physical, and biological sciences, that were presented at a symposium held at Kyoto University from November 28 to December 2, 2011. The symposium, sponsored by the International Union of Theoretical and Applied Mechanics, was called 50 Years of Chaos: Applied and Theoretical. Following some historical remarks to provide a background for the last 50 years, and for chaos, this Introduction surveys the papers and identifies some common themes that appear in them and in the theory of dynamical systems.

Anticontrol of Hopf bifurcation and control of chaos for a finance system through washout filters with time delay.

PubMed

Zhao, Huitao; Lu, Mengxia; Zuo, Junmei

2014-01-01

A controlled model for a financial system through washout-filter-aided dynamical feedback control laws is developed, the problem of anticontrol of Hopf bifurcation from the steady state is studied, and the existence, stability, and direction of bifurcated periodic solutions are discussed in detail. The obtained results show that the delay on price index has great influences on the financial system, which can be applied to suppress or avoid the chaos phenomenon appearing in the financial system.

Global Complexity: Information, Chaos, and Control at ASIS 1996 Annual Meeting.

ERIC Educational Resources Information Center

Jacob, M. E. L.

1996-01-01

Discusses proceedings of the 1996 ASIS (American Society for Information Science) annual meeting in Baltimore (Maryland), including chaos theory; electronic universities; distance education; intellectual property, including information privacy on the Internet; the need for leadership in libraries and information centers; information warfare and…

Socioeconomic risk moderates the link between household chaos and maternal executive function.

PubMed

Deater-Deckard, Kirby; Chen, Nan; Wang, Zhe; Bell, Martha Ann

2012-06-01

We examined the link between household chaos (i.e., noise, clutter, disarray, lack of routines) and maternal executive function (i.e., effortful regulation of attention and memory), and whether it varied as a function of socioeconomic risk (i.e., single parenthood, lower mother and father educational attainment, housing situation, and father unemployment). We hypothesized that: 1) higher levels of household chaos would be linked with poorer maternal executive function, even when controlling for other measures of cognitive functioning (e.g., verbal ability), and 2) this link would be strongest in the most socioeconomically distressed or lowest-socioeconomic status households. The diverse sample included 153 mothers from urban and rural areas who completed a questionnaire and a battery of cognitive executive function tasks and a verbal ability task in the laboratory. Results were mixed for Hypothesis 1, and consistent with Hypothesis 2. Two-thirds of the variance overlapped between household chaos and maternal executive function, but only in families with high levels of socioeconomic risk. This pattern was not found for chaos and maternal verbal ability, suggesting that the potentially deleterious effects of household chaos may be specific to maternal executive function. The findings implicate household chaos as a powerful statistical predictor of maternal executive function in socioeconomically distressed contexts. PsycINFO Database Record (c) 2012 APA, all rights reserved.

Socioeconomic Risk Moderates the Link between Household Chaos and Maternal Executive Function

PubMed Central

Deater-Deckard, Kirby; Chen, Nan; Wang, Zhe; Bell, Martha Ann

2012-01-01

We examined the link between household chaos (i.e., noise, clutter, disarray, lack of routines) and maternal executive function (i.e., effortful regulation of attention and memory), and whether it varied as a function of socioeconomic risk (i.e., single parenthood, lower mother and father educational attainment, housing situation, and father unemployment). We hypothesized that: 1) higher levels of household chaos would be linked with poorer maternal executive function, even when controlling for other measures of cognitive functioning (e.g., verbal ability), and 2) this link would be strongest in the most socioeconomically distressed or lowest-socioeconomic status households. The diverse sample included 153 mothers from urban and rural areas who completed a questionnaire and a battery of cognitive executive function tasks and a verbal ability task in the laboratory. Results were mixed for hypothesis 1, and consistent with hypothesis 2. Two-thirds of the variance overlapped between household chaos and maternal executive function, but only in families with high levels of socioeconomic risk. This pattern was not found for chaos and maternal verbal ability, suggesting that the potentially deleterious effects of household chaos may be specific to maternal executive function. The findings implicate household chaos as a powerful statistical predictor of maternal executive function in socioeconomically distressed contexts. PMID:22563703

Quasiperiodic instability and chaos in the bad-cavity laser with modulated inversion: Numerical analysis of a Toda oscillator system

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

Ogawa, T.

The exact equivalence between a bad-cavity laser with modulated inversion and a nonlinear oscillator in a Toda potential driven by an external modulation is presented. The dynamical properties of the laser system are investigated in detail by analyzing a Toda oscillator system. The temporal characteristics of the bad-cavity laser under strong modulation are analyzed extensively by numerically investigating the simpler Toda system as a function of two control parameters: the dc component of the population inversion and the modulation amplitude. The system exhibits two kinds of optical chaos: One is the quasiperiodic chaos in the region of the intermediate modulationmore » amplitude and the other is the intermittent kicked chaos in the region of strong modulation and large dc component of the pumping. The former is well described by a one-dimensional discrete map with a singular invariant probability measure. There are two types of onset of the chaos: quasiperiodic instability (continuous path to chaos) and catastrophic crisis (discontinuous path). The period-doubling cascade of bifurcation is also observed. The simple discrete model of the Toda system is presented to obtain analytically the one-dimensional map function and to understand the effect of the asymmetric potential curvature on yielding chaos.« less

Fisher information at the edge of chaos in random Boolean networks.

PubMed

Wang, X Rosalind; Lizier, Joseph T; Prokopenko, Mikhail

2011-01-01

We study the order-chaos phase transition in random Boolean networks (RBNs), which have been used as models of gene regulatory networks. In particular we seek to characterize the phase diagram in information-theoretic terms, focusing on the effect of the control parameters (activity level and connectivity). Fisher information, which measures how much system dynamics can reveal about the control parameters, offers a natural interpretation of the phase diagram in RBNs. We report that this measure is maximized near the order-chaos phase transitions in RBNs, since this is the region where the system is most sensitive to its parameters. Furthermore, we use this study of RBNs to clarify the relationship between Shannon and Fisher information measures.

Controlling chaotic behavior in CO2 and other lasers

NASA Astrophysics Data System (ADS)

1993-06-01

Additional substantial experimental progress has been made, in the third month of the project, in setting up equipment and testing for producing chaotic behavior with a CO2 laser. The project goal is to synchronize and control chaos in CO2 and other lasers, and thereby increase the power in ensembles of coupled laser sources. Numerous investigations into the chaos regime have been made, a second CO2 laser has been brought on stream, and work is progressing in the fourth month toward coupling the two lasers and control of the first laser. It is also intended to submit at least two papers to the Second Experimental Chaos Conference which is supported by the Office of Naval Research. Abstracts to those two papers are attached. Last month's report discussed the experimental investigation of nonlinear dynamics of CO2 lasers which involved a new technique of inducing chaos. In this new technique, an acoustically modulated feedback of the laser light was used and led to chaotic dynamics at a very low modulation frequency of 375 Hz. Since then, new results have been obtained by an Electro-Optical Modulation (EOM) technique. In the new setup, the electro-optical modulator is placed in an external cavity outside the laser.

Reliability of unstable periodic orbit based control strategies in biological systems

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

Mishra, Nagender; Singh, Harinder P.; Hasse, Maria

2015-04-15

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry ofmore » the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computer model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.« less

Routes to spatiotemporal chaos in Kerr optical frequency combs.

PubMed

Coillet, Aurélien; Chembo, Yanne K

2014-03-01

We investigate the various routes to spatiotemporal chaos in Kerr optical frequency combs, obtained through pumping an ultra-high Q-factor whispering-gallery mode resonator with a continuous-wave laser. The Lugiato-Lefever model is used to build bifurcation diagrams with regards to the parameters that are externally controllable, namely, the frequency and the power of the pumping laser. We show that the spatiotemporal chaos emerging from Turing patterns and solitons display distinctive dynamical features. Experimental spectra of chaotic Kerr combs are also presented for both cases, in excellent agreement with theoretical spectra.

Chaos in an imperfectly premixed model combustor.

PubMed

Kabiraj, Lipika; Saurabh, Aditya; Karimi, Nader; Sailor, Anna; Mastorakos, Epaminondas; Dowling, Ann P; Paschereit, Christian O

2015-02-01

This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration.

Administrators in Wonderland: Leadership through the New Sciences.

ERIC Educational Resources Information Center

Slowinski, Joseph

Recent theories associated with physical reality have increasingly been adapted as social-science paradigms. Chaos Theory and Perceptual Control Theory (PCT) are two advances that are applicable to the educational administration field. According to Edward Lorenz's Chaos Theory, profound changes in outcome can arise from small variations of input.…

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

Research on the Complexity of Dual-Channel Supply Chain Model in Competitive Retailing Service Market

NASA Astrophysics Data System (ADS)

Ma, Junhai; Li, Ting; Ren, Wenbo

2017-06-01

This paper examines the optimal decisions of dual-channel game model considering the inputs of retailing service. We analyze how adjustment speed of service inputs affect the system complexity and market performance, and explore the stability of the equilibrium points by parameter basin diagrams. And chaos control is realized by variable feedback method. The numerical simulation shows that complex behavior would trigger the system to become unstable, such as double period bifurcation and chaos. We measure the performances of the model in different periods by analyzing the variation of average profit index. The theoretical results show that the percentage share of the demand and cross-service coefficients have important influence on the stability of the system and its feasible basin of attraction.

Wiener Chaos and Nonlinear Filtering

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

Lototsky, S.V.

2006-11-15

The paper discusses two algorithms for solving the Zakai equation in the time-homogeneous diffusion filtering model with possible correlation between the state process and the observation noise. Both algorithms rely on the Cameron-Martin version of the Wiener chaos expansion, so that the approximate filter is a finite linear combination of the chaos elements generated by the observation process. The coefficients in the expansion depend only on the deterministic dynamics of the state and observation processes. For real-time applications, computing the coefficients in advance improves the performance of the algorithms in comparison with most other existing methods of nonlinear filtering. Themore » paper summarizes the main existing results about these Wiener chaos algorithms and resolves some open questions concerning the convergence of the algorithms in the noise-correlated setting. The presentation includes the necessary background on the Wiener chaos and optimal nonlinear filtering.« less

Life Chaos and Perceived Social Support Among Methamphetamine-Using Men Who Have Sex with Men Engaging in Transactional Sexual Encounters

PubMed Central

Viswanath, Humsini; Wilkerson, J. Michael; Breckenridge, Ellen; Selwyn, Beatrice J.

2017-01-01

Objective Social support and life chaos have been inversely associated with increased risk of HIV infection. The purpose of this study was to explore among a sample of HIV-negative methamphetamine-using men who have sex with men (MSM) the association between engaging in transactional sex, life chaos, and low social support. Methods HIV-negative methamphetamine-using MSM completed an online questionnaire between July and October 2012 about recent substance use and sexual behavior. Bivariate and multivariate tests were used to obtain statistically significant associations between demographic characteristics, engaging in transactional sex, life chaos, and the participants’ perception of their social support. Results Of the 325 participants, 23.7% reported engaging in transactional sex, 45.2% reported high life chaos, and 53.5% reported low perceived social support. Participants who engaged in transactional sex were more likely to have high life chaos than participants who did not (aOR = 1.70, 95% CI = [1.01, 2.84]); transactional sex was not associated with social support. Participants with high life chaos were more out about their sexual orientation (aOR = 2.29, 95% CI = [1.18, 4.42]) and more likely to perceive they had low social support (aOR = 3.78, 95% CI = [2.31, 6.22]) than participants with low life chaos. Non-Latinos perceived they had less social support than Latinos (aOR = 0.48, 95% CI = [0.25, 0.92]). Conclusions Methamphetamine-using MSM engaging in transactional sex experience more life chaos than those who do not engage in transactional sex. Outness, perceived social support, and ethnicity are associated with life chaos. PMID:27679931

The nature of nurture: a genomewide association scan for family chaos.

PubMed

Butcher, Lee M; Plomin, Robert

2008-07-01

Widely used measures of the environment, especially the family environment of children, show genetic influence in dozens of twin and adoption studies. This phenomenon is known as gene-environment correlation in which genetically driven influences of individuals affect their environments. We conducted the first genome-wide association (GWA) analysis of an environmental measure. We used a measure called CHAOS which assesses 'environmental confusion' in the home, a measure that is more strongly associated with cognitive development in childhood than any other environmental measure. CHAOS was assessed by parental report when the children were 3 years and again when the children were 4 years; a composite CHAOS measure was constructed across the 2 years. We screened 490,041 autosomal single-nucleotide polymorphisms (SNPs) in a two-stage design in which children in low chaos families (N = 469) versus high chaos families (N = 369) from 3,000 families of 4-year-old twins were screened in Stage 1 using pooled DNA. In Stage 2, following SNP quality control procedures, 41 nominated SNPs were tested for association with family chaos by individual genotyping an independent representative sample of 3,529. Despite having 99% power to detect associations that account for more than 0.5% of the variance, none of the 41 nominated SNPs met conservative criteria for replication. Similar to GWA analyses of other complex traits, it is likely that most of the heritable variation in environmental measures such as family chaos is due to many genes of very small effect size.

Hybrid Solution of Stochastic Optimal Control Problems Using Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithms

DTIC Science & Technology

2012-03-01

0-486-41183-4. 15. Brown , Robert G. and Patrick Y. C. Hwang . Introduction to Random Signals and Applied Kalman Filtering. Wiley, New York, 1996. ISBN...stability and perfor- mance criteria. In the 1960’s, Kalman introduced the Linear Quadratic Regulator (LQR) method using an integral performance index...feedback of the state variables and was able to apply this method to time-varying and Multi-Input Multi-Output (MIMO) systems. Kalman further showed

Predicting chaos in memristive oscillator via harmonic balance method.

PubMed

Wang, Xin; Li, Chuandong; Huang, Tingwen; Duan, Shukai

2012-12-01

This paper studies the possible chaotic behaviors in a memristive oscillator with cubic nonlinearities via harmonic balance method which is also called the method of describing function. This method was proposed to detect chaos in classical Chua's circuit. We first transform the considered memristive oscillator system into Lur'e model and present the prediction of the existence of chaotic behaviors. To ensure the prediction result is correct, the distortion index is also measured. Numerical simulations are presented to show the effectiveness of theoretical results.

Iceberg Ahead: The Effect of Bands and Ridges During Chaos Formation on Europa.

NASA Astrophysics Data System (ADS)

Hedgepeth, J. E.; Schmidt, B. E.

2016-12-01

Europa presents a dynamic and varied surface, but the most enticing component is arguably its chaos structures. With it, the surface and subsurface can interact, but in order to fully understand if this is occurring we have to properly parameterize the surface structural integrity. We consider the Schmidt et al. (2011) method of classifying icebergs by feature type to study what features remained intact in the chaos matrix. In this work we expand on this idea. We hypothesize that the ice that forms ridges and bands exhibit higher structural strengths than plains. Subsequently, this ice is more likely to remain during chaos formation in the form of icebergs. We begin by mapping the surface around Murias chaos and other prominent chaos features. Maps are used to infer what paleo-topographic features existed before chaos formation by using the features surrounding the chaos regions as blueprints for what existed before. We perform a multivariate regression to correlate the amount of icebergs present to the amount of surface that was covered by either bands, plains, or ridges. We find ridges play the biggest role in the production of icebergs with a weighted value of 40%. Bands may play a smaller role (13%), but plains show little to no correlation (5%). Further mapping will better reveal if this trend holds true in other regions. This statistical analysis supports our hypothesis, and further work will better quantify what is occurring. We will address the energy expended in the chaos regions via movement and rotation of icebergs during the formation event and through ice-melt.

A new diode laser acupuncture therapy apparatus

NASA Astrophysics Data System (ADS)

Li, Chengwei; Huang, Zhen; Li, Dongyu; Zhang, Xiaoyuan

2006-06-01

Since the first laser-needles acupuncture apparatus was introduced in therapy, this kind of apparatus has been well used in laser biomedicine as its non-invasive, pain- free, non-bacterium, and safetool. The laser acupuncture apparatus in this paper is based on single-chip microcomputer and associated by semiconductor laser technology. The function like traditional moxibustion including reinforcing and reducing is implemented by applying chaos method to control the duty cycle of moxibustion signal, and the traditional lifting and thrusting of acupuncture is implemented by changing power output of the diode laser. The radiator element of diode laser is made and the drive circuit is designed. And chaos mathematic model is used to produce deterministic class stochastic signal to avoid the body adaptability. This function covers the shortages of continuous irradiation or that of simple disciplinary stimulate signal, which is controlled by some simple electronic circuit and become easily adjusted by human body. The realization of reinforcing and reducing of moxibustion is technological innovation in traditional acupuncture coming true in engineering.

A period-doubling cascade precedes chaos for planar maps.

PubMed

Sander, Evelyn; Yorke, James A

2013-09-01

A period-doubling cascade is often seen in numerical studies of those smooth (one-parameter families of) maps for which as the parameter is varied, the map transitions from one without chaos to one with chaos. Our emphasis in this paper is on establishing the existence of such a cascade for many maps with phase space dimension 2. We use continuation methods to show the following: under certain general assumptions, if at one parameter there are only finitely many periodic orbits, and at another parameter value there is chaos, then between those two parameter values there must be a cascade. We investigate only families that are generic in the sense that all periodic orbit bifurcations are generic. Our method of proof in showing there is one cascade is to show there must be infinitely many cascades. We discuss in detail two-dimensional families like those which arise as a time-2π maps for the Duffing equation and the forced damped pendulum equation.

Dermoscopic 'Chaos and Clues' in the diagnosis of melanoma in situ.

PubMed

Ramji, Rajan; Valdes-Gonzalez, Guillermo; Oakley, Amanda; Rademaker, Marius

2017-11-02

To describe the dermoscopic features of melanoma in situ using the Chaos and Clues method. Histologically proven primary melanoma in situ (MIS) diagnosed through a specialist teledermoscopy clinic were reviewed by three dermatologists. By consensus they agreed on the global dermoscopic pattern, colours, presence of chaos (asymmetry of colour and structure and more than one pattern), and each of the nine clues described for malignancy. One hundred MIS in 92 patients of European ethnicity (45 males) were assessed. Mean age was 67.3 years (range 20-95). The mean dimensions of the lesions were 11.1 × 12.0 mm (range 2.5-31.3 × 2.3-32.3 mm). Using pattern analysis, 82% of the lesions had three or more patterns (multicomponent) and the rest had 2 patterns. Colours included light brown (100%), dark brown (98%) and grey (75%). All MIS demonstrated chaos. The most prevalent clues were thick lines (88%), eccentric structureless areas (88%), and grey or blue structures (75%). Dermoscopy can be very helpful in the early diagnosis of melanoma and MIS. The Chaos and Clues method is simple to use. Its unambiguous descriptors can be successfully used to describe MIS. The presence of chaos and clues to malignancy (including thick lines, eccentric structureless areas, and blue/grey structures) should raise a red flag and lead to referral or excision. © 2017 The Australasian College of Dermatologists.

Bifurcation and chaos in the simple passive dynamic walking model with upper body.

PubMed

Li, Qingdu; Guo, Jianli; Yang, Xiao-Song

2014-09-01

We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.

Short-term data forecasting based on wavelet transformation and chaos theory

NASA Astrophysics Data System (ADS)

Wang, Yi; Li, Cunbin; Zhang, Liang

2017-09-01

A sketch of wavelet transformation and its application was given. Concerning the characteristics of time sequence, Haar wavelet was used to do data reduction. After processing, the effect of “data nail” on forecasting was reduced. Chaos theory was also introduced, a new chaos time series forecasting flow based on wavelet transformation was proposed. The largest Lyapunov exponent was larger than zero from small data sets, it verified the data change behavior still met chaotic behavior. Based on this, chaos time series to forecast short-term change behavior could be used. At last, the example analysis of the price from a real electricity market showed that the forecasting method increased the precision of the forecasting more effectively and steadily.

Bifurcation and chaos in the simple passive dynamic walking model with upper body

NASA Astrophysics Data System (ADS)

Li, Qingdu; Guo, Jianli; Yang, Xiao-Song

2014-09-01

We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoe in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.

Delay-range-dependent chaos synchronization approach under varying time-lags and delayed nonlinear coupling.

PubMed

Zaheer, Muhammad Hamad; Rehan, Muhammad; Mustafa, Ghulam; Ashraf, Muhammad

2014-11-01

This paper proposes a novel state feedback delay-range-dependent control approach for chaos synchronization in coupled nonlinear time-delay systems. The coupling between two systems is esteemed to be nonlinear subject to time-lags. Time-varying nature of both the intrinsic and the coupling delays is incorporated to broad scope of the present study for a better-quality synchronization controller synthesis. Lyapunov-Krasovskii (LK) functional is employed to derive delay-range-dependent conditions that can be solved by means of the conventional linear matrix inequality (LMI)-tools. The resultant control approach for chaos synchronization of the master-slave time-delay systems considers non-zero lower bound of the intrinsic as well as the coupling time-delays. Further, the delay-dependent synchronization condition has been established as a special case of the proposed LK functional treatment. Furthermore, a delay-range-dependent condition, independent of the delay-rate, has been provided to address the situation when upper bound of the delay-derivative is unknown. A robust state feedback control methodology is formulated for synchronization of the time-delay chaotic networks against the L2 norm bounded perturbations by minimizing the L2 gain from the disturbance to the synchronization error. Numerical simulation results are provided for the time-delay chaotic networks to show effectiveness of the proposed delay-range-dependent chaos synchronization methodologies. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

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.

Stability and chaos of Rulkov map-based neuron network with electrical synapse

NASA Astrophysics Data System (ADS)

Wang, Caixia; Cao, Hongjun

2015-02-01

In this paper, stability and chaos of a simple system consisting of two identical Rulkov map-based neurons with the bidirectional electrical synapse are investigated in detail. On the one hand, as a function of control parameters and electrical coupling strengthes, the conditions for stability of fixed points of this system are obtained by using the qualitative analysis. On the other hand, chaos in the sense of Marotto is proved by a strict mathematical way. These results could be useful for building-up large-scale neurons networks with specific dynamics and rich biophysical phenomena.

Chaos, ergodic convergence, and fractal instability for a thermostated canonical harmonic oscillator

NASA Astrophysics Data System (ADS)

Hoover, Wm. G.; Hoover, Carol G.; Isbister, Dennis J.

2001-02-01

The authors thermostat a qp harmonic oscillator using the two additional control variables ζ and ξ to simulate Gibbs' canonical distribution. In contrast to the motion of purely Hamiltonian systems, the thermostated oscillator motion is completely ergodic, covering the full four-dimensional \\{q,p,ζ,ξ\\} phase space. The local Lyapunov spectrum (instantaneous growth rates of a comoving corotating phase-space hypersphere) exhibits singularities like those found earlier for Hamiltonian chaos, reinforcing the notion that chaos requires kinetic-as opposed to statistical-study, both at and away from equilibrium. The exponent singularities appear to have a fractal character.

The Nature of Nurture: A Genomewide Association Scan for Family Chaos

PubMed Central

Plomin, Robert

2008-01-01

Widely used measures of the environment, especially the family environment of children, show genetic influence in dozens of twin and adoption studies. This phenomenon is known as gene-environment correlation in which genetically driven influences of individuals affect their environments. We conducted the first genome-wide association (GWA) analysis of an environmental measure. We used a measure called CHAOS which assesses ‘environmental confusion’ in the home, a measure that is more strongly associated with cognitive development in childhood than any other environmental measure. CHAOS was assessed by parental report when the children were 3 years and again when the children were 4 years; a composite CHAOS measure was constructed across the 2 years. We screened 490,041 autosomal single-nucleotide polymorphisms (SNPs) in a two-stage design in which children in low chaos families (N = 469) versus high chaos families (N = 369) from 3,000 families of 4-year-old twins were screened in Stage 1 using pooled DNA. In Stage 2, following SNP quality control procedures, 41 nominated SNPs were tested for association with family chaos by individual genotyping an independent representative sample of 3,529. Despite having 99% power to detect associations that account for more than 0.5% of the variance, none of the 41 nominated SNPs met conservative criteria for replication. Similar to GWA analyses of other complex traits, it is likely that most of the heritable variation in environmental measures such as family chaos is due to many genes of very small effect size. PMID:18360741

An Efficient Interval Type-2 Fuzzy CMAC for Chaos Time-Series Prediction and Synchronization.

PubMed

Lee, Ching-Hung; Chang, Feng-Yu; Lin, Chih-Min

2014-03-01

This paper aims to propose a more efficient control algorithm for chaos time-series prediction and synchronization. A novel type-2 fuzzy cerebellar model articulation controller (T2FCMAC) is proposed. In some special cases, this T2FCMAC can be reduced to an interval type-2 fuzzy neural network, a fuzzy neural network, and a fuzzy cerebellar model articulation controller (CMAC). So, this T2FCMAC is a more generalized network with better learning ability, thus, it is used for the chaos time-series prediction and synchronization. Moreover, this T2FCMAC realizes the un-normalized interval type-2 fuzzy logic system based on the structure of the CMAC. It can provide better capabilities for handling uncertainty and more design degree of freedom than traditional type-1 fuzzy CMAC. Unlike most of the interval type-2 fuzzy system, the type-reduction of T2FCMAC is bypassed due to the property of un-normalized interval type-2 fuzzy logic system. This causes T2FCMAC to have lower computational complexity and is more practical. For chaos time-series prediction and synchronization applications, the training architectures with corresponding convergence analyses and optimal learning rates based on Lyapunov stability approach are introduced. Finally, two illustrated examples are presented to demonstrate the performance of the proposed T2FCMAC.

On stability of fixed points and chaos in fractional systems.

PubMed

Edelman, Mark

2018-02-01

In this paper, we propose a method to calculate asymptotically period two sinks and define the range of stability of fixed points for a variety of discrete fractional systems of the order 0<α<2. The method is tested on various forms of fractional generalizations of the standard and logistic maps. Based on our analysis, we make a conjecture that chaos is impossible in the corresponding continuous fractional systems.

Bifurcation and chaos analysis of a nonlinear electromechanical coupling relative rotation system

NASA Astrophysics Data System (ADS)

Liu, Shuang; Zhao, Shuang-Shuang; Sun, Bao-Ping; Zhang, Wen-Ming

2014-09-01

Hopf bifurcation and chaos of a nonlinear electromechanical coupling relative rotation system are studied in this paper. Considering the energy in air-gap field of AC motor, the dynamical equation of nonlinear electromechanical coupling relative rotation system is deduced by using the dissipation Lagrange equation. Choosing the electromagnetic stiffness as a bifurcation parameter, the necessary and sufficient conditions of Hopf bifurcation are given, and the bifurcation characteristics are studied. The mechanism and conditions of system parameters for chaotic motions are investigated rigorously based on the Silnikov method, and the homoclinic orbit is found by using the undetermined coefficient method. Therefore, Smale horseshoe chaos occurs when electromagnetic stiffness changes. Numerical simulations are also given, which confirm the analytical results.

Estimating the size of an open population using sparse capture-recapture data.

PubMed

Huggins, Richard; Stoklosa, Jakub; Roach, Cameron; Yip, Paul

2018-03-01

Sparse capture-recapture data from open populations are difficult to analyze using currently available frequentist statistical methods. However, in closed capture-recapture experiments, the Chao sparse estimator (Chao, 1989, Biometrics 45, 427-438) may be used to estimate population sizes when there are few recaptures. Here, we extend the Chao (1989) closed population size estimator to the open population setting by using linear regression and extrapolation techniques. We conduct a small simulation study and apply the models to several sparse capture-recapture data sets. © 2017, The International Biometric Society.

Chaos: Understanding and Controlling Laser Instability

NASA Technical Reports Server (NTRS)

Blass, William E.

1997-01-01

In order to characterize the behavior of tunable diode lasers (TDL), the first step in the project involved the redesign of the TDL system here at the University of Tennessee Molecular Systems Laboratory (UTMSL). Having made these changes it was next necessary to optimize the new optical system. This involved the fine adjustments to the optical components, particularly in the monochromator, to minimize the aberrations of coma and astigmatism and to assure that the energy from the beam is focused properly on the detector element. The next step involved the taking of preliminary data. We were then ready for the analysis of the preliminary data. This required the development of computer programs that use mathematical techniques to look for signatures of chaos. Commercial programs were also employed. We discovered some indication of high dimensional chaos, but were hampered by the low sample rate of 200 KSPS (kilosamples/sec) and even more by our sample size of 1024 (1K) data points. These limitations were expected and we added a high speed data acquisition board. We incorporated into the system a computer with a 40 MSPS (million samples/sec) data acquisition board. This board can also capture 64K of data points so that were then able to perform the more accurate tests for chaos. The results were dramatic and compelling, we had demonstrated that the lead salt diode laser had a chaotic frequency output. Having identified the chaotic character in our TDL data, we proceeded to stage two as outlined in our original proposal. This required the use of an Occasional Proportional Feedback (OPF) controller to facilitate the control and stabilization of the TDL system output. The controller was designed and fabricated at GSFC and debugged in our laboratories. After some trial and error efforts, we achieved chaos control of the frequency emissions of the laser. The two publications appended to this introduction detail the entire project and its results.

Cryptanalysis of "an improvement over an image encryption method based on total shuffling"

NASA Astrophysics Data System (ADS)

Akhavan, A.; Samsudin, A.; Akhshani, A.

2015-09-01

In the past two decades, several image encryption algorithms based on chaotic systems had been proposed. Many of the proposed algorithms are meant to improve other chaos based and conventional cryptographic algorithms. Whereas, many of the proposed improvement methods suffer from serious security problems. In this paper, the security of the recently proposed improvement method for a chaos-based image encryption algorithm is analyzed. The results indicate the weakness of the analyzed algorithm against chosen plain-text.

FALSE DETERMINATIONS OF CHAOS IN SHORT NOISY TIME SERIES. (R828745)

EPA Science Inventory

A method (NEMG) proposed in 1992 for diagnosing chaos in noisy time series with 50 or fewer observations entails fitting the time series with an empirical function which predicts an observation in the series from previous observations, and then estimating the rate of divergenc...

Dynamics of a New 5D Hyperchaotic System of Lorenz Type

NASA Astrophysics Data System (ADS)

Zhang, Fuchen; Chen, Rui; Wang, Xingyuan; Chen, Xiusu; Mu, Chunlai; Liao, Xiaofeng

Ultimate boundedness of chaotic dynamical systems is one of the fundamental concepts in dynamical systems, which plays an important role in investigating the stability of the equilibrium, estimating the Lyapunov dimension of attractors and the Hausdorff dimension of attractors, the existence of periodic solutions, chaos control, chaos synchronization. However, it is often difficult to obtain the bounds of the hyperchaotic systems due to the complex algebraic structure of the hyperchaotic systems. This paper has investigated the boundedness of solutions of a nonlinear hyperchaotic system. We have obtained the global exponential attractive set and the ultimate bound set for this system. To obtain the ellipsoidal ultimate bound, the ultimate bound of the proposed system is theoretically estimated using Lagrange multiplier method, Lyapunov stability theory and optimization theory. To show the ultimate bound region, numerical simulations are provided.

Chaos, Fractals and Their Applications

NASA Astrophysics Data System (ADS)

Thompson, J. Michael T.

2016-12-01

This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.

Impact of predator dormancy on prey-predator dynamics

NASA Astrophysics Data System (ADS)

Freire, Joana G.; Gallas, Marcia R.; Gallas, Jason A. C.

2018-05-01

The impact of predator dormancy on the population dynamics of phytoplankton-zooplankton in freshwater ecosystems is investigated using a simple model including dormancy, a strategy to avoid extinction. In addition to recently reported chaos-mediated mixed-mode oscillations, as the carrying capacity grows, we find surprisingly wide phases of nonchaos-mediated mixed-mode oscillations to be present well before the onset of chaos in the system. Nonchaos-mediated cascades display spike-adding sequences, while chaos-mediated cascades show spike-doubling. A host of braided periodic phases with exotic shapes is found embedded in a region of control parameters dominated by chaotic oscillations. We describe the organization of these complicated phases and show how they are interconnected and how their complexity unfolds as control parameters change. The novel nonchaos-mediated phases are found to be large and stable, even for low carrying capacity.

An effective chaos-geometric computational approach to analysis and prediction of evolutionary dynamics of the environmental systems: Atmospheric pollution dynamics

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Bunyakova, Yu Ya; Florko, T. A.; Agayar, E. V.; Solyanikova, E. P.

2017-10-01

The present paper concerns the results of computational studying dynamics of the atmospheric pollutants (dioxide of nitrogen, sulphur etc) concentrations in an atmosphere of the industrial cities (Odessa) by using the dynamical systems and chaos theory methods. A chaotic behaviour in the nitrogen dioxide and sulphurous anhydride concentration time series at several sites of the Odessa city is numerically investigated. As usually, to reconstruct the corresponding attractor, the time delay and embedding dimension are needed. The former is determined by the methods of autocorrelation function and average mutual information, and the latter is calculated by means of a correlation dimension method and algorithm of false nearest neighbours. Further, the Lyapunov’s exponents spectrum, Kaplan-Yorke dimension and Kolmogorov entropy are computed. It has been found an existence of a low-D chaos in the time series of the atmospheric pollutants concentrations.

Relationships of family conflict, cohesion, and chaos in the home environment on maternal and child food-related behaviours.

PubMed

Martin-Biggers, Jennifer; Quick, Virginia; Zhang, Man; Jin, Yanhong; Byrd-Bredbenner, Carol

2018-04-01

This study examined how food-related behaviours differed in mothers and their preschool children by levels of family functioning (cohesion and conflict) and household disorganization (chaos). A nationally representative sample of mothers of preschoolers completed an online survey assessing food-related behaviours of themselves and their children. Maternal and child diet, eating behaviours, and health status; household availability of fruits/vegetables, salty/fatty snacks, and sugar-sweetened beverages; family mealtime atmosphere; and family conflict, cohesion, and household chaos were assessed with valid, reliable scales. Cluster analyses assigned families into low, middle, and high conflict, cohesion, and chaos groups. Participants (n = 550) were 72% White, and 82% had some post-secondary education. Regression analysis examining the association of cluster grouping levels on diet-related behaviour measures revealed that positive home environments (i.e., low family conflict, high family cohesion, and low household chaos) were associated with healthier food-related behaviours (e.g., increased fruits/vegetables intake), whereas negative home environments (i.e., high family conflict, low family cohesion, and high household chaos) were associated with unhealthy food-related behaviours (e.g., greater % total calories from fat) even after controlling for sociodemographic and related behavioural factors. Findings suggest family functioning and household chaos are associated with food-related behaviours. This frequently overlooked component of family interaction may affect intervention outcomes and objectives of educational and interventional initiatives. © 2017 John Wiley & Sons Ltd.

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.

Chaos Control of Epileptiform Bursting in the Brain

NASA Astrophysics Data System (ADS)

Slutzky, M. W.; Cvitanovic, P.; Mogul, D. J.

Epilepsy, defined as recurrent seizures, is a pathological state of the brain that afflicts over one percent of the world's population. Seizures occur as populations of neurons in the brain become overly synchronized. Although pharmacological agents are the primary treatment for preventing or reducing the incidence of these seizures, over 30% of epilepsy cases are not adequately helped by standard medical therapies. Several groups are exploring the use of electrical stimulation to terminate or prevent epileptic seizures. One experimental model used to test these algorithms is the brain slice where a select region of the brain is cut and kept viable in a well-oxygenated artificial cerebrospinal fluid. Under certain conditions, such slices may be made to spontaneously and repetitively burst, thereby providing an in vitro model of epilepsy. In this chapter, we discuss our efforts at applying chaos analysis and chaos control algorithms for manipulating this seizure-like behavior in a brain slice model. These techniques may provide a nonlinear control pathway for terminating or potentially preventing epileptic seizures in the whole brain.

"Thriving on Chaos." A Colloquium Review (Hagerstown, Maryland, May 18, 1988).

ERIC Educational Resources Information Center

Ernst, Charles M.; And Others

Three authors discuss Tom Peters' management guide, "Thriving on Chaos," and its implications for community colleges. First, Dixie D. LeHardy delineates Peters' main points concerning the U.S. economic system, the need for new organizational structures, the importance of quality in an unstable, competitive world market, methods of…

Detecting chaos in irregularly sampled time series.

PubMed

Kulp, C W

2013-09-01

Recently, Wiebe and Virgin [Chaos 22, 013136 (2012)] developed an algorithm which detects chaos by analyzing a time series' power spectrum which is computed using the Discrete Fourier Transform (DFT). Their algorithm, like other time series characterization algorithms, requires that the time series be regularly sampled. Real-world data, however, are often irregularly sampled, thus, making the detection of chaotic behavior difficult or impossible with those methods. In this paper, a characterization algorithm is presented, which effectively detects chaos in irregularly sampled time series. The work presented here is a modification of Wiebe and Virgin's algorithm and uses the Lomb-Scargle Periodogram (LSP) to compute a series' power spectrum instead of the DFT. The DFT is not appropriate for irregularly sampled time series. However, the LSP is capable of computing the frequency content of irregularly sampled data. Furthermore, a new method of analyzing the power spectrum is developed, which can be useful for differentiating between chaotic and non-chaotic behavior. The new characterization algorithm is successfully applied to irregularly sampled data generated by a model as well as data consisting of observations of variable stars.

Simple diffusion can support the pitchfork, the flip bifurcations, and the chaos

NASA Astrophysics Data System (ADS)

Meng, Lili; Li, Xinfu; Zhang, Guang

2017-12-01

In this paper, a discrete rational fration population model with the Dirichlet boundary conditions will be considered. According to the discrete maximum principle and the sub- and supper-solution method, the necessary and sufficient conditions of uniqueness and existence of positive steady state solutions will be obtained. In addition, the dynamical behavior of a special two patch metapopulation model is investigated by using the bifurcation method, the center manifold theory, the bifurcation diagrams and the largest Lyapunov exponent. The results show that there exist the pitchfork, the flip bifurcations, and the chaos. Clearly, these phenomena are caused by the simple diffusion. The theoretical analysis of chaos is very imortant, unfortunately, there is not any results in this hand. However, some open problems are given.

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.

The Chaos of Katrina

DTIC Science & Technology

2007-03-01

partners for their mutual benefit. Unfortunately, based on government reports, FEMA did not have adequate control of its supply chain information ...is one attractor . “Edge of chaos” systems have two to eight attractors and in chaotic systems many attractors . Some are called strange attractors ...investigates whether chaos theory, part of complexity science, can extract information from Katrina contracting data to help managers make better logistics

Order in the House!: Associations among Household Chaos, the Home Literacy Environment, Maternal Reading Ability, and Children's Early Reading

ERIC Educational Resources Information Center

Johnson, Anna D.; Martin, Anne; Brooks-Gunn, Jeanne; Petrill, Stephen A.

2008-01-01

The current study examines whether associations exist between household chaos and children's early reading skills, after controlling for a comprehensive battery of home literacy environment characteristics. Our sample included 455 kindergarten and first-grade children who are enrolled in the Western Reserve Reading Project. We go on to test…

Determination of the exact range of the value of the parameter corresponding to chaos based on the Silnikov criterion

NASA Astrophysics Data System (ADS)

Li, Wei-Yi; Zhang, Qi-Chang; Wang, Wei

2010-06-01

Based on the Silnikov criterion, this paper studies a chaotic system of cubic polynomial ordinary differential equations in three dimensions. Using the Cardano formula, it obtains the exact range of the value of the parameter corresponding to chaos by means of the centre manifold theory and the method of multiple scales combined with Floque theory. By calculating the manifold near the equilibrium point, the series expression of the homoclinic orbit is also obtained. The space trajectory and Lyapunov exponent are investigated via numerical simulation, which shows that there is a route to chaos through period-doubling bifurcation and that chaotic attractors exist in the system. The results obtained here mean that chaos occurred in the exact range given in this paper. Numerical simulations also verify the analytical results.

Chaos in an Eulerian Based Model of Sickle Cell Blood Flow

NASA Astrophysics Data System (ADS)

Apori, Akwasi; Harris, Wesley

2001-11-01

A novel Eulerian model describing the manifestation of sickle cell blood flow in the capillaries has been formulated to study the apparently chaotic onset of sickle cell crises. This Eulerian model was based on extending previous models of sickle cell blood flow which were limited due to their Lagrangian formulation. Oxygen concentration, red blood cell velocity, cell stiffness, and plasma viscosity were modeled as system state variables. The governing equations of the system were expressed in canonical form. The non-linear coupling of velocity-viscosity and viscosity- stiffness proved to be the origin of chaos in the system. The system was solved with respect to a control parameter representing the unique rheology of the sickle cell erythrocytes. Results of chaos tests proved positive for various ranges of the control parameter. The results included con-tinuous patterns found in the Poincare section, spectral broadening of the Fourier power spectrum, and positive Lyapunov exponent values. The onset of chaos predicted by this sickle cell flow model as the control parameter was varied appeared to coincide with the change from a healthy state to a crisis state in a sickle cell patient. This finding that sickle cell crises may be caused from the well understood change of a solution from a steady state to chaotic could point to new ways in preventing and treating crises and should be validated in clinical trials.

[The new methods in gerontology for life expectancy prediction of the indigenous population of Yugra].

PubMed

Gavrilenko, T V; Es'kov, V M; Khadartsev, A A; Khimikova, O I; Sokolova, A A

2014-01-01

The behavior of the state vector of human cardio-vascular system in different age groups according to methods of theory of chaos-self-organization and methods of classical statistics was investigated. Observations were made on the indigenous people of North of the Russian Federation. Using methods of the theory of chaos-self-organization the differences in the parameters of quasi-attractors of the human state vector of cardio-vascular system of the people of Russian Federation North were shown. Comparison with the results obtained by classical statistics was made.

Tuning quantum measurements to control chaos.

PubMed

Eastman, Jessica K; Hope, Joseph J; Carvalho, André R R

2017-03-20

Environment-induced decoherence has long been recognised as being of crucial importance in the study of chaos in quantum systems. In particular, the exact form and strength of the system-environment interaction play a major role in the quantum-to-classical transition of chaotic systems. In this work we focus on the effect of varying monitoring strategies, i.e. for a given decoherence model and a fixed environmental coupling, there is still freedom on how to monitor a quantum system. We show here that there is a region between the deep quantum regime and the classical limit where the choice of the monitoring parameter allows one to control the complex behaviour of the system, leading to either the emergence or suppression of chaos. Our work shows that this is a result from the interplay between quantum interference effects induced by the nonlinear dynamics and the effectiveness of the decoherence for different measurement schemes.

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.

Control of Chaos: New Perspectives in Experimental and Theoretical Science. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. Theme Issue. Part 2, Volume 8, Number 9, September 1998.

DTIC Science & Technology

1998-09-01

discharges in the Onchidium pacemaker neu- "Episodic multiregional cortical coherence at multiple ron," J. Theor. Biol. 156, 269-291. frequencies during...with delay: A model of synchronization of Sepulchre, J. A. & Babloyantz, A. [1993] "Controlling cortical tissue," Neural Comput. 6, 1141-1154...generating circuit of different 363, 411 417. networks," Nature 351, 60-63. Singer, W. [1993] "Synchronization of cortical activity Mpitsos, G. J., Burton, R

Predictive control of a chaotic permanent magnet synchronous generator in a wind turbine system

NASA Astrophysics Data System (ADS)

Manal, Messadi; Adel, Mellit; Karim, Kemih; Malek, Ghanes

2015-01-01

This paper investigates how to address the chaos problem in a permanent magnet synchronous generator (PMSG) in a wind turbine system. Predictive control approach is proposed to suppress chaotic behavior and make operating stable; the advantage of this method is that it can only be applied to one state of the wind turbine system. The use of the genetic algorithms to estimate the optimal parameter values of the wind turbine leads to maximization of the power generation. Moreover, some simulation results are included to visualize the effectiveness and robustness of the proposed method. Project supported by the CMEP-TASSILI Project (Grant No. 14MDU920).

Global Optimal Trajectory in Chaos and NP-Hardness

NASA Astrophysics Data System (ADS)

Latorre, Vittorio; Gao, David Yang

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

Vehicle Sprung Mass Estimation for Rough Terrain

DTIC Science & Technology

2011-03-01

distributions are greater than zero. The multivariate polynomials are functions of the Legendre polynomials (Poularikas (1999...developed methods based on polynomial chaos theory and on the maximum likelihood approach to estimate the most likely value of the vehicle sprung...mass. The polynomial chaos estimator is compared to benchmark algorithms including recursive least squares, recursive total least squares, extended

Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series

NASA Astrophysics Data System (ADS)

Sugihara, George; May, Robert M.

1990-04-01

An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems. The method is applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.

Dynamical Epidemic Suppression Using Stochastic Prediction and Control

DTIC Science & Technology

2004-10-28

initial probability density function (PDF), p: D C R2 -- R, is defined by the stochastic Frobenius - Perron For deterministic systems, normal methods of...induced chaos. To analyze the qualitative change, we apply the technique of the stochastic Frobenius - Perron operator [L. Billings et al., Phys. Rev. Lett...transition matrix describing the probability of transport from one region of phase space to another, which approximates the stochastic Frobenius - Perron

Complex dynamics of a MC-MS pricing model for a risk-averse supply chain with after-sale investment

NASA Astrophysics Data System (ADS)

Ma, Junhai; Sun, Lijian

2015-09-01

In this paper, we investigate the pricing strategy of the manufacturers and that of a common retailer, including their after-sale investment in a risk-averse supply chain. As the demand is not always for sure, the supply chain follows Manufacturers Cooperating (MC) and Manufacturers Stackelberg (MS). The main objective of the paper is to investigate the influence of the decision parameters such as the after-sale investment, wholesale price adjustment speed and risk preference on the stability and utilities of the risk-averse supply chain. The dynamic phenomena, such as the bifurcation, chaos and sensitivity to initial values are analyzed with 2D-bifurcation diagrams, double largest Lyapunov exponent and basins of attraction. The study shows that the faster the adjustment speed is, the more profits the retailer can make, but on the other hand, it is no good to manufacturers. Risk tolerance levels (RM and RR) affect the utility of the manufacturers and that of the retailer differently. A feedback control method is used to control the chaos in the supply chain.

Uncertainty Propagation for Turbulent, Compressible Flow in a Quasi-1D Nozzle Using Stochastic Methods

NASA Technical Reports Server (NTRS)

Zang, Thomas A.; Mathelin, Lionel; Hussaini, M. Yousuff; Bataille, Francoise

2003-01-01

This paper describes a fully spectral, Polynomial Chaos method for the propagation of uncertainty in numerical simulations of compressible, turbulent flow, as well as a novel stochastic collocation algorithm for the same application. The stochastic collocation method is key to the efficient use of stochastic methods on problems with complex nonlinearities, such as those associated with the turbulence model equations in compressible flow and for CFD schemes requiring solution of a Riemann problem. Both methods are applied to compressible flow in a quasi-one-dimensional nozzle. The stochastic collocation method is roughly an order of magnitude faster than the fully Galerkin Polynomial Chaos method on the inviscid problem.

Nitrite-Oxidizing Bacteria Community Composition and Diversity Are Influenced by Fertilizer Regimes, but Are Independent of the Soil Aggregate in Acidic Subtropical Red Soil.

PubMed

Han, Shun; Li, Xiang; Luo, Xuesong; Wen, Shilin; Chen, Wenli; Huang, Qiaoyun

2018-01-01

Nitrification is the two-step aerobic oxidation of ammonia to nitrate via nitrite in the nitrogen-cycle on earth. However, very limited information is available on how fertilizer regimes affect the distribution of nitrite oxidizers, which are involved in the second step of nitrification, across aggregate size classes in soil. In this study, the community compositions of nitrite oxidizers ( Nitrobacter and Nitrospira ) were characterized from a red soil amended with four types of fertilizer regimes over a 26-year fertilization experiment, including control without fertilizer (CK), swine manure (M), chemical fertilization (NPK), and chemical/organic combined fertilization (MNPK). Our results showed that the addition of M and NPK significantly decreased Nitrobacter Shannon and Chao1 index, while M and MNPK remarkably increased Nitrospira Shannon and Chao1 index, and NPK considerably decreased Nitrospira Shannon and Chao1 index, with the greatest diversity achieved in soils amended with MNPK. However, the soil aggregate fractions had no impact on that alpha-diversity of Nitrobacter and Nitrospira under the fertilizer treatment. Soil carbon, nitrogen and phosphorus in the soil had a significant correlation with Nitrospira Shannon and Chao1 diversity index, while total potassium only had a significant correlation with Nitrospira Shannon diversity index. However, all of them had no significant correlation with Nitrobacter Shannon and Chao1 diversity index. The resistance indices for alpha-diversity indexes (Shannon and Chao1) of Nitrobacter were higher than those of Nitrospira in response to the fertilization regimes. Manure fertilizer is important in enhancing the Nitrospira Shannon and Chao1 index resistance. Principal co-ordinate analysis revealed that Nitrobacter - and Nitrospira -like NOB communities under four fertilizer regimes were differentiated from each other, but soil aggregate fractions had less effect on the nitrite oxidizers community. Redundancy analysis and Mantel test indicated that soil nitrogen, carbon, phosphorus, and available potassium content were important environmental attributes that control the Nitrobacter - and Nitrospira -like NOB community structure across different fertilization treatments under aggregate levels in the red soil. In general, nitrite-oxidizing bacteria community composition and alpha-diversity are depending on fertilizer regimes, but independent of the soil aggregate.

Experimental verification of rank 1 chaos in switch-controlled Chua circuit.

PubMed

Oksasoglu, Ali; Ozoguz, Serdar; Demirkol, Ahmet S; Akgul, Tayfun; Wang, Qiudong

2009-03-01

In this paper, we provide the first experimental proof for the existence of rank 1 chaos in the switch-controlled Chua circuit by following a step-by-step procedure given by the theory of rank 1 maps. At the center of this procedure is a periodically kicked limit cycle obtained from the unforced system. Then, this limit cycle is subjected to periodic kicks by adding externally controlled switches to the original circuit. Both the smooth nonlinearity and the piecewise linear cases are considered in this experimental investigation. Experimental results are found to be in concordance with the conclusions of the theory.

Chaotic behaviour of the Rossler model and its analysis by using bifurcations of limit cycles and chaotic attractors

NASA Astrophysics Data System (ADS)

Ibrahim, K. M.; Jamal, R. K.; Ali, F. H.

2018-05-01

The behaviour of certain dynamical nonlinear systems are described in term as chaos, i.e., systems’ variables change with the time, displaying very sensitivity to initial conditions of chaotic dynamics. In this paper, we study archetype systems of ordinary differential equations in two-dimensional phase spaces of the Rössler model. A system displays continuous time chaos and is explained by three coupled nonlinear differential equations. We study its characteristics and determine the control parameters that lead to different behavior of the system output, periodic, quasi-periodic and chaos. The time series, attractor, Fast Fourier Transformation and bifurcation diagram for different values have been described.

Chaotic electron diffusion through stochastic webs enhances current flow in superlattices.

PubMed

Fromhold, T M; Patanè, A; Bujkiewicz, S; Wilkinson, P B; Fowler, D; Sherwood, D; Stapleton, S P; Krokhin, A A; Eaves, L; Henini, M; Sankeshwar, N S; Sheard, F W

2004-04-15

Understanding how complex systems respond to change is of fundamental importance in the natural sciences. There is particular interest in systems whose classical newtonian motion becomes chaotic as an applied perturbation grows. The transition to chaos usually occurs by the gradual destruction of stable orbits in parameter space, in accordance with the Kolmogorov-Arnold-Moser (KAM) theorem--a cornerstone of nonlinear dynamics that explains, for example, gaps in the asteroid belt. By contrast, 'non-KAM' chaos switches on and off abruptly at critical values of the perturbation frequency. This type of dynamics has wide-ranging implications in the theory of plasma physics, tokamak fusion, turbulence, ion traps, and quasicrystals. Here we realize non-KAM chaos experimentally by exploiting the quantum properties of electrons in the periodic potential of a semiconductor superlattice with an applied voltage and magnetic field. The onset of chaos at discrete voltages is observed as a large increase in the current flow due to the creation of unbound electron orbits, which propagate through intricate web patterns in phase space. Non-KAM chaos therefore provides a mechanism for controlling the electrical conductivity of a condensed matter device: its extreme sensitivity could find applications in quantum electronics and photonics.

Turbulence transition and the edge of chaos in pipe flow.

PubMed

Schneider, Tobias M; Eckhardt, Bruno; Yorke, James A

2007-07-20

The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the edge of chaos which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in Skufca et al., Phys. Rev. Lett. 96, 174101 (2006), we show that superimposed on an overall 1/Re scaling predicted and studied previously there are small, nonmonotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.

An investigation into possible quantum chaos in the H2 molecule under intense laser fields via Ehrenfest phase space (EPS) trajectories.

PubMed

Sadhukhan, Mainak; Deb, B M

2018-06-21

By employing the Ehrenfest "phase space" trajectory method for studying quantum chaos, developed in our laboratory, the present study reveals that the H 2 molecule under intense laser fields of three different intensities, I = 1 × 10 14  W/cm 2 , 5 × 10 14  W/cm 2 , and 1 × 10 15  W/cm 2 , does not show quantum chaos. A similar conclusion is also reached through the Loschmidt echo (also called quantum fidelity) calculations reported here for the first time for a real molecule under intense laser fields. Thus, a long-standing conjecture about the possible existence of quantum chaos in atoms and molecules under intense laser fields has finally been tested and not found to be valid in the present case.

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

Rydberg Atoms in Strong Fields: a Testing Ground for Quantum Chaos.

NASA Astrophysics Data System (ADS)

Courtney, Michael

1995-01-01

Rydberg atoms in strong static electric and magnetic fields provide experimentally accessible systems for studying the connections between classical chaos and quantum mechanics in the semiclassical limit. This experimental accessibility has motivated the development of reliable quantum mechanical solutions. This thesis uses both experimental and computed quantum spectra to test the central approaches to quantum chaos. These central approaches consist mainly of developing methods to compute the spectra of quantum systems in non -perturbative regimes, correlating statistical descriptions of eigenvalues with the classical behavior of the same Hamiltonian, and the development of semiclassical methods such as periodic-orbit theory. Particular emphasis is given to identifying the spectral signature of recurrences --quantum wave packets which follow classical orbits. The new findings include: the breakdown of the connection between energy-level statistics and classical chaos in odd-parity diamagnetic lithium, the discovery of the signature of very long period orbits in atomic spectra, quantitative evidence for the scattering of recurrences by the alkali -metal core, quantitative description of the behavior of recurrences near bifurcations, and a semiclassical interpretation of the evolution of continuum Stark spectra. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.).

On Chaotic and Hyperchaotic Complex Nonlinear Dynamical Systems

NASA Astrophysics Data System (ADS)

Mahmoud, Gamal M.

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

Input reconstruction of chaos sensors.

PubMed

Yu, Dongchuan; Liu, Fang; Lai, Pik-Yin

2008-06-01

Although the sensitivity of sensors can be significantly enhanced using chaotic dynamics due to its extremely sensitive dependence on initial conditions and parameters, how to reconstruct the measured signal from the distorted sensor response becomes challenging. In this paper we suggest an effective method to reconstruct the measured signal from the distorted (chaotic) response of chaos sensors. This measurement signal reconstruction method applies the neural network techniques for system structure identification and therefore does not require the precise information of the sensor's dynamics. We discuss also how to improve the robustness of reconstruction. Some examples are presented to illustrate the measurement signal reconstruction method suggested.

Improved Adaptive LSB Steganography Based on Chaos and Genetic Algorithm

NASA Astrophysics Data System (ADS)

Yu, Lifang; Zhao, Yao; Ni, Rongrong; Li, Ting

2010-12-01

We propose a novel steganographic method in JPEG images with high performance. Firstly, we propose improved adaptive LSB steganography, which can achieve high capacity while preserving the first-order statistics. Secondly, in order to minimize visual degradation of the stego image, we shuffle bits-order of the message based on chaos whose parameters are selected by the genetic algorithm. Shuffling message's bits-order provides us with a new way to improve the performance of steganography. Experimental results show that our method outperforms classical steganographic methods in image quality, while preserving characteristics of histogram and providing high capacity.

The physics of mental acts: coherence and creativity

NASA Astrophysics Data System (ADS)

Tito Arecchi, F.

2009-06-01

Coherence is a long range order absent at thermal equilibrium, where a system is the superposition of many uncorrelated components. To build non-trivial correlations, the system must enter a nonlinear dynamical regime. The nonlinearity leads to a multiplicity of equilibrium states, the number of which increases exponentially with the number of partners; we call complexity such a situation. Complete exploration of complexity would require a very large amount of time. On the contrary, in cognitive tasks, one reaches a decision within a few hundred milliseconds. Neuron synchronization lasting around 301 msec is the indicator of a conscious perception (Gestalt); however, the loss of information in the chaotic spike train of a single neuron takes a few msec, thus a conscious perception implies a control of chaos, whereby the information stored in a brain area survives for a time sufficient to elicit an action. Control of chaos is achieved by the interaction of a bottom-up stimulus with a top-down control (induced by the semantic memory). We call creativity this optimal control of neuronal chaos; it goes beyond the Bayesian inference, which is the way a computer operates, thus it represent a non-algorithmic step.

Nonlinear Dynamics, Chaotic and Complex Systems

NASA Astrophysics Data System (ADS)

Infeld, E.; Zelazny, R.; Galkowski, A.

2011-04-01

Part I. Dynamic Systems Bifurcation Theory and Chaos: 1. Chaos in random dynamical systems V. M. Gunldach; 2. Controlling chaos using embedded unstable periodic orbits: the problem of optimal periodic orbits B. R. Hunt and E. Ott; 3. Chaotic tracer dynamics in open hydrodynamical flows G. Karolyi, A. Pentek, T. Tel and Z. Toroczkai; 4. Homoclinic chaos L. P. Shilnikov; Part II. Spatially Extended Systems: 5. Hydrodynamics of relativistic probability flows I. Bialynicki-Birula; 6. Waves in ionic reaction-diffusion-migration systems P. Hasal, V. Nevoral, I. Schreiber, H. Sevcikova, D. Snita, and M. Marek; 7. Anomalous scaling in turbulence: a field theoretical approach V. Lvov and I. Procaccia; 8. Abelian sandpile cellular automata M. Markosova; 9. Transport in an incompletely chaotic magnetic field F. Spineanu; Part III. Dynamical Chaos Quantum Physics and Foundations Of Statistical Mechanics: 10. Non-equilibrium statistical mechanics and ergodic theory L. A. Bunimovich; 11. Pseudochaos in statistical physics B. Chirikov; 12. Foundations of non-equilibrium statistical mechanics J. P. Dougherty; 13. Thermomechanical particle simulations W. G. Hoover, H. A. Posch, C. H. Dellago, O. Kum, C. G. Hoover, A. J. De Groot and B. L. Holian; 14. Quantum dynamics on a Markov background and irreversibility B. Pavlov; 15. Time chaos and the laws of nature I. Prigogine and D. J. Driebe; 16. Evolutionary Q and cognitive systems: dynamic entropies and predictability of evolutionary processes W. Ebeling; 17. Spatiotemporal chaos information processing in neural networks H. Szu; 18. Phase transitions and learning in neural networks C. Van den Broeck; 19. Synthesis of chaos A. Vanecek and S. Celikovsky; 20. Computational complexity of continuous problems H. Wozniakowski; Part IV. Complex Systems As An Interface Between Natural Sciences and Environmental Social and Economic Sciences: 21. Stochastic differential geometry in finance studies V. G. Makhankov; Part V. Conference Banquet Speech: Where will the future go? M. J. Feigenbaum.

A Chaotic Home Environment Accounts for the Association between Respect for Rules Disposition and Reading Comprehension: A Twin Study

PubMed Central

Taylor, Jeanette; Hart, Sara A.

2014-01-01

This study examined the association between socioemotional dispositions from the developmental propensity model and reading comprehension and whether those associations could be accounted for by level of chaos in the home. Data from 342 monozygotic and 333 same-sex dizygotic twin pairs age 7-13 years were used. A parent rated the twins on sympathy, respect for rules, negative emotionality, and daring and level of chaos in the twins’ home. Reading comprehension was measured using a state-wide school assessment. Only respect for rules significantly and uniquely predicted reading comprehension. Biometric models indicated that respect for rules was positively associated with reading comprehension via the shared environment and home chaos accounted for a significant amount of that shared environmental variance even after controlling for family income. Children with higher respect for rules have better reading comprehension scores in school and this relationship owes partly to the level of chaos in the family home. PMID:25328362

Chaos-on-a-chip secures data transmission in optical fiber links.

PubMed

Argyris, Apostolos; Grivas, Evangellos; Hamacher, Michael; Bogris, Adonis; Syvridis, Dimitris

2010-03-01

Security in information exchange plays a central role in the deployment of modern communication systems. Besides algorithms, chaos is exploited as a real-time high-speed data encryption technique which enhances the security at the hardware level of optical networks. In this work, compact, fully controllable and stably operating monolithic photonic integrated circuits (PICs) that generate broadband chaotic optical signals are incorporated in chaos-encoded optical transmission systems. Data sequences with rates up to 2.5 Gb/s with small amplitudes are completely encrypted within these chaotic carriers. Only authorized counterparts, supplied with identical chaos generating PICs that are able to synchronize and reproduce the same carriers, can benefit from data exchange with bit-rates up to 2.5Gb/s with error rates below 10(-12). Eavesdroppers with access to the communication link experience a 0.5 probability to detect correctly each bit by direct signal detection, while eavesdroppers supplied with even slightly unmatched hardware receivers are restricted to data extraction error rates well above 10(-3).

A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism

NASA Astrophysics Data System (ADS)

Chen, Jun-xin; Zhu, Zhi-liang; Fu, Chong; Yu, Hai; Zhang, Li-bo

2015-03-01

In recent years, a variety of chaos-based image cryptosystems have been investigated to meet the increasing demand for real-time secure image transmission. Most of them are based on permutation-diffusion architecture, in which permutation and diffusion are two independent procedures with fixed control parameters. This property results in two flaws. (1) At least two chaotic state variables are required for encrypting one plain pixel, in permutation and diffusion stages respectively. Chaotic state variables produced with high computation complexity are not sufficiently used. (2) The key stream solely depends on the secret key, and hence the cryptosystem is vulnerable against known/chosen-plaintext attacks. In this paper, a fast chaos-based image encryption scheme with a dynamic state variables selection mechanism is proposed to enhance the security and promote the efficiency of chaos-based image cryptosystems. Experimental simulations and extensive cryptanalysis have been carried out and the results prove the superior security and high efficiency of the scheme.

Chaos control of Hastings–Powell model by combining chaotic motions

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

Danca, Marius-F., E-mail: danca@rist.ro; Chattopadhyay, Joydev, E-mail: joydev@isical.ac.in

2016-04-15

In this paper, we propose a Parameter Switching (PS) algorithm as a new chaos control method for the Hastings–Powell (HP) system. The PS algorithm is a convergent scheme that switches the control parameter within a set of values while the controlled system is numerically integrated. The attractor obtained with the PS algorithm matches the attractor obtained by integrating the system with the parameter replaced by the averaged value of the switched parameter values. The switching rule can be applied periodically or randomly over a set of given values. In this way, every stable cycle of the HP system can bemore » approximated if its underlying parameter value equalizes the average value of the switching values. Moreover, the PS algorithm can be viewed as a generalization of Parrondo's game, which is applied for the first time to the HP system, by showing that losing strategy can win: “losing + losing = winning.” If “loosing” is replaced with “chaos” and, “winning” with “order” (as the opposite to “chaos”), then by switching the parameter value in the HP system within two values, which generate chaotic motions, the PS algorithm can approximate a stable cycle so that symbolically one can write “chaos + chaos = regular.” Also, by considering a different parameter control, new complex dynamics of the HP model are revealed.« less

Transition to chaos in an open unforced 2D flow

NASA Technical Reports Server (NTRS)

Pulliam, Thomas H.; Vastano, John A.

1993-01-01

The present numerical study of unsteady, low Reynolds number flow past a 2D airfoil attempts to ascertain the bifurcation sequence leading from simple periodic to complex aperiodic flow with rising Reynolds number, as well as to characterize the degree of chaos present in the aperiodic flow and assess the role of numerics in the modification and control of the observed bifurcation scenario. The ARC2D Navier-Stokes code is used in an unsteady time-accurate mode for most of these computations. The system undergoes a period-doubling bifurcation to chaos as the Reynolds number is increased from 800 to 1600; its chaotic attractors are characterized by estimates of the fractal dimension and partial Liapunov exponent spectra.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice

NASA Astrophysics Data System (ADS)

Bonilla, L. L.; Carretero, M.; Segura, A.

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Two-dimensional collective electron magnetotransport, oscillations, and chaos in a semiconductor superlattice.

PubMed

Bonilla, L L; Carretero, M; Segura, A

2017-12-01

When quantized, traces of classically chaotic single-particle systems include eigenvalue statistics and scars in eigenfuntions. Since 2001, many theoretical and experimental works have argued that classically chaotic single-electron dynamics influences and controls collective electron transport. For transport in semiconductor superlattices under tilted magnetic and electric fields, these theories rely on a reduction to a one-dimensional self-consistent drift model. A two-dimensional theory based on self-consistent Boltzmann transport does not support that single-electron chaos influences collective transport. This theory agrees with existing experimental evidence of current self-oscillations, predicts spontaneous collective chaos via a period doubling scenario, and could be tested unambiguously by measuring the electric potential inside the superlattice under a tilted magnetic field.

Electro-optic chaotic system based on the reverse-time chaos theory and a nonlinear hybrid feedback loop.

PubMed

Jiang, Xingxing; Cheng, Mengfan; Luo, Fengguang; Deng, Lei; Fu, Songnian; Ke, Changjian; Zhang, Minming; Tang, Ming; Shum, Ping; Liu, Deming

2016-12-12

A novel electro-optic chaos source is proposed on the basis of the reverse-time chaos theory and an analog-digital hybrid feedback loop. The analog output of the system can be determined by the numeric states of shift registers, which makes the system robust and easy to control. The dynamical properties as well as the complexity dependence on the feedback parameters are investigated in detail. The correlation characteristics of the system are also studied. Two improving strategies which were established in digital field and analog field are proposed to conceal the time-delay signature. The proposed scheme has the potential to be used in radar and optical secure communication systems.

Chaos-Assisted Quantum Tunneling and Delocalization Caused by Resonance or Near-Resonance

NASA Astrophysics Data System (ADS)

Liang, Danfu; Zhang, Jiawei; Zhang, Xili

2018-05-01

We investigate the quantum transport of a single particle trapped in a tilted optical lattice modulated with periodical delta kicks, and attempt to figure out the relationship between chaos and delocalization or quantum tunneling. We illustrate some resonant parameter lines existing in both chaotic and regular parameter regions, and discover the velocity of delocalization of particle tends to faster in the resonant line as well as the lines in which the lattice tilt is an integral multiple n of tilt driving frequency in chaotic region. While the degree of localization is linked to the distance between parameter points and resonant lines. Those useful results can be experimentally applied to control chaos-assisted transport of single particle held in optical lattices.

Chaos Modeling: An Introduction and Research Application.

ERIC Educational Resources Information Center

Newman, Isadore; And Others

1993-01-01

Introduces the basic concepts of chaos theory and chaos modeling. Relates chaos theory to qualitative research and factor analysis. Describes some current research in education and psychology using chaos theory. Claims that the philosophical implications of chaos theory have been misapplied in practical terms. (KS)

DAQ application of PC oscilloscope for chaos fiber-optic fence system based on LabVIEW

NASA Astrophysics Data System (ADS)

Lu, Manman; Fang, Nian; Wang, Lutang; Huang, Zhaoming; Sun, Xiaofei

2011-12-01

In order to obtain simultaneously high sample rate and large buffer in data acquisition (DAQ) for a chaos fiber-optic fence system, we developed a double-channel high-speed DAQ application of a digital oscilloscope of PicoScope 5203 based on LabVIEW. We accomplished it by creating call library function (CLF) nodes to call the DAQ functions in the two dynamic link libraries (DLLs) of PS5000.dll and PS5000wrap.dll provided by Pico Technology Company. The maximum real-time sample rate of the DAQ application can reach 1GS/s. We can control the resolutions of the application at the sample time and data amplitudes by changing their units in the block diagram, and also control the start and end times of the sampling operations. The experimental results show that the application has enough high sample rate and large buffer to meet the demanding DAQ requirements of the chaos fiber-optic fence system.

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

Li, Qingdu; Guo, Jianli; Yang, Xiao-Song, E-mail: yangxs@hust.edu.cn

We present some rich new complex gaits in the simple walking model with upper body by Wisse et al. in [Robotica 22, 681 (2004)]. We first show that the stable gait found by Wisse et al. may become chaotic via period-doubling bifurcations. Such period-doubling routes to chaos exist for all parameters, such as foot mass, upper body mass, body length, hip spring stiffness, and slope angle. Then, we report three new gaits with period 3, 4, and 6; for each gait, there is also a period-doubling route to chaos. Finally, we show a practical method for finding a topological horseshoemore » in 3D Poincaré map, and present a rigorous verification of chaos from these gaits.« less

Analysis of correlations and search for evidence of deterministic chaos in rhythmic motor control by the human brain

NASA Astrophysics Data System (ADS)

Roberts, Sean; Eykholt, R.; Thaut, Michael H.

2000-08-01

We investigate rhythmic finger tapping in both the presence and the absence of a metronome. We examine both the time intervals between taps and the time lags between the stimulus tones from the metronome and the response taps by the subject. We analyze the correlations in these data sets, and we search for evidence of deterministic chaos, as opposed to randomness, in the fluctuations.

Wave Chaos and Coupling to EM Structures

DTIC Science & Technology

2006-07-01

Antonsen, E. Ott and S. Anlage, Aspects of the Scattering and Impedance Properties of Chaotic Microwave Cavities, Acta Physica Polonica A 109, 65...other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a ...currently valid OMB control number. 1. REPORT DATE JUL 2006 2. REPORT TYPE N/ A 3. DATES COVERED - 4. TITLE AND SUBTITLE Wave Chaos and Coupling

Fractal Point Process and Queueing Theory and Application to Communication Networks

DTIC Science & Technology

1999-12-31

use of nonlinear dynamics and chaos in the design of innovative analog error-protection codes for com- munications applications. In the chaos...the fol- lowing theses, patent, and papers. 1. A. Narula, M. D. Trott , and G. W. Wornell, "Information-Theoretic Analysis of Multiple-Antenna...Bounds," in Proc. Int. Conf. Dec. Control, (Japan), Dec. 1996. 5. G. W. Wornell and M. D. Trott , "Efficient Signal Processing Tech- niques for

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.

Analysis and control of the dynamical response of a higher order drifting oscillator

PubMed Central

Páez Chávez, Joseph; Pavlovskaia, Ekaterina; Wiercigroch, Marian

2018-01-01

This paper studies a position feedback control strategy for controlling a higher order drifting oscillator which could be used in modelling vibro-impact drilling. Special attention is given to two control issues, eliminating bistability and suppressing chaos, which may cause inefficient and unstable drilling. Numerical continuation methods implemented via the continuation platform COCO are adopted to investigate the dynamical response of the system. Our analyses show that the proposed controller is capable of eliminating coexisting attractors and mitigating chaotic behaviour of the system, providing that its feedback control gain is chosen properly. Our investigations also reveal that, when the slider’s property modelling the drilled formation changes, the rate of penetration for the controlled drilling can be significantly improved. PMID:29507508

Analysis and control of the dynamical response of a higher order drifting oscillator

NASA Astrophysics Data System (ADS)

Liu, Yang; Páez Chávez, Joseph; Pavlovskaia, Ekaterina; Wiercigroch, Marian

2018-02-01

This paper studies a position feedback control strategy for controlling a higher order drifting oscillator which could be used in modelling vibro-impact drilling. Special attention is given to two control issues, eliminating bistability and suppressing chaos, which may cause inefficient and unstable drilling. Numerical continuation methods implemented via the continuation platform COCO are adopted to investigate the dynamical response of the system. Our analyses show that the proposed controller is capable of eliminating coexisting attractors and mitigating chaotic behaviour of the system, providing that its feedback control gain is chosen properly. Our investigations also reveal that, when the slider's property modelling the drilled formation changes, the rate of penetration for the controlled drilling can be significantly improved.

Nonlinear dynamics as an engine of computation.

PubMed

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

2017-03-06

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

Nonlinear dynamics as an engine of computation

PubMed Central

Lindner, John F.; Ditto, William L.

2017-01-01

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

Robustness analysis of an air heating plant and control law by using polynomial chaos

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

Colón, Diego; Ferreira, Murillo A. S.; Bueno, Átila M.

2014-12-10

This paper presents a robustness analysis of an air heating plant with a multivariable closed-loop control law by using the polynomial chaos methodology (MPC). The plant consists of a PVC tube with a fan in the air input (that forces the air through the tube) and a mass flux sensor in the output. A heating resistance warms the air as it flows inside the tube, and a thermo-couple sensor measures the air temperature. The plant has thus two inputs (the fan's rotation intensity and heat generated by the resistance, both measured in percent of the maximum value) and two outputsmore » (air temperature and air mass flux, also in percent of the maximal value). The mathematical model is obtained by System Identification techniques. The mass flux sensor, which is nonlinear, is linearized and the delays in the transfer functions are properly approximated by non-minimum phase transfer functions. The resulting model is transformed to a state-space model, which is used for control design purposes. The multivariable robust control design techniques used is the LQG/LTR, and the controllers are validated in simulation software and in the real plant. Finally, the MPC is applied by considering some of the system's parameters as random variables (one at a time, and the system's stochastic differential equations are solved by expanding the solution (a stochastic process) in an orthogonal basis of polynomial functions of the basic random variables. This method transforms the stochastic equations in a set of deterministic differential equations, which can be solved by traditional numerical methods (That is the MPC). Statistical data for the system (like expected values and variances) are then calculated. The effects of randomness in the parameters are evaluated in the open-loop and closed-loop pole's positions.« less

Nitrite-Oxidizing Bacteria Community Composition and Diversity Are Influenced by Fertilizer Regimes, but Are Independent of the Soil Aggregate in Acidic Subtropical Red Soil

PubMed Central

Han, Shun; Li, Xiang; Luo, Xuesong; Wen, Shilin; Chen, Wenli; Huang, Qiaoyun

2018-01-01

Nitrification is the two-step aerobic oxidation of ammonia to nitrate via nitrite in the nitrogen-cycle on earth. However, very limited information is available on how fertilizer regimes affect the distribution of nitrite oxidizers, which are involved in the second step of nitrification, across aggregate size classes in soil. In this study, the community compositions of nitrite oxidizers (Nitrobacter and Nitrospira) were characterized from a red soil amended with four types of fertilizer regimes over a 26-year fertilization experiment, including control without fertilizer (CK), swine manure (M), chemical fertilization (NPK), and chemical/organic combined fertilization (MNPK). Our results showed that the addition of M and NPK significantly decreased Nitrobacter Shannon and Chao1 index, while M and MNPK remarkably increased Nitrospira Shannon and Chao1 index, and NPK considerably decreased Nitrospira Shannon and Chao1 index, with the greatest diversity achieved in soils amended with MNPK. However, the soil aggregate fractions had no impact on that alpha-diversity of Nitrobacter and Nitrospira under the fertilizer treatment. Soil carbon, nitrogen and phosphorus in the soil had a significant correlation with Nitrospira Shannon and Chao1 diversity index, while total potassium only had a significant correlation with Nitrospira Shannon diversity index. However, all of them had no significant correlation with Nitrobacter Shannon and Chao1 diversity index. The resistance indices for alpha-diversity indexes (Shannon and Chao1) of Nitrobacter were higher than those of Nitrospira in response to the fertilization regimes. Manure fertilizer is important in enhancing the Nitrospira Shannon and Chao1 index resistance. Principal co-ordinate analysis revealed that Nitrobacter- and Nitrospira-like NOB communities under four fertilizer regimes were differentiated from each other, but soil aggregate fractions had less effect on the nitrite oxidizers community. Redundancy analysis and Mantel test indicated that soil nitrogen, carbon, phosphorus, and available potassium content were important environmental attributes that control the Nitrobacter- and Nitrospira-like NOB community structure across different fertilization treatments under aggregate levels in the red soil. In general, nitrite-oxidizing bacteria community composition and alpha-diversity are depending on fertilizer regimes, but independent of the soil aggregate. PMID:29867799

Subharmonic generation, chaos, and subharmonic resurrection in an acoustically driven fluid-filled cavity.

PubMed

Cantrell, John H; Adler, Laszlo; Yost, William T

2015-02-01

Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5 MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2 nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported.

Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy.

PubMed

Pillai, Nikhil; Craig, Morgan; Dokoumetzidis, Aristeidis; Schwartz, Sorell L; Bies, Robert; Freedman, Immanuel

2018-06-19

In mathematical pharmacology, models are constructed to confer a robust method for optimizing treatment. The predictive capability of pharmacological models depends heavily on the ability to track the system and to accurately determine parameters with reference to the sensitivity in projected outcomes. To closely track chaotic systems, one may choose to apply chaos synchronization. An advantageous byproduct of this methodology is the ability to quantify model parameters. In this paper, we illustrate the use of chaos synchronization combined with Nelder-Mead search to estimate parameters of the well-known Kirschner-Panetta model of IL-2 immunotherapy from noisy data. Chaos synchronization with Nelder-Mead search is shown to provide more accurate and reliable estimates than Nelder-Mead search based on an extended least squares (ELS) objective function. Our results underline the strength of this approach to parameter estimation and provide a broader framework of parameter identification for nonlinear models in pharmacology. Copyright © 2018 Elsevier Ltd. All rights reserved.

Walking dynamics of the passive compass-gait model under OGY-based control: Emergence of bifurcations and chaos

NASA Astrophysics Data System (ADS)

Gritli, Hassène; Belghith, Safya

2017-06-01

An analysis of the passive dynamic walking of a compass-gait biped model under the OGY-based control approach using the impulsive hybrid nonlinear dynamics is presented in this paper. We describe our strategy for the development of a simplified analytical expression of a controlled hybrid Poincaré map and then for the design of a state-feedback control. Our control methodology is based mainly on the linearization of the impulsive hybrid nonlinear dynamics around a desired nominal one-periodic hybrid limit cycle. Our analysis of the controlled walking dynamics is achieved by means of bifurcation diagrams. Some interesting nonlinear phenomena are displayed, such as the period-doubling bifurcation, the cyclic-fold bifurcation, the period remerging, the period bubbling and chaos. A comparison between the raised phenomena in the impulsive hybrid nonlinear dynamics and the hybrid Poincaré map under control was also presented.

Topological chaos, braiding and bifurcation of almost-cyclic sets.

PubMed

Grover, Piyush; Ross, Shane D; Stremler, Mark A; Kumar, Pankaj

2012-12-01

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.

Adaptive polynomial chaos techniques for uncertainty quantification of a gas cooled fast reactor transient

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

Perko, Z.; Gilli, L.; Lathouwers, D.

2013-07-01

Uncertainty quantification plays an increasingly important role in the nuclear community, especially with the rise of Best Estimate Plus Uncertainty methodologies. Sensitivity analysis, surrogate models, Monte Carlo sampling and several other techniques can be used to propagate input uncertainties. In recent years however polynomial chaos expansion has become a popular alternative providing high accuracy at affordable computational cost. This paper presents such polynomial chaos (PC) methods using adaptive sparse grids and adaptive basis set construction, together with an application to a Gas Cooled Fast Reactor transient. Comparison is made between a new sparse grid algorithm and the traditionally used techniquemore » proposed by Gerstner. An adaptive basis construction method is also introduced and is proved to be advantageous both from an accuracy and a computational point of view. As a demonstration the uncertainty quantification of a 50% loss of flow transient in the GFR2400 Gas Cooled Fast Reactor design was performed using the CATHARE code system. The results are compared to direct Monte Carlo sampling and show the superior convergence and high accuracy of the polynomial chaos expansion. Since PC techniques are easy to implement, they can offer an attractive alternative to traditional techniques for the uncertainty quantification of large scale problems. (authors)« less

Analysis of tristable energy harvesting system having fractional order viscoelastic material

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

Oumbé Tékam, G. T.; Woafo, P.; Kitio Kwuimy, C. A.

2015-01-15

A particular attention is devoted to analyze the dynamics of a strongly nonlinear energy harvester having fractional order viscoelastic flexible material. The strong nonlinearity is obtained from the magnetic interaction between the end free of the flexible material and three equally spaced magnets. Periodic responses are computed using the KrylovBogoliubov averaging method, and the effects of fractional order damping on the output electric energy are analyzed. It is obtained that the harvested energy is enhanced for small order of the fractional derivative. Considering the order and strength of the fractional viscoelastic property as control parameter, the complexity of the systemmore » response is investigated through the Melnikov criteria for horseshoes chaos, which allows us to derive the mathematical expression of the boundary between intra-well motion and bifurcations appearance domain. We observe that the order and strength of the fractional viscoelastic property can be effectively used to control chaos in the system. The results are confirmed by the smooth and fractal shape of the basin of attraction as the order of derivative decreases. The bifurcation diagrams and the corresponding Lyapunov exponents are plotted to get insight into the nonlinear response of the system.« less

Multi-Baker Map as a Model of Digital PD Control

NASA Astrophysics Data System (ADS)

Csernák, Gábor; Gyebrószki, Gergely; Stépán, Gábor

Digital stabilization of unstable equilibria of linear systems may lead to small amplitude stochastic-like oscillations. We show that these vibrations can be related to a deterministic chaotic dynamics induced by sampling and quantization. A detailed analytical proof of chaos is presented for the case of a PD controlled oscillator: it is shown that there exists a finite attracting domain in the phase-space, the largest Lyapunov exponent is positive and the existence of a Smale horseshoe is also pointed out. The corresponding two-dimensional micro-chaos map is a multi-baker map, i.e. it consists of a finite series of baker’s maps.

Distinguishing Error from Chaos in Ecological Time Series

NASA Astrophysics Data System (ADS)

Sugihara, George; Grenfell, Bryan; May, Robert M.

1990-11-01

Over the years, there has been much discussion about the relative importance of environmental and biological factors in regulating natural populations. Often it is thought that environmental factors are associated with stochastic fluctuations in population density, and biological ones with deterministic regulation. We revisit these ideas in the light of recent work on chaos and nonlinear systems. We show that completely deterministic regulatory factors can lead to apparently random fluctuations in population density, and we then develop a new method (that can be applied to limited data sets) to make practical distinctions between apparently noisy dynamics produced by low-dimensional chaos and population variation that in fact derives from random (high-dimensional)noise, such as environmental stochasticity or sampling error. To show its practical use, the method is first applied to models where the dynamics are known. We then apply the method to several sets of real data, including newly analysed data on the incidence of measles in the United Kingdom. Here the additional problems of secular trends and spatial effects are explored. In particular, we find that on a city-by-city scale measles exhibits low-dimensional chaos (as has previously been found for measles in New York City), whereas on a larger, country-wide scale the dynamics appear as a noisy two-year cycle. In addition to shedding light on the basic dynamics of some nonlinear biological systems, this work dramatizes how the scale on which data is collected and analysed can affect the conclusions drawn.

A cryptographic hash function based on chaotic network automata

NASA Astrophysics Data System (ADS)

Machicao, Jeaneth; Bruno, Odemir M.

2017-12-01

Chaos theory has been used to develop several cryptographic methods relying on the pseudo-random properties extracted from simple nonlinear systems such as cellular automata (CA). Cryptographic hash functions (CHF) are commonly used to check data integrity. CHF “compress” arbitrary long messages (input) into much smaller representations called hash values or message digest (output), designed to prevent the ability to reverse the hash values into the original message. This paper proposes a chaos-based CHF inspired on an encryption method based on chaotic CA rule B1357-S2468. Here, we propose an hybrid model that combines CA and networks, called network automata (CNA), whose chaotic spatio-temporal outputs are used to compute a hash value. Following the Merkle and Damgård model of construction, a portion of the message is entered as the initial condition of the network automata, so that the rest parts of messages are iteratively entered to perturb the system. The chaotic network automata shuffles the message using flexible control parameters, so that the generated hash value is highly sensitive to the message. As demonstrated in our experiments, the proposed model has excellent pseudo-randomness and sensitivity properties with acceptable performance when compared to conventional hash functions.

The Smaller Alignment Index (SALI) applied in a study of stellar orbits in barred galaxies potential models using the LP-VIcode

NASA Astrophysics Data System (ADS)

Caritá, Lucas Antonio; Rodrigues, Irapuan; Puerari, Ivânio; Schiavo, Luiz Eduardo Camargo Aranha

2018-04-01

The Smaller Alignment Index (SALI) is a mathematical tool, not yet conventional, for chaos detection in the phase space of Hamiltonian Dynamical Systems. The SALI values has temporal behaviors very specific to ordered or chaotic motions, what makes the distinction between order and chaos easily observable in these systems. In this paper, this method will be applied to the stability study of stellar orbits immersed in gravitational potential of barred galaxies, since the motion of a test particle in a rotating barred galaxy model is given by a Hamiltonian function. Extracting four parameter sets from the Manos and Athanassoula (2011) work and elaborating a different initial conditions set for each case, we were able to introduce another point of view of their stability study for two degrees of freedom. We have also introduced two new extreme models that corroborates with the conclusions that more axisymmetric bars create an environment with less chaos and that more massive bars create an environment with more chaos. Separate studies were carried out for prograde and retrograde orbits that showed that the retrograde orbits seem more conducive to chaos. To perform all the orbits integrations we used the LP-VIcode program.

Topological characterization and early detection of bifurcations and chaos in complex systems using persistent homology.

PubMed

Mittal, Khushboo; Gupta, Shalabh

2017-05-01

Early detection of bifurcations and chaos and understanding their topological characteristics are essential for safe and reliable operation of various electrical, chemical, physical, and industrial processes. However, the presence of non-linearity and high-dimensionality in system behavior makes this analysis a challenging task. The existing methods for dynamical system analysis provide useful tools for anomaly detection (e.g., Bendixson-Dulac and Poincare-Bendixson criteria can detect the presence of limit cycles); however, they do not provide a detailed topological understanding about system evolution during bifurcations and chaos, such as the changes in the number of subcycles and their positions, lifetimes, and sizes. This paper addresses this research gap by using topological data analysis as a tool to study system evolution and develop a mathematical framework for detecting the topological changes in the underlying system using persistent homology. Using the proposed technique, topological features (e.g., number of relevant k-dimensional holes, etc.) are extracted from nonlinear time series data which are useful for deeper analysis of the system behavior and early detection of bifurcations and chaos. When applied to a Logistic map, a Duffing oscillator, and a real life Op-amp based Jerk circuit, these features are shown to accurately characterize the system dynamics and detect the onset of chaos.

Geometric chaos indicators and computations of the spherical hypertube manifolds of the spatial circular restricted three-body problem

NASA Astrophysics Data System (ADS)

Guzzo, Massimiliano; Lega, Elena

2018-06-01

The circular restricted three-body problem has five relative equilibria L1 ,L2, . . . ,L5. The invariant stable-unstable manifolds of the center manifolds originating at the partially hyperbolic equilibria L1 ,L2 have been identified as the separatrices for the motions which transit between the regions of the phase-space which are internal or external with respect to the two massive bodies. While the stable and unstable manifolds of the planar problem have been extensively studied both theoretically and numerically, the spatial case has not been as deeply investigated. This paper is devoted to the global computation of these manifolds in the spatial case with a suitable finite time chaos indicator. The definition of the chaos indicator is not trivial, since the mandatory use of the regularizing Kustaanheimo-Stiefel variables may introduce discontinuities in the finite time chaos indicators. From the study of such discontinuities, we define geometric chaos indicators which are globally defined and smooth, and whose ridges sharply approximate the stable and unstable manifolds of the center manifolds of L1 ,L2. We illustrate the method for the Sun-Jupiter mass ratio, and represent the topology of the asymptotic manifolds using sections and three-dimensional representations.

Adaptive fuzzy dynamic surface control for the chaotic permanent magnet synchronous motor using Nussbaum gain.

PubMed

Luo, Shaohua

2014-09-01

This paper is concerned with the problem of adaptive fuzzy dynamic surface control (DSC) for the permanent magnet synchronous motor (PMSM) system with chaotic behavior, disturbance and unknown control gain and parameters. Nussbaum gain is adopted to cope with the situation that the control gain is unknown. And the unknown items can be estimated by fuzzy logic system. The proposed controller guarantees that all the signals in the closed-loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal. Finally, the numerical simulations indicate that the proposed scheme can suppress the chaos of PMSM and show the effectiveness and robustness of the proposed method.

Deconstructing spatiotemporal chaos using local symbolic dynamics.

PubMed

Pethel, Shawn D; Corron, Ned J; Bollt, Erik

2007-11-23

We find that the global symbolic dynamics of a diffusively coupled map lattice is well approximated by a very small local model for weak to moderate coupling strengths. A local symbolic model is a truncation of the full symbolic model to one that considers only a single element and a few neighbors. Using interval analysis, we give rigorous results for a range of coupling strengths and different local model widths. Examples are presented of extracting a local symbolic model from data and of controlling spatiotemporal chaos.

Investigating a link between large and small-scale chaos features on Europa

NASA Astrophysics Data System (ADS)

Tognetti, L.; Rhoden, A.; Nelson, D. M.

2017-12-01

Chaos is one of the most recognizable, and studied, features on Europa's surface. Most models of chaos formation invoke liquid water at shallow depths within the ice shell; the liquid destabilizes the overlying ice layer, breaking it into mobile rafts and destroying pre-existing terrain. This class of model has been applied to both large-scale chaos like Conamara and small-scale features (i.e. microchaos), which are typically <10 km in diameter. Currently unknown, however, is whether both large-scale and small-scale features are produced together, e.g. through a network of smaller sills linked to a larger liquid water pocket. If microchaos features do form as satellites of large-scale chaos features, we would expect a drop off in the number density of microchaos with increasing distance from the large chaos feature; the trend should not be observed in regions without large-scale chaos features. Here, we test the hypothesis that large chaos features create "satellite" systems of smaller chaos features. Either outcome will help us better understand the relationship between large-scale chaos and microchaos. We focus first on regions surrounding the large chaos features Conamara and Murias (e.g. the Mitten). We map all chaos features within 90,000 sq km of the main chaos feature and assign each one a ranking (High Confidence, Probable, or Low Confidence) based on the observed characteristics of each feature. In particular, we look for a distinct boundary, loss of preexisting terrain, the existence of rafts or blocks, and the overall smoothness of the feature. We also note features that are chaos-like but lack sufficient characteristics to be classified as chaos. We then apply the same criteria to map microchaos features in regions of similar area ( 90,000 sq km) that lack large chaos features. By plotting the distribution of microchaos with distance from the center point of the large chaos feature or the mapping region (for the cases without a large feature), we determine whether there is a distinct signature linking large-scale chaos features with nearby microchaos. We discuss the implications of these results on the process of chaos formation and the extent of liquid water within Europa's ice shell.

Chaos, Complexity and Deterrence

DTIC Science & Technology

2000-04-19

populations of adversary countries but which seldom affect their leadership . Conclusion The jury is still out on the applicability of chaos theory to...Advent of Chaos Chaos theory in the West (considerable work on chaos was also conducted in the Soviet Union) developed from the 1960s work of...predicted by his model over time.1 This discovery, sensitivity to initial conditions, is one of the fundamental characteristics of chaos theory . Lorenz

Local Bifurcation Control,

DTIC Science & Technology

1987-01-01

X, (0) in the open left half complex plane . (S) Eq. (1) has an equilibrium zo(p) when u = 0. Furthermore, the linearization of (1) near z0, p = 0...possesses a simple eigenvalue X(p) with XI(O) = 0, X; (0) 74 0, with the remaining eigenvalues X(0), . . . , X. (0) in the open left half complex plane ...Conference, Lausanne, June 1984. (11) "Chaos In dynamical systems by the Poincare -Melnikov-Arnold method" Proc. ARO Workshop, March 1984. %I 2.I JUAN C

Numerical investigation of bubble nonlinear dynamics characteristics

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

Shi, Jie, E-mail: shijie@hrbeu.edu.cn; Yang, Desen; Shi, Shengguo

2015-10-28

The complicated dynamical behaviors of bubble oscillation driven by acoustic wave can provide favorable conditions for many engineering applications. On the basis of Keller-Miksis model, the influences of control parameters, including acoustic frequency, acoustic pressure and radius of gas bubble, are discussed by utilizing various numerical analysis methods, Furthermore, the law of power spectral variation is studied. It is shown that the complicated dynamic behaviors of bubble oscillation driven by acoustic wave, such as bifurcation and chaos, further the stimulated scattering processes are revealed.

Reinforcement Learning with Orthonormal Basis Adaptation Based on Activity-Oriented Index Allocation

NASA Astrophysics Data System (ADS)

Satoh, Hideki

An orthonormal basis adaptation method for function approximation was developed and applied to reinforcement learning with multi-dimensional continuous state space. First, a basis used for linear function approximation of a control function is set to an orthonormal basis. Next, basis elements with small activities are replaced with other candidate elements as learning progresses. As this replacement is repeated, the number of basis elements with large activities increases. Example chaos control problems for multiple logistic maps were solved, demonstrating that the method for adapting an orthonormal basis can modify a basis while holding the orthonormality in accordance with changes in the environment to improve the performance of reinforcement learning and to eliminate the adverse effects of redundant noisy states.

Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model.

PubMed

Papasavvas, Christoforos A; Wang, Yujiang; Trevelyan, Andrew J; Kaiser, Marcus

2015-09-01

Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics.

Maintenance and suppression of chaos by weak harmonic perturbations: a unified view.

PubMed

Chacón, R

2001-02-26

General results concerning maintenance or enhancement of chaos are presented for dissipative systems subjected to two harmonic perturbations (one chaos inducing and the other chaos enhancing). The connection with previous results on chaos suppression is also discussed in a general setting. It is demonstrated that, in general, a second harmonic perturbation can reliably play an enhancer or inhibitor role by solely adjusting its initial phase. Numerical results indicate that general theoretical findings concerning periodic chaos-inducing perturbations also work for aperiodic chaos-inducing perturbations, and in arrays of identical chaotic coupled oscillators.

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Kuznetsova, A. A.; Buyadzhi, A. A.; Prepelitsa, G. P.; Ternovsky, V. B.

2017-10-01

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

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.

Fault detection and isolation in GPS receiver autonomous integrity monitoring based on chaos particle swarm optimization-particle filter algorithm

NASA Astrophysics Data System (ADS)

Wang, Ershen; Jia, Chaoying; Tong, Gang; Qu, Pingping; Lan, Xiaoyu; Pang, Tao

2018-03-01

The receiver autonomous integrity monitoring (RAIM) is one of the most important parts in an avionic navigation system. Two problems need to be addressed to improve this system, namely, the degeneracy phenomenon and lack of samples for the standard particle filter (PF). However, the number of samples cannot adequately express the real distribution of the probability density function (i.e., sample impoverishment). This study presents a GPS receiver autonomous integrity monitoring (RAIM) method based on a chaos particle swarm optimization particle filter (CPSO-PF) algorithm with a log likelihood ratio. The chaos sequence generates a set of chaotic variables, which are mapped to the interval of optimization variables to improve particle quality. This chaos perturbation overcomes the potential for the search to become trapped in a local optimum in the particle swarm optimization (PSO) algorithm. Test statistics are configured based on a likelihood ratio, and satellite fault detection is then conducted by checking the consistency between the state estimate of the main PF and those of the auxiliary PFs. Based on GPS data, the experimental results demonstrate that the proposed algorithm can effectively detect and isolate satellite faults under conditions of non-Gaussian measurement noise. Moreover, the performance of the proposed novel method is better than that of RAIM based on the PF or PSO-PF algorithm.

How to couple identical ring oscillators to get quasiperiodicity, extended chaos, multistability, and the loss of symmetry

NASA Astrophysics Data System (ADS)

Hellen, Edward H.; Volkov, Evgeny

2018-09-01

We study the dynamical regimes demonstrated by a pair of identical 3-element ring oscillators (reduced version of synthetic 3-gene genetic Repressilator) coupled using the design of the 'quorum sensing (QS)' process natural for interbacterial communications. In this work QS is implemented as an additional network incorporating elements of the ring as both the source and the activation target of the fast diffusion QS signal. This version of indirect nonlinear coupling, in cooperation with the reasonable extension of the parameters which control properties of the isolated oscillators, exhibits the formation of a very rich array of attractors. Using a parameter-space defined by the individual oscillator amplitude and the coupling strength, we found the extended area of parameter-space where the identical oscillators demonstrate quasiperiodicity, which evolves to chaos via the period doubling of either resonant limit cycles or complex antiphase symmetric limit cycles with five winding numbers. The symmetric chaos extends over large parameter areas up to its loss of stability, followed by a system transition to an unexpected mode: an asymmetric limit cycle with a winding number of 1:2. In turn, after long evolution across the parameter-space, this cycle demonstrates a period doubling cascade which restores the symmetry of dynamics by formation of symmetric chaos, which nevertheless preserves the memory of the asymmetric limit cycles in the form of stochastic alternating "polarization" of the time series. All stable attractors coexist with some others, forming remarkable and complex multistability including the coexistence of torus and limit cycles, chaos and regular attractors, symmetric and asymmetric regimes. We traced the paths and bifurcations leading to all areas of chaos, and presented a detailed map of all transformations of the dynamics.

Adaptation to the edge of chaos in a self-starting Kerr-lens mode-locked laser

NASA Astrophysics Data System (ADS)

Hsu, C. C.; Lin, J. H.; Hsieh, W. F.

2009-08-01

We experimentally and numerically demonstrated that self-focusing acts as a slow-varying control parameter that suppresses the transient chaos to reach a stable mode-locking (ML) state in a self-starting Kerr-lens mode-locked Ti:sapphire laser without external modulation and feedback control. Based on Fox-Li’s approach, including the self-focusing effect, the theoretical simulation reveals that the self-focusing effect is responsible for the self-adaptation. The self-adaptation occurs at the boundary between the chaotic and continuous output regions in which the laser system begins with a transient chaotic state with fractal correlation dimension, and then evolves with reducing dimension into the stable ML state.

Chaotic dynamics of flexible beams driven by external white noise

NASA Astrophysics Data System (ADS)

Awrejcewicz, J.; Krysko, A. V.; Papkova, I. V.; Zakharov, V. M.; Erofeev, N. P.; Krylova, E. Yu.; Mrozowski, J.; Krysko, V. A.

2016-10-01

Mathematical models of continuous structural members (beams, plates and shells) subjected to an external additive white noise are studied. The structural members are considered as systems with infinite number of degrees of freedom. We show that in mechanical structural systems external noise can not only lead to quantitative changes in the system dynamics (that is obvious), but also cause the qualitative, and sometimes surprising changes in the vibration regimes. Furthermore, we show that scenarios of the transition from regular to chaotic regimes quantified by Fast Fourier Transform (FFT) can lead to erroneous conclusions, and a support of the wavelet analysis is needed. We have detected and illustrated the modifications of classical three scenarios of transition from regular vibrations to deterministic chaos. The carried out numerical experiment shows that the white noise lowers the threshold for transition into spatio-temporal chaotic dynamics. A transition into chaos via the proposed modified scenarios developed in this work is sensitive to small noise and significantly reduces occurrence of periodic vibrations. Increase of noise intensity yields decrease of the duration of the laminar signal range, i.e., time between two successive turbulent bursts decreases. Scenario of transition into chaos of the studied mechanical structures essentially depends on the control parameters, and it can be different in different zones of the constructed charts (control parameter planes). Furthermore, we found an interesting phenomenon, when increase of the noise intensity yields surprisingly the vibrational characteristics with a lack of noisy effect (chaos is destroyed by noise and windows of periodicity appear).

Does chaos assist localization or delocalization?

PubMed

Tan, Jintao; Lu, Gengbiao; Luo, Yunrong; Hai, Wenhua

2014-12-01

We aim at a long-standing contradiction between chaos-assisted tunneling and chaos-related localization study quantum transport of a single particle held in an amplitude-modulated and tilted optical lattice. We find some near-resonant regions crossing chaotic and regular regions in the parameter space, and demonstrate that chaos can heighten velocity of delocalization in the chaos-resonance overlapping regions, while chaos may aid localization in the other chaotic regions. The degree of localization enhances with increasing the distance between parameter points and near-resonant regions. The results could be useful for experimentally manipulating chaos-assisted transport of single particles in optical or solid-state lattices.

Household chaos, sociodemographic risk, coparenting, and parent-infant relations during infants' first year.

PubMed

Whitesell, Corey J; Teti, Douglas M; Crosby, Brian; Kim, Bo-Ram

2015-04-01

Household chaos is a construct often overlooked in studies of human development, despite its theoretical links with the integrity of individual well-being, family processes, and child development. The present longitudinal study examined relations between household chaos and well-established correlates of chaos (sociodemographic risk, major life events, and personal distress) and several constructs that, to date, are theoretically linked with chaos but never before assessed as correlates (quality of coparenting and emotional availability with infants at bedtime). In addressing this aim, we introduce a new measure of household chaos (the Descriptive In-home Survey of Chaos--Observer ReporteD, or DISCORD), wholly reliant on independent observer report, which draws from household chaos theory and prior empirical work but extends the measurement of chaos to include information about families' compliance with a home visiting protocol. Household chaos was significantly associated with socioeconomic risk, negative life events, less favorable coparenting, and less emotionally available bedtime parenting, but not with personal distress. These findings emphasize the need to examine household chaos as a direct and indirect influence on child and family outcomes, as a moderator of intervention attempts to improving parenting and child development, and as a target of intervention in its own right. (c) 2015 APA, all rights reserved).

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

PubMed

Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

When the firm prevents the crash: Avoiding market collapse with partial control.

PubMed

Levi, Asaf; Sabuco, Juan; A F Sanjuán, Miguel

2017-01-01

Market collapse is one of the most dramatic events in economics. Such a catastrophic event can emerge from the nonlinear interactions between the economic agents at the micro level of the economy. Transient chaos might be a good description of how a collapsing market behaves. In this work, we apply a new control method, the partial control method, with the goal of avoiding this disastrous event. Contrary to common control methods that try to influence the system from the outside, here the market is controlled from the bottom up by one of the most basic components of the market-the firm. This is the first time that the partial control method is applied on a strictly economical system in which we also introduce external disturbances. We show how the firm is capable of controlling the system avoiding the collapse by only adjusting the selling price of the product or the quantity of production in accordance to the market circumstances. Additionally, we demonstrate how a firm with a large market share is capable of influencing the demand achieving price stability across the retail and wholesale markets. Furthermore, we prove that the control applied in both cases is much smaller than the external disturbances.

Advanced Targeting Cost Function Design for Evolutionary Optimization of Control of Logistic Equation

NASA Astrophysics Data System (ADS)

Senkerik, Roman; Zelinka, Ivan; Davendra, Donald; Oplatkova, Zuzana

2010-06-01

This research deals with the optimization of the control of chaos by means of evolutionary algorithms. This work is aimed on an explanation of how to use evolutionary algorithms (EAs) and how to properly define the advanced targeting cost function (CF) securing very fast and precise stabilization of desired state for any initial conditions. As a model of deterministic chaotic system, the one dimensional Logistic equation was used. The evolutionary algorithm Self-Organizing Migrating Algorithm (SOMA) was used in four versions. For each version, repeated simulations were conducted to outline the effectiveness and robustness of used method and targeting CF.

Psychotherapy Is Chaotic—(Not Only) in a Computational World

PubMed Central

Schiepek, Günter K.; Viol, Kathrin; Aichhorn, Wolfgang; Hütt, Marc-Thorsten; Sungler, Katharina; Pincus, David; Schöller, Helmut J.

2017-01-01

Objective: The aim of this article is to outline the role of chaotic dynamics in psychotherapy. Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client's functioning can be integrated into a comprehensive nonlinear model of human change processes. Methods: The model combines 5 variables (intensity of emotions, problem intensity, motivation to change, insight and new perspectives, therapeutic success) and 4 parameters into a set of 5 coupled nonlinear difference equations. The results of these simulations are presented as time series, as phase space embedding of these time series (i.e., attractors), and as bifurcation diagrams. Results: The model creates chaotic dynamics, phase transition-like phenomena, bi- or multi-stability, and sensibility of the dynamic patterns on parameter drift. These features are predicted by chaos theory and by Synergetics and correspond to empirical findings. The spectrum of these behaviors illustrates the complexity of psychotherapeutic processes. Conclusion: The model contributes to the development of an integrative conceptualization of psychotherapy. It is consistent with the state of scientific knowledge of common factors, as well as other psychological topics, such as: motivation, emotion regulation, and cognitive processing. The role of chaos theory is underpinned, not only in the world of computer simulations, but also in practice. In practice, chaos demands technologies capable of real-time monitoring and reporting on the nonlinear features of the ongoing process (e.g., its stability or instability). Based on this monitoring, a client-centered, continuous, and cooperative process of feedback and control becomes possible. By contrast, restricted predictability and spontaneous changes challenge the usefulness of prescriptive treatment manuals or other predefined programs of psychotherapy. PMID:28484401

Psychotherapy Is Chaotic-(Not Only) in a Computational World.

PubMed

Schiepek, Günter K; Viol, Kathrin; Aichhorn, Wolfgang; Hütt, Marc-Thorsten; Sungler, Katharina; Pincus, David; Schöller, Helmut J

2017-01-01

Objective: The aim of this article is to outline the role of chaotic dynamics in psychotherapy. Besides some empirical findings of chaos at different time scales, the focus is on theoretical modeling of change processes explaining and simulating chaotic dynamics. It will be illustrated how some common factors of psychotherapeutic change and psychological hypotheses on motivation, emotion regulation, and information processing of the client's functioning can be integrated into a comprehensive nonlinear model of human change processes. Methods: The model combines 5 variables (intensity of emotions, problem intensity, motivation to change, insight and new perspectives, therapeutic success) and 4 parameters into a set of 5 coupled nonlinear difference equations. The results of these simulations are presented as time series, as phase space embedding of these time series (i.e., attractors), and as bifurcation diagrams. Results: The model creates chaotic dynamics, phase transition-like phenomena, bi- or multi-stability, and sensibility of the dynamic patterns on parameter drift. These features are predicted by chaos theory and by Synergetics and correspond to empirical findings. The spectrum of these behaviors illustrates the complexity of psychotherapeutic processes. Conclusion: The model contributes to the development of an integrative conceptualization of psychotherapy. It is consistent with the state of scientific knowledge of common factors, as well as other psychological topics, such as: motivation, emotion regulation, and cognitive processing. The role of chaos theory is underpinned, not only in the world of computer simulations, but also in practice. In practice, chaos demands technologies capable of real-time monitoring and reporting on the nonlinear features of the ongoing process (e.g., its stability or instability). Based on this monitoring, a client-centered, continuous, and cooperative process of feedback and control becomes possible. By contrast, restricted predictability and spontaneous changes challenge the usefulness of prescriptive treatment manuals or other predefined programs of psychotherapy.

Effects of boundary proximity on monodispersed microbubbles in ultrasonic fields

NASA Astrophysics Data System (ADS)

Dzaharudin, F.; Ooi, A.; Manasseh, R.

2017-12-01

Microbubbles have demonstrated the potential to redraw the boundaries of biomedical applications and revolutionize diagnostic and therapeutic applications. However, the ability to distinguish the acoustic response from a cluster of microbubbles in close proximity to the vessel endothelial cell from those that are not is a challenge that needs to be addressed. To address this, the present paper modifies the Keller-Miksis model to include the effects of a boundary. The acoustic responses are analysed via techniques from dynamical systems theory such as Poincaré plots and bifurcation diagrams. It is found that the presence of a boundary causes an intermittent route to chaos while microbubbles far from the boundary result in a period-doubling route to chaos as the single control parameter pressure amplitude is varied. The route to chaos is altered via antimonotinicity with increasing bubble-wall distance. It has also been found that the effects of coupling are significant as it alters the chaotic threshold to occur at lower driving pressure amplitudes. The results also suggest that the increase in coupling effects between microbubbles near a boundary lowers the pressure amplitude required for chaos and lowers the natural frequency of the cluster.

Bifurcations and chaos in convection taking non-Fourier heat-flux

NASA Astrophysics Data System (ADS)

Layek, G. C.; Pati, N. C.

2017-11-01

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.

A Cascadable, Monolithic Laser/Modulator/Amplifier Transmitter.

DTIC Science & Technology

1997-03-01

for Use at 1.55um Wavelength", M. Fetterman , C-P Chao and S. R. Forrest, IEEE Photonics Technology Lett., 8, 69 (1995). 7. "Modelling of a...waveguide device using the Helmholtz beam propagation method", M. R. Fetterman and S. R. Forrest, Top. Mtg. on Integrated Photonics Research, Paper ThD4...Systems", OP. Chao, G. J. Shiau, M. Fetterman and S. R. Forrest, PSAA-V, Monterey CA (Jan., 1995). 13. "Photoluminescence Study of Excess Carrier

Chaos in Environmental Education.

ERIC Educational Resources Information Center

Hardy, Joy

1999-01-01

Explores chaos theory, the evolutionary capacity of chaotic systems, and the philosophical implications of chaos theory in general and for education. Compares the relationships between curriculum vision based on chaos theory and critical education for the environment. (Author/CCM)

Hyperbolic chaos in the klystron-type microwave vacuum tube oscillator

NASA Astrophysics Data System (ADS)

Emel'yanov, V. V.; Kuznetsov, S. P.; Ryskin, N. M.

2010-12-01

The ring-loop oscillator consisting of two coupled klystrons which is capable of generating hyperbolic chaotic signal in the microwave band is considered. The system of delayed-differential equations describing the dynamics of the oscillator is derived. This system is further reduced to the two-dimensional return map under the assumption of the instantaneous build-up of oscillations in the cavities. The results of detailed numerical simulation for both models are presented showing that there exists large enough range of control parameters where the sustained regime corresponds to the structurally stable hyperbolic chaos.

Gain control through divisive inhibition prevents abrupt transition to chaos in a neural mass model

PubMed Central

Papasavvas, Christoforos A.; Wang, Yujiang; Trevelyan, Andrew J.; Kaiser, Marcus

2016-01-01

Experimental results suggest that there are two distinct mechanisms of inhibition in cortical neuronal networks: subtractive and divisive inhibition. They modulate the input-output function of their target neurons either by increasing the input that is needed to reach maximum output or by reducing the gain and the value of maximum output itself, respectively. However, the role of these mechanisms on the dynamics of the network is poorly understood. We introduce a novel population model and numerically investigate the influence of divisive inhibition on network dynamics. Specifically, we focus on the transitions from a state of regular oscillations to a state of chaotic dynamics via period-doubling bifurcations. The model with divisive inhibition exhibits a universal transition rate to chaos (Feigenbaum behavior). In contrast, in an equivalent model without divisive inhibition, transition rates to chaos are not bounded by the universal constant (non-Feigenbaum behavior). This non-Feigenbaum behavior, when only subtractive inhibition is present, is linked to the interaction of bifurcation curves in the parameter space. Indeed, searching the parameter space showed that such interactions are impossible when divisive inhibition is included. Therefore, divisive inhibition prevents non-Feigenbaum behavior and, consequently, any abrupt transition to chaos. The results suggest that the divisive inhibition in neuronal networks could play a crucial role in keeping the states of order and chaos well separated and in preventing the onset of pathological neural dynamics. PMID:26465514

Child-care chaos and teachers' responsiveness: The indirect associations through teachers' emotion regulation and coping.

PubMed

Jeon, Lieny; Hur, Eunhye; Buettner, Cynthia K

2016-12-01

Teachers in early child-care settings are key contributors to children's development. However, the role of teachers' emotional abilities (i.e., emotion regulation and coping skills) and the role of teacher-perceived environmental chaos in relation to their responsiveness to children are understudied. The current study explored the direct and indirect associations between teachers' perceptions of child-care chaos and their self-reported contingent reactions towards children's negative emotions and challenging social interactions via teachers' emotional regulation and coping strategies. The sample consisted of 1129 preschool-aged classroom teachers in day care and public pre-K programs across the US. We first found that child-care chaos was directly associated with teachers' non-supportive reactions after controlling for multiple program and teacher characteristics. In addition, teachers in more chaotic child-care settings had less reappraisal and coping skills, which in turn, was associated with lower levels of positive responsiveness to children. Teachers reporting a higher degree of chaos used more suppression strategies, which in turn, was associated with teachers' non-supportive reactions and fewer expressive encouragement reactions to children's emotions. Results of this exploratory study suggest that it is important to prepare teachers to handle chaotic environments with clear guidelines and rules. In order to encourage teachers' supportive responses to children, intervention programs are needed to address teachers' coping and emotion regulation strategies in early childhood education. Copyright © 2016 Society for the Study of School Psychology. Published by Elsevier Ltd. All rights reserved.

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.

Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence

NASA Technical Reports Server (NTRS)

Lipsitz, L. A.; Goldberger, A. L.

1992-01-01

The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.

Chaotic homes and school achievement: a twin study

PubMed Central

Hanscombe, Ken B; Haworth, Claire MA; Davis, Oliver SP; Jaffee, Sara R; Plomin, Robert

2011-01-01

Background Chaotic homes predict poor school performance. Given that it is known that genes affect both children's experience of household chaos and their school achievement, to what extent is the relationship between high levels of noise and environmental confusion in the home, and children's school performance, mediated by heritable child effects? This is the first study to explore the genetic and environmental pathways between household chaos and academic performance. Method Children's perceptions of family chaos at ages 9 and 12 and their school performance at age 12 were assessed in more than 2,300 twin pairs. The use of child-specific measures in a multivariate genetic analysis made it possible to investigate the genetic and environmental origins of the covariation between children's experience of chaos in the home and their school achievement. Results Children's experience of family chaos and their school achievement were significantly correlated in the expected negative direction (r = −.26). As expected, shared environmental factors explained a large proportion (63%) of the association. However, genetic factors accounted for a significant proportion (37%) of the association between children's experience of household chaos and their school performance. Conclusions The association between chaotic homes and poor performance in school, previously assumed to be entirely environmental in origin, is in fact partly genetic. How children's home environment affects their academic achievement is not simply in the direction environment → child → outcome. Instead, genetic factors that influence children's experience of the disordered home environment also affect how well they do at school. The relationship between the child, their environment and their performance at school is complex: both genetic and environmental factors play a role. PMID:21675992

Meaning Finds a Way: Chaos (Theory) and Composition

ERIC Educational Resources Information Center

Kyburz, Bonnie Lenore

2004-01-01

The explanatory power provided by the chaos theory is explored. A dynamic and reciprocal relationship between culture and chaos theory indicates that the progressive cultural work may be formed by the cross-disciplinary resonance of chaos theory.

Shape and size distribution of chaos areas on Europa

NASA Astrophysics Data System (ADS)

Mikell, T.; Cox, R.

2008-12-01

Chaos terrain is ubiquitous on Europa's surface, but not randomly distributed. The global distribution of chaos areas shows a significant concentration between 30° N and S latitude, decreasing dramatically at higher latitudes. The low-latitude clustering is not an artifact of recognizability, as there is a greater proportion of images with high solar incidence angle (low light) at higher latitudes. Clustering is especially marked in context of the few but vast regional chaos tracts (>15,000 km2) that occupy a substantial proportion of the equatorial region: i.e. the low latitudes have not only greater numbers but much greater areal chaos coverage. Apex-antapex asymmetry is difficult to evaluate because the Galileo longitudinal coverage is so poor; but comparison of the image swaths that follow great circles across the leading and trailing hemispheres respectively shows greater numbers of chaos areas on the leading side. In spite of the equatorial location of a few vast chaos tracts, there is no apparent relationship between chaos area size and latitude. Chaos area outlines vary from smoothly circular to extremely jagged: the irregularity index ranges from 2- 270% (based on the ratio between measured chaos area perimeter and the circumference of a circle of equal area). There is a range of shapes in all size brackets, but smaller chaos areas on average have simpler, more equidimensional shapes, and edge complexity increases for larger chaos areas. Chaos areas of ~10 km equivalent circle diameter (ECD) have outlines that are 4-90% irregular, ones ~50 km ECD are 15-180% and those >100 km ECD are 35-270% irregular. In general, chaos areas with higher irregularity indices also have a higher raft:matrix ratio. These results, while preliminary, are consistent with experimental evidence suggesting an impact origin for some chaos terrain on Europa. In particular, the relationship between shape and size parallels the results of impact experiments into ice over water, in which lower-energy impacts produce small, circular bullet-holes with few or no rafts; and higher-energy impacts generate wide-field fragmentation of the ice, producing large and highly irregular openings with abundant floating crustal blocks.

Neutral line chaos and phase space structure

NASA Technical Reports Server (NTRS)

Burkhart, Grant R.; Speiser, Theodore W.; Martin, Richard F., Jr.; Dusenbery, Paul B.

1991-01-01

Phase space structure and chaos near a neutral line are studied with numerical surface-of-section (SOS) techniques and analytic methods. Results are presented for a linear neutral line model with zero crosstail electric field. It was found that particle motion can be divided into three regimes dependening on the value of the conserved canonical momentum, Py, and the conserved Hamiltonian, h. The phase space structure, using Poincare SOS plots, is highly sensitive to bn = Bn/B0 variations, but not to h variations. It is verified that the slow motion preserves the action, Jz, as evaluated by Sonnerup (1971), when the period of the fast motion is smaller than the time scale of the slow motion. Results show that the phase space structure and particle chaos depend sensitively upon Py and bn, but are independent of h.

Polynomial chaos representation of databases on manifolds

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

Soize, C., E-mail: christian.soize@univ-paris-est.fr; Ghanem, R., E-mail: ghanem@usc.edu

2017-04-15

Characterizing the polynomial chaos expansion (PCE) of a vector-valued random variable with probability distribution concentrated on a manifold is a relevant problem in data-driven settings. The probability distribution of such random vectors is multimodal in general, leading to potentially very slow convergence of the PCE. In this paper, we build on a recent development for estimating and sampling from probabilities concentrated on a diffusion manifold. The proposed methodology constructs a PCE of the random vector together with an associated generator that samples from the target probability distribution which is estimated from data concentrated in the neighborhood of the manifold. Themore » method is robust and remains efficient for high dimension and large datasets. The resulting polynomial chaos construction on manifolds permits the adaptation of many uncertainty quantification and statistical tools to emerging questions motivated by data-driven queries.« less

Chaos synchronization in networks of semiconductor superlattices

NASA Astrophysics Data System (ADS)

Li, Wen; Aviad, Yaara; Reidler, Igor; Song, Helun; Huang, Yuyang; Biermann, Klaus; Rosenbluh, Michael; Zhang, Yaohui; Grahn, Holger T.; Kanter, Ido

2015-11-01

Chaos synchronization has been demonstrated as a useful building block for various tasks in secure communications, including a source of all-electronic ultrafast physical random number generators based on room temperature spontaneous chaotic oscillations in a DC-biased weakly coupled GaAs/Al0.45Ga0.55As semiconductor superlattice (SSL). Here, we experimentally demonstrate the emergence of several types of chaos synchronization, e.g. leader-laggard, face-to-face and zero-lag synchronization in network motifs of coupled SSLs consisting of unidirectional and mutual coupling as well as self-feedback coupling. Each type of synchronization clearly reflects the symmetry of the topology of its network motif. The emergence of a chaotic SSL without external feedback and synchronization among different structured SSLs open up the possibility for advanced secure multi-user communication methods based on large networks of coupled SSLs.

The Importance of Chaos and Lenticulae on Europa for the JIMO Mission

NASA Technical Reports Server (NTRS)

Spaun, Nicole A.

2003-01-01

The Galileo Solid State Imaging (SSI) experiment provided high-resolution images of Europa's surface allowing identification of surface features barely distinguishable at Voyager's resolution. SSI revealed the visible pitting on Europa's surface to be due to large disrupted features, chaos, and smaller sub-circular patches, lenticulae. Chaos features contain a hummocky matrix material and commonly contain dislocated blocks of ridged plains. Lenticulae are morphologically interrelated and can be divided into three classes: domes, spots, and micro-chaos. Domes are broad, upwarped features that generally do not disrupt the texture of the ridged plains. Spots are areas of low albedo that are generally smooth in texture compared to other units. Micro-chaos are disrupted features with a hummocky matrix material, resembling that observed within chaos regions. Chaos and lenticulae are ubiquitous in the SSI regional map observations, which average approximately 200 meters per pixel (m/pxl) in resolution, and appear in several of the ultra-high resolution, i.e., better than 50 m/pxl, images of Europa as well. SSI also provided a number of multi-spectral observations of chaos and lenticulae. Using this dataset we have undertaken a thorough study of the morphology, size, spacing, stratigraphy, and color of chaos and lenticulae to determine their properties and evaluate models of their formation. Geological mapping indicates that chaos and micro-chaos have a similar internal morphology of in-situ degradation suggesting that a similar process was operating during their formation. The size distribution denotes a dominant size of 4-8 km in diameter for features containing hummocky material (i.e., chaos and micro-chaos). Results indicate a dominant spacing of 15 - 36 km apart. Chaos and lenticulae are generally among the youngest features stratigraphically observed on the surface, suggesting a recent change in resurfacing style. Also, the reddish non-icy materials on Europa's surface have high concentrations in many chaos and lenticulae features. Nonetheless, a complete global map of the distribution of chaos and lenticulae is not possible with the SSI dataset. Only <20% of the surface has been imaged at 200 m/pxl or better resolution, mostly of the near-equatorial regions. Color and ultra-high-res images have much less surface coverage. Thus we suggest that full global imaging of Europa at 200 m/pxl or better resolution, preferably in multi-spectral wavelengths, should be a high priority for the JIMO mission.

Invoking the muse: Dada's chaos.

PubMed

Rosen, Diane

2014-07-01

Dada, a self-proclaimed (anti)art (non)movement, took shape in 1916 among a group of writers and artists who rejected the traditions of a stagnating bourgeoisie. Instead, they adopted means of creative expression that embraced chaos, stoked instability and undermined logic, an outburst that overturned centuries of classical and Romantic aesthetics. Paradoxically, this insistence on disorder foreshadowed a new order in understanding creativity. Nearly one hundred years later, Nonlinear Dynamical Systems theory (NDS) gives renewed currency to Dada's visionary perspective on chance, chaos and creative cognition. This paper explores commonalities between NDS-theory and this early precursor of the nonlinear paradigm, suggesting that their conceptual synergy illuminates what it means to 'be creative' beyond the disciplinary boundaries of either. Key features are discussed within a 5P model of creativity based on Rhodes' 4P framework (Person, Process, Press, Product), to which I add Participant-Viewer for the interactivity of observer-observed. Grounded in my own art practice, several techniques are then put forward as non-methodical methods that invoke creative border zones, those regions where Dada's chance and design are wedded in a dialectical tension of opposites.

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

Relations between distributional and Devaney chaos.

PubMed

Oprocha, Piotr

2006-09-01

Recently, it was proven that chaos in the sense of Devaney and weak mixing both imply chaos in the sense of Li and Yorke. In this article we give explicit examples that any of these two implications do not hold for distributional chaos.

Chaos in the heart: the interaction between body and mind

NASA Astrophysics Data System (ADS)

Redington, Dana

1993-11-01

A number of factors influence the chaotic dynamics of heart function. Genetics, age, sex, disease, the environment, experience, and of course the mind, play roles in influencing cardiovascular dynamics. The mind is of particular interest because it is an emergent phenomenon of the body admittedly seated and co-occurrent in the brain. The brain serves as the body's controller, and commands the heart through complex multipathway feedback loops. Structures deep within the brain, the hypothalamus and other centers in the brainstem, modulate heart function, partially as a result of afferent input from the body but also a result of higher mental processes. What can chaos in the body, i.e., the nonlinear dynamics of the heart, tell of the mind? This paper presents a brief overview of the spectral structure of heart rate activity followed by a summary of experimental results based on phase space analysis of data from semi-structured interviews. This paper then describes preliminary quantification of cardiovascular dynamics during different stressor conditions in an effort to apply more quantitative methods to clinical data.

Lyapunov exponent for aging process in induction motor

NASA Astrophysics Data System (ADS)

Bayram, Duygu; Ünnü, Sezen Yıdırım; Şeker, Serhat

2012-09-01

Nonlinear systems like electrical circuits and systems, mechanics, optics and even incidents in nature may pass through various bifurcations and steady states like equilibrium point, periodic, quasi-periodic, chaotic states. Although chaotic phenomena are widely observed in physical systems, it can not be predicted because of the nature of the system. On the other hand, it is known that, chaos is strictly dependent on initial conditions of the system [1-3]. There are several methods in order to define the chaos. Phase portraits, Poincaré maps, Lyapunov Exponents are the most common techniques. Lyapunov Exponents are the theoretical indicator of the chaos, named after the Russian mathematician Aleksandr Lyapunov (1857-1918). Lyapunov Exponents stand for the average exponential divergence or convergence of nearby system states, meaning estimating the quantitive measure of the chaotic attractor. Negative numbers of the exponents stand for a stable system whereas zero stands for quasi-periodic systems. On the other hand, at least if one of the exponents is positive, this situation is an indicator of the chaos. For estimating the exponents, the system should be modeled by differential equation but even in that case mathematical calculation of Lyapunov Exponents are not very practical and evaluation of these values requires a long signal duration [4-7]. For experimental data sets, it is not always possible to acquire the differential equations. There are several different methods in literature for determining the Lyapunov Exponents of the system [4, 5]. Induction motors are the most important tools for many industrial processes because they are cheap, robust, efficient and reliable. In order to have healthy processes in industrial applications, the conditions of the machines should be monitored and the different working conditions should be addressed correctly. To the best of our knowledge, researches related to Lyapunov exponents and electrical motors are mostly focused on the controlling the mechanical parameters of the electrical machines. Brushless DC motor (BLDCM) and the other general purpose permanent magnet (PM) motors are the most widely examined motors [1, 8, 9]. But the researches, about Lyapunov Exponent, subjected to the induction motors are mostly focused on the control theory of the motors. Flux estimation of rotor, external load disturbances and speed tracking and vector control position system are the main research areas for induction motors [10, 11, 12-14]. For all the data sets which can be collected from an induction motor, vibration data have the key role for understanding the mechanical behaviours like aging, bearing damage and stator insulation damage [15-18]. In this paper aging of an induction motor is investigated by using the vibration signals. The signals consist of new and aged motor data. These data are examined by their 2 dimensional phase portraits and the geometric interpretation is applied for detecting the Lyapunov Exponents. These values are compared in order to define the character and state estimation of the aging processes.

COMPUTATIONAL METHODS FOR SENSITIVITY AND UNCERTAINTY ANALYSIS FOR ENVIRONMENTAL AND BIOLOGICAL MODELS

EPA Science Inventory

This work introduces a computationally efficient alternative method for uncertainty propagation, the Stochastic Response Surface Method (SRSM). The SRSM approximates uncertainties in model outputs through a series expansion in normal random variables (polynomial chaos expansion)...

Reversed Field Pinch helical self-organization studies with the volume preserving field line tracing code NEMATO

NASA Astrophysics Data System (ADS)

Bonfiglio, D.; Veranda, M.; Cappello, S.; Chacon, L.; Escande, D. F.; Piovesan, P.

2009-11-01

The existence of a Reversed Field Pinch (RFP) dynamo as a (laminar) helical self-organization was anticipated by MHD numerical studies [1]. High current operation in RFX-mod experiment shows such a helical self-organization: strong internal electron transport barriers (ITB) appear and magnetic chaos healing is diagnosed when Single Helical Axis (SHAx) regimes are achieved [2]. We present results of the field line tracing code NEMATO [3] applied to study the magnetic topology resulting from 3D MHD simulations, with the aim of clarifying the conditions for chaos healing in SHAx states. First tests confirm the basic picture: the magnetic chaos due to island overlap is significantly reduced after the expulsion of the dominant mode separatrix. The possible synergy with the presence of magnetic and/or flow shear at the SHAx ITB will also be discussed [4].[4pt] [1] S. Cappello, Plasma Phys. Control. Fusion (2004) & references therein [0pt] [2] R. Lorenzini et al., Nature Phys. (2009) [0pt] [3] J. M. Finn and L. Chacon, Phys. Plasmas (2005) [0pt] [4] M.E. Puiatti et al invited presentation EPS 2009 conference, submitted to Plasma Phys. Control. Fusion

Bifurcation Analysis and Chaos Control in a Modified Finance System with Delayed Feedback

NASA Astrophysics Data System (ADS)

Yang, Jihua; Zhang, Erli; Liu, Mei

2016-06-01

We investigate the effect of delayed feedback on the finance system, which describes the time variation of the interest rate, for establishing the fiscal policy. By local stability analysis, we theoretically prove the existences of Hopf bifurcation and Hopf-zero bifurcation. By using the normal form method and center manifold theory, we determine the stability and direction of a bifurcating periodic solution. Finally, we give some numerical solutions, which indicate that when the delay passes through certain critical values, chaotic oscillation is converted into a stable equilibrium or periodic orbit.

Experimental and Theoretical Investigations of a Mechanical Lever System Driven by a DC Motor

NASA Astrophysics Data System (ADS)

Nana, B.; Fautso Kuiate, G.; Yamgoué, S. B.

This paper presents theoretical and experimental results on the investigation of the dynamics of a nonlinear electromechanical system made of a lever arm actuated by a DC motor and controlled through a repulsive magnetic force. We use the method of harmonic balance to derive oscillatory solutions. Theoretical tools such as, bifurcation diagrams, Lyapunov exponents, phase portraits, are used to unveil the rich nonlinear behavior of the system including chaos and hysteresis. The experimental results are in close accordance with the theoretical predictions.

Chaos in neurons and its application: perspective of chaos engineering.

PubMed

Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki

2012-12-01

We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.

Numerical simulation of the transition to chaos in a dissipative Duffing oscillator with two-frequency excitation

NASA Astrophysics Data System (ADS)

Zavrazhina, T. V.

2007-10-01

A mathematical modeling technique is proposed for oscillation chaotization in an essentially nonlinear dissipative Duffing oscillator with two-frequency excitation on an invariant torus in ℝ2. The technique is based on the joint application of the parameter continuation method, Floquet stability criteria, bifurcation theory, and the Everhart high-accuracy numerical integration method. This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations. The value of a universal constant obtained earlier by the author while investigating oscillation chaotization in dissipative oscillators with single-frequency periodic excitation is confirmed.

Using chaos theory: the implications for nursing.

PubMed

Haigh, Carol

2002-03-01

The purpose of this paper is to review chaos theory and to examine the role that it may have in the discipline of nursing. In this paper, the fundamental ingredients of chaotic thinking are outlined. The earlier days of chaos thinking were characterized by an almost exclusively physiological focus. By the 21st century, nurse theorists were applying its principles to the organization and evaluation of care delivery with varying levels of success. Whilst the biological use of chaos has focused on pragmatic approaches to knowledge enhancement, nursing has often focused on the mystical aspects of chaos as a concept. The contention that chaos theory has yet to find a niche within nursing theory and practice is examined. The application of chaotic thinking across nursing practice, nursing research and statistical modelling is reviewed. The use of chaos theory as a way of identifying the attractor state of specific systems is considered and the suggestion is made that it is within statistical modelling of services that chaos theory is most effective.

Image Encryption Algorithm Based on Hyperchaotic Maps and Nucleotide Sequences Database

PubMed Central

2017-01-01

Image encryption technology is one of the main means to ensure the safety of image information. Using the characteristics of chaos, such as randomness, regularity, ergodicity, and initial value sensitiveness, combined with the unique space conformation of DNA molecules and their unique information storage and processing ability, an efficient method for image encryption based on the chaos theory and a DNA sequence database is proposed. In this paper, digital image encryption employs a process of transforming the image pixel gray value by using chaotic sequence scrambling image pixel location and establishing superchaotic mapping, which maps quaternary sequences and DNA sequences, and by combining with the logic of the transformation between DNA sequences. The bases are replaced under the displaced rules by using DNA coding in a certain number of iterations that are based on the enhanced quaternary hyperchaotic sequence; the sequence is generated by Chen chaos. The cipher feedback mode and chaos iteration are employed in the encryption process to enhance the confusion and diffusion properties of the algorithm. Theoretical analysis and experimental results show that the proposed scheme not only demonstrates excellent encryption but also effectively resists chosen-plaintext attack, statistical attack, and differential attack. PMID:28392799

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

NASA Astrophysics Data System (ADS)

Rajagopal, Karthikeyan; Karthikeyan, Anitha; Duraisamy, Prakash

2017-06-01

In this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

A framework for simultaneous aerodynamic design optimization in the presence of chaos

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

Günther, Stefanie, E-mail: stefanie.guenther@scicomp.uni-kl.de; Gauger, Nicolas R.; Wang, Qiqi

Integrating existing solvers for unsteady partial differential equations into a simultaneous optimization method is challenging due to the forward-in-time information propagation of classical time-stepping methods. This paper applies the simultaneous single-step one-shot optimization method to a reformulated unsteady constraint that allows for both forward- and backward-in-time information propagation. Especially in the presence of chaotic and turbulent flow, solving the initial value problem simultaneously with the optimization problem often scales poorly with the time domain length. The new formulation relaxes the initial condition and instead solves a least squares problem for the discrete partial differential equations. This enables efficient one-shot optimizationmore » that is independent of the time domain length, even in the presence of chaos.« less

Experimental identification of a comb-shaped chaotic region in multiple parameter spaces simulated by the Hindmarsh—Rose neuron model

NASA Astrophysics Data System (ADS)

Jia, Bing

2014-03-01

A comb-shaped chaotic region has been simulated in multiple two-dimensional parameter spaces using the Hindmarsh—Rose (HR) neuron model in many recent studies, which can interpret almost all of the previously simulated bifurcation processes with chaos in neural firing patterns. In the present paper, a comb-shaped chaotic region in a two-dimensional parameter space was reproduced, which presented different processes of period-adding bifurcations with chaos with changing one parameter and fixed the other parameter at different levels. In the biological experiments, different period-adding bifurcation scenarios with chaos by decreasing the extra-cellular calcium concentration were observed from some neural pacemakers at different levels of extra-cellular 4-aminopyridine concentration and from other pacemakers at different levels of extra-cellular caesium concentration. By using the nonlinear time series analysis method, the deterministic dynamics of the experimental chaotic firings were investigated. The period-adding bifurcations with chaos observed in the experiments resembled those simulated in the comb-shaped chaotic region using the HR model. The experimental results show that period-adding bifurcations with chaos are preserved in different two-dimensional parameter spaces, which provides evidence of the existence of the comb-shaped chaotic region and a demonstration of the simulation results in different two-dimensional parameter spaces in the HR neuron model. The results also present relationships between different firing patterns in two-dimensional parameter spaces.

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

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

Ahlfeld, R., E-mail: r.ahlfeld14@imperial.ac.uk; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrixmore » is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.« less

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

NASA Astrophysics Data System (ADS)

Ahlfeld, R.; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10 different input distributions or histograms.

Neglected chaos in international stock markets: Bayesian analysis of the joint return-volatility dynamical system

NASA Astrophysics Data System (ADS)

Tsionas, Mike G.; Michaelides, Panayotis G.

2017-09-01

We use a novel Bayesian inference procedure for the Lyapunov exponent in the dynamical system of returns and their unobserved volatility. In the dynamical system, computation of largest Lyapunov exponent by traditional methods is impossible as the stochastic nature has to be taken explicitly into account due to unobserved volatility. We apply the new techniques to daily stock return data for a group of six countries, namely USA, UK, Switzerland, Netherlands, Germany and France, from 2003 to 2014, by means of Sequential Monte Carlo for Bayesian inference. The evidence points to the direction that there is indeed noisy chaos both before and after the recent financial crisis. However, when a much simpler model is examined where the interaction between returns and volatility is not taken into consideration jointly, the hypothesis of chaotic dynamics does not receive much support by the data ("neglected chaos").

Semiconductor lasers driven by self-sustained chaotic electronic oscillators and applications to optical chaos cryptography.

PubMed

Kingni, Sifeu Takougang; Mbé, Jimmi Hervé Talla; Woafo, Paul

2012-09-01

In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate.

Riemannian geometry of Hamiltonian chaos: hints for a general theory.

PubMed

Cerruti-Sola, Monica; Ciraolo, Guido; Franzosi, Roberto; Pettini, Marco

2008-10-01

We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity.

Using simplified Chaos Theory to manage nursing services.

PubMed

Haigh, Carol A

2008-04-01

The purpose of this study was to evaluate the part simplified chaos theory could play in the management of nursing services. As nursing care becomes more complex, practitioners need to become familiar with business planning and objective time management. There are many time-limited methods that facilitate this type of planning but few that can help practitioners to forecast the end-point outcome of the service they deliver. A growth model was applied to a specialist service to plot service trajectory. Components of chaos theory can play a role in forecasting service outcomes and consequently the impact upon the management of such services. The ability to (1) track the trajectory of a service and (2) manipulate that trajectory by introducing new variables can allow managers to forward plan for service development and to evaluate the effectiveness of a service by plotting its end-point state.

Embrace the Chaos

ERIC Educational Resources Information Center

Huwe, Terence K.

2009-01-01

"Embracing the chaos" is an ongoing challenge for librarians. Embracing the chaos means librarians must have a plan for responding to the flood of new products, widgets, web tools, and gizmos that students use daily. In this article, the author argues that library instruction and access services have been grappling with that chaos with…

Solitary solutions including spatially localized chaos and their interactions in two-dimensional Kolmogorov flow.

PubMed

Hiruta, Yoshiki; Toh, Sadayoshi

2015-12-01

Two-dimensional Kolmogorov flow in wide periodic boxes is numerically investigated. It is shown that the total flow rate in the direction perpendicular to the force controls the characteristics of the flow, especially the existence of spatially localized solitary solutions such as traveling waves, periodic solutions, and chaotic solutions, which can behave as elementary components of the flow. We propose a procedure to construct approximate solutions consisting of solitary solutions. It is confirmed by direct numerical simulations that these solutions are stable and represent interactions between elementary components such as collisions, coexistence, and collapse of chaos.

Noise tolerant spatiotemporal chaos computing.

PubMed

Kia, Behnam; Kia, Sarvenaz; Lindner, John F; Sinha, Sudeshna; Ditto, William L

2014-12-01

We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.

Noise tolerant spatiotemporal chaos computing

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

Kia, Behnam; Kia, Sarvenaz; Ditto, William L.

We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture.

Relativistic chaos is coordinate invariant.

PubMed

Motter, Adilson E

2003-12-05

The noninvariance of Lyapunov exponents in general relativity has led to the conclusion that chaos depends on the choice of the space-time coordinates. Strikingly, we uncover the transformation laws of Lyapunov exponents under general space-time transformations and we find that chaos, as characterized by positive Lyapunov exponents, is coordinate invariant. As a result, the previous conclusion regarding the noninvariance of chaos in cosmology, a major claim about chaos in general relativity, necessarily involves the violation of hypotheses required for a proper definition of the Lyapunov exponents.

Numerical Researches on Dynamical Systems with Relativistic Spin

NASA Astrophysics Data System (ADS)

Han, W. B.

2010-04-01

It is well known that spinning compact binaries are one of the most important research objects in the universe. Especially, EMRIs (extreme mass ratio inspirals) involving stellar compact objects which orbit massive black holes, are considered to be primary sources of gravitational radiation (GW) which could be detected by the space-based interferometer LISA. GW signals from EMRIs can be used to test general relativity, measure the masses and spins of central black holes and study essential physics near horizons. Compared with the situation without spin, the complexity of extreme objects, most of which rotate very fast, is much higher. So the dynamics of EMRI systems are numerically and analytically studied. We focus on how the spin effects on the dynamics of these systems and the produced GW radiations. Firstly, an ideal model of spinning test particles around Kerr black hole is considered. For equatorial orbits, we present the correct expression of effective potential and analyze the stability of circular orbits. Especially, the gravitational binding energy and frame-dragging effect of extreme Kerr black hole are much bigger than those without spin. For general orbits, spin can monotonically enlarge orbital inclination and destroy the symmetry of orbits about equatorial plane. It is the most important that extreme spin can produce orbital chaos. By carefully investigating the relations between chaos and orbital parameters, we point out that chaos usually appears for orbits with small pericenter, big eccentricity and orbital inclination. It is emphasized that Poincaré section method is invalid to detect the chaos of spinning particles, and the way of systems toward chaos is the period-doubling bifurcation. Furthermore, we study how spins effect on GW radiations from spinning test particles orbiting Kerr black holes. It is found that spins can increase orbit eccentricity and then make h+ component be detected more easily. But for h× component, because spins change orbital inclination in a complicated way, it is more difficult to build GW signal templates. Secondly, based on the scalar gravity theory, a numerical relativistic model of EMRIs is constructed to consider the self-gravity and radiation reaction of low-mass objects. Finally, we develop a new method with multiple steps for Hamilton systems to meet the needs of numerical researches. This method can effectively maintain each conserved quantity of the separable Hamilton system. In addition, for constrained system with a few first integrals, we present a new numerical stabilization method named as adjustment-stabilization method, which can maintain all known conserved quantities in a given dynamical system and greatly improve the numerical accuracy. Our new method is the most complete stabilization method up to now.

Examining the Relationship Between Children's ADHD Symptomatology and Inadequate Parenting: The Role of Household Chaos.

PubMed

Wirth, Andrea; Reinelt, Tilman; Gawrilow, Caterina; Schwenck, Christina; Freitag, Christine M; Rauch, Wolfgang A

2017-02-01

This study examines the interrelations of parenting practices, emotional climate, and household chaos in families with children with and without ADHD. In particular, indirect pathways from children's ADHD symptomatology to inadequate parenting and negative emotional climate via household chaos were investigated. Parenting, emotional climate, and household chaos were assessed using questionnaires and a speech sample of parents of 31 children with and 53 without ADHD, aged 7 to 13 years. Group differences were found for certain parenting dimensions, the parent-child relationship, critical comments, and household chaos. While we found significant indirect effects between children's ADHD and certain parenting dimensions through household chaos, no effects were found for any aspect of emotional climate. Children's ADHD symptoms translate into inadequate parenting through household chaos, which underlines the need for interventions to improve household organization skills in parents of children with ADHD.

Chaos and Christianity: A Response to Butz and a Biblical Alternative.

ERIC Educational Resources Information Center

Watts, Richard E.; Trusty, Jerry

1997-01-01

M.R. Butz's position regarding chaos theory and Christianity is reviewed. The compatibility of biblical theology and the sciences is discussed. Parallels between chaos theory and the philosophical perspective of Soren Kierkegaard are explored. A biblical model is offered for counselors in assisting Christian clients in embracing chaos. (Author/EMK)

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.

Innovative Trajectory Designs to meet Exploration Challenges

NASA Technical Reports Server (NTRS)

Folta, David C.

2006-01-01

This document is a viewgraph presentation of the conference paper. Missions incorporated into NASA's Vision for Space Exploration include many different destinations and regions; are challenging to plan; and need new and innovative trajectory design methods to enable them. By combining proven methods with chaos dynamics, exploration goals that require maximum payload mass or minimum duration can be achieved. The implementation of these innovative methods, such as weak stability boundaries, has altered NASA's approach to meet exploration challenges and is described to show how exploration goals may be met in the next decade. With knowledge that various perturbations play a significant role, the mission designer must rely on both traditional design strategies as well as these innovative methods. Over the past decades, improvements have been made that would at first glance seem dramatic. This paper provides a brief narrative on how a fundamental shift has occurred and how chaos dynamics improve the design of exploration missions with complex constraints.

When the firm prevents the crash: Avoiding market collapse with partial control

PubMed Central

2017-01-01

Market collapse is one of the most dramatic events in economics. Such a catastrophic event can emerge from the nonlinear interactions between the economic agents at the micro level of the economy. Transient chaos might be a good description of how a collapsing market behaves. In this work, we apply a new control method, the partial control method, with the goal of avoiding this disastrous event. Contrary to common control methods that try to influence the system from the outside, here the market is controlled from the bottom up by one of the most basic components of the market—the firm. This is the first time that the partial control method is applied on a strictly economical system in which we also introduce external disturbances. We show how the firm is capable of controlling the system avoiding the collapse by only adjusting the selling price of the product or the quantity of production in accordance to the market circumstances. Additionally, we demonstrate how a firm with a large market share is capable of influencing the demand achieving price stability across the retail and wholesale markets. Furthermore, we prove that the control applied in both cases is much smaller than the external disturbances. PMID:28832608

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

NASA Technical Reports Server (NTRS)

Rauch, Kevin P.; Holman, Matthew

1999-01-01

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

The Nature (and Nurture) of Children's Perceptions of Family Chaos

ERIC Educational Resources Information Center

Hanscombe, Ken B.; Haworth, Claire M. A.; Davis, Oliver S. P.; Jaffee, Sara R.; Plomin, Robert

2010-01-01

Chaos in the home is a key environment in cognitive and behavioural development. However, we show that children's experience of home chaos is partly genetically mediated. We assessed children's perceptions of household chaos at ages 9 and 12 in 2337 pairs of twins. Using child-specific reports allowed us to use structural equation modelling to…

Chaos Theory as a Model for Managing Issues and Crises.

ERIC Educational Resources Information Center

Murphy, Priscilla

1996-01-01

Uses chaos theory to model public relations situations in which the salient feature is volatility of public perceptions. Discusses the premises of chaos theory and applies them to issues management, the evolution of interest groups, crises, and rumors. Concludes that chaos theory is useful as an analogy to structure image problems and to raise…

Chaos Theory and Its Application to Education: Mehmet Akif Ersoy University Case

ERIC Educational Resources Information Center

Akmansoy, Vesile; Kartal, Sadik

2014-01-01

Discussions have arisen regarding the application of the new paradigms of chaos theory to social sciences as compared to physical sciences. This study examines what role chaos theory has within the education process and what effect it has by describing the views of university faculty regarding chaos and education. The participants in this study…

Viewing Eye Movements During Reading through the Lens of Chaos Theory: How Reading Is Like the Weather

ERIC Educational Resources Information Center

Paulson, Eric J.

2005-01-01

This theoretical article examines reading processes using chaos theory as an analogy. Three principles of chaos theory are identified and discussed, then related to reading processes as revealed through eye movement research. Used as an analogy, the chaos theory principle of sensitive dependence contributes to understanding the difficulty in…

God's Stuff: The Constructive Powers of Chaos for Teaching Religion

ERIC Educational Resources Information Center

Willhauck, Susan

2010-01-01

Order and organization are valued in the classroom, and there is a prevailing understanding that chaos should be avoided. Yet chaos can also be potent space or a source from which new things spring forth. This article investigates biblical, scientific, and cultural understandings of chaos to discover how these contribute to a revelatory metaphor…

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

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stabilitymore » parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.« less

Scaling of chaos in strongly nonlinear lattices.

PubMed

Mulansky, Mario

2014-06-01

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

[Shedding light on chaos theory].

PubMed

Chou, Shieu-Ming

2004-06-01

Gleick (1987) said that only three twentieth century scientific theories would be important enough to continue be of use in the twenty-first century: The Theory of Relativity, Quantum Theory, and Chaos Theory. Chaos Theory has become a craze which is being used to forge a new scientific system. It has also been extensively applied in a variety of professions. The purpose of this article is to introduce chaos theory and its nursing applications. Chaos is a sign of regular order. This is to say that chaos theory emphasizes the intrinsic potential for regular order within disordered phenomena. It is to be hoped that this article will inspire more nursing scientists to apply this concept to clinical, research, or administrative fields in our profession.

A Chaos MIMO-OFDM Scheme for Mobile Communication with Physical-Layer Security

NASA Astrophysics Data System (ADS)

Okamoto, Eiji

Chaos communications enable a physical-layer security, which can enhance the transmission security in combining with upper-layer encryption techniques, or can omit the upper-layer secure protocol and enlarges the transmission efficiency. However, the chaos communication usually degrades the error rate performance compared to unencrypted digital modulations. To achieve both physical-layer security and channel coding gain, we have proposed a chaos multiple-input multiple-output (MIMO) scheme in which a rate-one chaos convolution is applied to MIMO multiplexing. However, in the conventional study only flat fading is considered. To apply this scheme to practical mobile environments, i.e., multipath fading channels, we propose a chaos MIMO-orthogonal frequency division multi-plexing (OFDM) scheme and show its effectiveness through computer simulations.

Deterministic convergence of chaos injection-based gradient method for training feedforward neural networks.

PubMed

Zhang, Huisheng; Zhang, Ying; Xu, Dongpo; Liu, Xiaodong

2015-06-01

It has been shown that, by adding a chaotic sequence to the weight update during the training of neural networks, the chaos injection-based gradient method (CIBGM) is superior to the standard backpropagation algorithm. This paper presents the theoretical convergence analysis of CIBGM for training feedforward neural networks. We consider both the case of batch learning as well as the case of online learning. Under mild conditions, we prove the weak convergence, i.e., the training error tends to a constant and the gradient of the error function tends to zero. Moreover, the strong convergence of CIBGM is also obtained with the help of an extra condition. The theoretical results are substantiated by a simulation example.

Adjoint-Based Climate Model Tuning: Application to the Planet Simulator

NASA Astrophysics Data System (ADS)

Lyu, Guokun; Köhl, Armin; Matei, Ion; Stammer, Detlef

2018-01-01

The adjoint method is used to calibrate the medium complexity climate model "Planet Simulator" through parameter estimation. Identical twin experiments demonstrate that this method can retrieve default values of the control parameters when using a long assimilation window of the order of 2 months. Chaos synchronization through nudging, required to overcome limits in the temporal assimilation window in the adjoint method, is employed successfully to reach this assimilation window length. When assimilating ERA-Interim reanalysis data, the observations of air temperature and the radiative fluxes are the most important data for adjusting the control parameters. The global mean net longwave fluxes at the surface and at the top of the atmosphere are significantly improved by tuning two model parameters controlling the absorption of clouds and water vapor. The global mean net shortwave radiation at the surface is improved by optimizing three model parameters controlling cloud optical properties. The optimized parameters improve the free model (without nudging terms) simulation in a way similar to that in the assimilation experiments. Results suggest a promising way for tuning uncertain parameters in nonlinear coupled climate models.

The Mediating Role of Parenting in the Associations between Household Chaos and Children’s Representations of Family Dysfunction

PubMed Central

Zvara, B.J.; Mills-Koonce, W.R.; Garrett-Peters, P.; Wagner, N.J.; Vernon-Feagans, L.; Cox, M.

2014-01-01

Children’s drawings are thought to reflect their mental representations of self and their interpersonal relations within families. Household chaos is believed to disrupt key proximal processes related to optimal development. The present study examines the mediating role of parenting behaviors in the relations between two measures of household chaos, instability and disorganization, and how they may be evidenced in children’s representations of family dysfunction as derived from their drawings. The sample (N= 962) is from a longitudinal study of rural poverty exploring the ways in which child, family, and contextual factors shape development over time. Findings reveal that, after controlling for numerous factors including child and primary caregiver covariates, there were significant indirect effects from cumulative family disorganization, but not cumulative family instability, on children’s representation of family dysfunction through parenting behaviors. Results suggest that the proximal effects of daily disorganization outweigh the effects of periodic instability overtime. PMID:25329862

Regular and Chaotic Quantum Dynamics of Two-Level Atoms in a Selfconsistent Radiation Field

NASA Technical Reports Server (NTRS)

Konkov, L. E.; Prants, S. V.

1996-01-01

Dynamics of two-level atoms interacting with their own radiation field in a single-mode high-quality resonator is considered. The dynamical system consists of two second-order differential equations, one for the atomic SU(2) dynamical-group parameter and another for the field strength. With the help of the maximal Lyapunov exponent for this set, we numerically investigate transitions from regularity to deterministic quantum chaos in such a simple model. Increasing the collective coupling constant b is identical with 8(pi)N(sub 0)(d(exp 2))/hw, we observed for initially unexcited atoms a usual sharp transition to chaos at b(sub c) approx. equal to 1. If we take the dimensionless individual Rabi frequency a = Omega/2w as a control parameter, then a sequence of order-to-chaos transitions has been observed starting with the critical value a(sub c) approx. equal to 0.25 at the same initial conditions.

An advanced analysis and modelling the air pollutant concentration temporal dynamics in atmosphere of the industrial cities: Odessa city

NASA Astrophysics Data System (ADS)

Buyadzhi, V. V.; Glushkov, A. V.; Khetselius, O. Yu; Ternovsky, V. B.; Serga, I. N.; Bykowszczenko, N.

2017-10-01

Results of analysis and modelling the air pollutant (dioxide of nitrogen) concentration temporal dynamics in atmosphere of the industrial city Odessa are presented for the first time and based on computing by nonlinear methods of the chaos and dynamical systems theories. A chaotic behaviour is discovered and investigated. To reconstruct the corresponding strange chaotic attractor, the time delay and embedding dimension are computed. The former is determined by the methods of autocorrelation function and average mutual information, and the latter is calculated by means of correlation dimension method and algorithm of false nearest neighbours. It is shown that low-dimensional chaos exists in the nitrogen dioxide concentration time series under investigation. Further, the Lyapunov’s exponents spectrum, Kaplan-Yorke dimension and Kolmogorov entropy are computed.

How to test for partially predictable chaos.

PubMed

Wernecke, Hendrik; Sándor, Bulcsú; Gros, Claudius

2017-04-24

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.

3D pulsed chaos lidar system.

PubMed

Cheng, Chih-Hao; Chen, Chih-Ying; Chen, Jun-Da; Pan, Da-Kung; Ting, Kai-Ting; Lin, Fan-Yi

2018-04-30

We develop an unprecedented 3D pulsed chaos lidar system for potential intelligent machinery applications. Benefited from the random nature of the chaos, conventional CW chaos lidars already possess excellent anti-jamming and anti-interference capabilities and have no range ambiguity. In our system, we further employ self-homodyning and time gating to generate a pulsed homodyned chaos to boost the energy-utilization efficiency. Compared to the original chaos, we show that the pulsed homodyned chaos improves the detection SNR by more than 20 dB. With a sampling rate of just 1.25 GS/s that has a native sampling spacing of 12 cm, we successfully achieve millimeter-level accuracy and precision in ranging. Compared with two commercial lidars tested side-by-side, namely the pulsed Spectroscan and the random-modulation continuous-wave Lidar-lite, the pulsed chaos lidar that is in compliance with the class-1 eye-safe regulation shows significantly better precision and a much longer detection range up to 100 m. Moreover, by employing a 2-axis MEMS mirror for active laser scanning, we also demonstrate real-time 3D imaging with errors of less than 4 mm in depth.

Conditions for order and chaos in the dynamics of a trapped Bose-Einstein condensate in coordinate and energy space

NASA Astrophysics Data System (ADS)

Sakhel, Roger R.; Sakhel, Asaad R.; Ghassib, Humam B.; Balaz, Antun

2016-03-01

We investigate numerically conditions for order and chaos in the dynamics of an interacting Bose-Einstein condensate (BEC) confined by an external trap cut off by a hard-wall box potential. The BEC is stirred by a laser to induce excitations manifesting as irregular spatial and energy oscillations of the trapped cloud. Adding laser stirring to the external trap results in an effective time-varying trapping frequency in connection with the dynamically changing combined external+laser potential trap. The resulting dynamics are analyzed by plotting their trajectories in coordinate phase space and in energy space. The Lyapunov exponents are computed to confirm the existence of chaos in the latter space. Quantum effects and trap anharmonicity are demonstrated to generate chaos in energy space, thus confirming its presence and implicating either quantum effects or trap anharmonicity as its generator. The presence of chaos in energy space does not necessarily translate into chaos in coordinate space. In general, a dynamic trapping frequency is found to promote chaos in a trapped BEC. An apparent means to suppress chaos in a trapped BEC is achieved by increasing the characteristic scale of the external trap with respect to the condensate size.

Decrease of cardiac chaos in congestive heart failure

NASA Astrophysics Data System (ADS)

Poon, Chi-Sang; Merrill, Christopher K.

1997-10-01

The electrical properties of the mammalian heart undergo many complex transitions in normal and diseased states. It has been proposed that the normal heartbeat may display complex nonlinear dynamics, including deterministic chaos,, and that such cardiac chaos may be a useful physiological marker for the diagnosis and management, of certain heart trouble. However, it is not clear whether the heartbeat series of healthy and diseased hearts are chaotic or stochastic, or whether cardiac chaos represents normal or abnormal behaviour. Here we have used a highly sensitive technique, which is robust to random noise, to detect chaos. We analysed the electrocardiograms from a group of healthy subjects and those with severe congestive heart failure (CHF), a clinical condition associated with a high risk of sudden death. The short-term variations of beat-to-beat interval exhibited strongly and consistently chaotic behaviour in all healthy subjects, but were frequently interrupted by periods of seemingly non-chaotic fluctuations in patients with CHF. Chaotic dynamics in the CHF data, even when discernible, exhibited a high degree of random variability over time, suggesting a weaker form of chaos. These findings suggest that cardiac chaos is prevalent in healthy heart, and a decrease in such chaos may be indicative of CHF.

Chaos and the (un)predictability of evolution in a changing environment

PubMed Central

Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

2018-01-01

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution, by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. PMID:29235104

Chaotic Homes and Children’s Disruptive Behavior

PubMed Central

Jaffee, Sara R.; Haworth, Claire M. A.; Davis, Oliver S. P.; Plomin, Robert

2012-01-01

Chaotic home lives are correlated with behavior problems in children. In the study reported here, we tested whether there was a cross-lagged relation between children’s experience of chaos and their disruptive behaviors (conduct problems and hyperactivity-inattention). Using genetically informative models, we then tested for the first time whether the influence of household chaos on disruptive behavior was environmentally mediated and whether genetic influences on children’s disruptive behaviors accounted for the heritability of household chaos. We measured children’s perceptions of household chaos and parents’ ratings of children’s disruptive behavior at ages 9 and 12 in a sample of 6,286 twin pairs from the Twins Early Development Study (TEDS). There was a phenotypic cross-lagged relation between children’s experiences of household chaos and their disruptive behavior. In genetically informative models, we found that the effect of household chaos on subsequent disruptive behavior was environmentally mediated. However, genetic influences on disruptive behavior did not explain why household chaos was heritable. PMID:22547656

Chaos Criminology: A critical analysis

NASA Astrophysics Data System (ADS)

McCarthy, Adrienne L.

There has been a push since the early 1980's for a paradigm shift in criminology from a Newtonian-based ontology to one of quantum physics. Primarily this effort has taken the form of integrating Chaos Theory into Criminology into what this thesis calls 'Chaos Criminology'. However, with the melding of any two fields, terms and concepts need to be translated properly, which has yet to be done. In addition to proving a translation between fields, this thesis also uses a set of criteria to evaluate the effectiveness of the current use of Chaos Theory in Criminology. While the results of the theory evaluation reveal that the current Chaos Criminology work is severely lacking and in need of development, there is some promise in the development of Marx's dialectical materialism with Chaos Theory.

Dealing with chaos and complexity: the reality of interviewing children and families in their own homes.

PubMed

MacDonald, Kath; Greggans, Alison

2008-12-01

The aim of this paper is to share our experiences of dealing with chaos and complexity in interview situations in the home with children and young people. We highlight dilemmas relevant to dealing with multiple interruptions, building a rapport, consent and confidentiality. Furthermore, we discuss issues regarding the locus of power and control and offer some solutions based on our experiences. Creating a safe environment is essential for qualitative research. Participants are more likely to open up and communicate if they feel safe, comfortable and relaxed. We conclude that interviewing parents and their children with cystic fibrosis in their own homes, is chaotic and appears to threaten the rigour of data collection processes. Limited attention or print space is paid to this issue, with published articles frequently sanitising the messiness of real world qualitative research. Position paper. In this position paper, we use two case studies to illustrate ethical and pragmatic challenges of interviewing out in the field. These case studies, typical of families we encountered, help emphasise the concerns we had in balancing researcher-participant rapport with the quality of the research process. Dealing with perceived chaos is hard in reality, but capturing it is part of the complexity of qualitative enquiry. The context is interdependent with children's perceived reality, because they communicate with others through their environment. This paper gives researchers an insight into the tensions of operating out in the field and helps raise the importance of the environmental 'chaos' in revealing significant issues relevant to peoples daily lives. Knowing that unexpected chaos is part and parcel of qualitative research, will equip researchers with skills fundamental for balancing the well being of all those involved with the quality of the research process.

Quasiperiodicity and Frequency Locking in Electronic Conduction in Germanium.

NASA Astrophysics Data System (ADS)

Gwinn, Elisabeth Gray

1987-09-01

This thesis presents an experimental study of a driven spatio-temporal instability in high-field transport in cooled, p-type Ge. The instability is produced at liquid He temperatures by d.c. voltage bias above the threshold for breakdown by impurity impact ionization, and is associated experimentally with voltage-controlled negative differential conductivity. The instability is coupled to an external oscillator by applying a sinusoidal voltage bias across the Ge sample. The driven instability exhibits frequency locking, quasiperiodicity, and chaos as the frequency and amplitude of the sinusoidal bias are varied. An iterative map of the circle provides a simple model for such a coupled, dissipative nonlinear oscillator system. The transition from quasiperiodicity to chaos in this model system occurs in a universal way; for example, the circle map has a universal, self-similar power spectrum at the onset of chaos with the golden mean winding number. When normalized appropriately, the power spectrum at the onset of chaos in the driven instability in Ge displays the same structure, with good agreement between the amplitudes of the experimental and theoretical spectral peaks. The relevance of universal theory to experiment can also be tested with a spectrum of scaling indices f( alpha), which is used to compare the probability distribution for the circle map at the onset of chaos with the golden mean winding number to the distribution of probability on a Poincare section of the experimental attractor. The procedure used to find f(alpha ) for the driven transport instability overcomes the sensitivity of f(alpha) to noise and to deviation from the critical amplitude. The f( alpha) curve for the driven instability in Ge is found to be in good agreement with the universal circle map result.

Secure communications of CAP-4 and OOK signals over MMF based on electro-optic chaos.

PubMed

Ai, Jianzhou; Wang, Lulu; Wang, Jian

2017-09-15

Chaos-based secure communication can provide a high level of privacy in data transmission. Here, we experimentally demonstrate secure signal transmission over two kinds of multimode fiber (MMF) based on electro-optic intensity chaos. High-quality synchronization is achieved in an electro-optic feedback configuration. Both 5  Gbit/s carrier-less amplitude/phase (CAP-4) modulation and 10  Gbit/s on-off key (OOK) signals are recovered efficiently in electro-optic chaos-based communication systems. Degradations of chaos synchronization and communication system due to mismatch of various hardware keys are also discussed.

Congenital high airway obstruction syndrome (CHAOS) associated with cervical myelomeningocele.

PubMed

Adin, Mehmet Emin

2017-10-01

Congenital high airway obstruction syndrome (CHAOS) is a rare and potentially fatal entity resulting from complete or near complete developmental airway obstruction. Although most reported cases of CHAOS are sporadic, the condition may also be associated with certain syndromes and a variety of cervical masses. Meningocele and myelomeningocele have not yet been reported in association with CHAOS. We describe the typical constellation of sonographic findings in a case of early diagnosis of CHAOS associated with cervical myelomeningocele. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:507-510, 2017. © 2016 Wiley Periodicals, Inc.

Influence of the black hole spin on the chaotic particle dynamics within a dipolar halo

NASA Astrophysics Data System (ADS)

Nag, Sankhasubhra; Sinha, Siddhartha; Ananda, Deepika B.; Das, Tapas K.

2017-04-01

We investigate the role of the spin angular momentum of astrophysical black holes in controlling the special relativistic chaotic dynamics of test particles moving under the influence of a post-Newtonian pseudo-Kerr black hole potential, along with a perturbative potential created by an asymmetrically placed (dipolar) halo. Proposing a Lyapunov-like exponent to be the effective measure of the degree of chaos observed in the system under consideration, it has been found that black hole spin anti-correlates with the degree of chaos for the aforementioned dynamics. Our findings have been explained applying the general principles of dynamical systems analysis.

"I Had Seen Order and Chaos, but Had Thought They Were Different." The Challenges of the Chaos Theory for Career Development

ERIC Educational Resources Information Center

Pryor, Robert; Bright, Jim

2004-01-01

This paper highlights five challenges to the accepted wisdom in career development theory and practice. It presents the chaos theory of careers and argues that the chaos theory provides a more complete and authentic account of human behaviour. The paper argues that positivism, reductionism and assumptions of linearity are inappropriate for…

Phase plane analysis: applying chaos theory in health care.

PubMed

Priesmeyer, H R; Sharp, L F

1995-01-01

This article applies the new science of nonlinearity to administrative issues and accounts receivable management in health care, and it provides a new perspective on common operating and quality control measures.

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.

Impact of Chaos Functions on Modern Swarm Optimizers.

PubMed

Emary, E; Zawbaa, Hossam M

2016-01-01

Exploration and exploitation are two essential components for any optimization algorithm. Much exploration leads to oscillation and premature convergence while too much exploitation slows down the optimization algorithm and the optimizer may be stuck in local minima. Therefore, balancing the rates of exploration and exploitation at the optimization lifetime is a challenge. This study evaluates the impact of using chaos-based control of exploration/exploitation rates against using the systematic native control. Three modern algorithms were used in the study namely grey wolf optimizer (GWO), antlion optimizer (ALO) and moth-flame optimizer (MFO) in the domain of machine learning for feature selection. Results on a set of standard machine learning data using a set of assessment indicators prove advance in optimization algorithm performance when using variational repeated periods of declined exploration rates over using systematically decreased exploration rates.

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.

Optimizing chaos time-delay signature in two mutually-coupled semiconductor lasers through controlling internal parameters

NASA Astrophysics Data System (ADS)

Mu, Penghua; Pan, Wei; Yan, Lianshan; Luo, Bin; Zou, Xihua

2017-04-01

In this contribution, the effects of two key internal parameters, i.e. the linewidth-enhancement factor (α) and gain nonlinearity (𝜀), on time-delay signatures (TDS) concealment of two mutually-coupled semiconductor lasers (MCSLs) are numerically investigated. In particular, the influences of α and 𝜀 on the TDS concealment are compared and discussed systematically by setting different values of frequency detuning (Δf) and injection strength (η). The results show that the TDS can be better suppressed with high α or lower 𝜀 in the MCSLs. Two sets of desired optical chaos with TDS being strongly suppressed can be generated simultaneously in a wide injection parameter plane provided that α and 𝜀 are properly chosen, indicating that optimizing TDS suppression through controlling internal parameters can be generalized to any delayed-coupled laser systems.

DTU candidate field models for IGRF-12 and the CHAOS-5 geomagnetic field model

NASA Astrophysics Data System (ADS)

Finlay, Christopher C.; Olsen, Nils; Tøffner-Clausen, Lars

2015-07-01

We present DTU's candidate field models for IGRF-12 and the parent field model from which they were derived, CHAOS-5. Ten months of magnetic field observations from ESA's Swarm mission, together with up-to-date ground observatory monthly means, were used to supplement the data sources previously used to construct CHAOS-4. The internal field part of CHAOS-5, from which our IGRF-12 candidate models were extracted, is time-dependent up to spherical harmonic degree 20 and involves sixth-order splines with a 0.5 year knot spacing. In CHAOS-5, compared with CHAOS-4, we update only the low-degree internal field model (degrees 1 to 24) and the associated external field model. The high-degree internal field (degrees 25 to 90) is taken from the same model CHAOS-4h, based on low-altitude CHAMP data, which was used in CHAOS-4. We find that CHAOS-5 is able to consistently fit magnetic field data from six independent low Earth orbit satellites: Ørsted, CHAMP, SAC-C and the three Swarm satellites (A, B and C). It also adequately describes the secular variation measured at ground observatories. CHAOS-5 thus contributes to an initial validation of the quality of the Swarm magnetic data, in particular demonstrating that Huber weighted rms model residuals to Swarm vector field data are lower than those to Ørsted and CHAMP vector data (when either one or two star cameras were operating). CHAOS-5 shows three pulses of secular acceleration at the core surface over the past decade; the 2006 and 2009 pulses have previously been documented, but the 2013 pulse has only recently been identified. The spatial signature of the 2013 pulse at the core surface, under the Atlantic sector where it is strongest, is well correlated with the 2006 pulse, but anti-correlated with the 2009 pulse.

Life Chaos and Perceived Social Support Among Methamphetamine-Using Men Who Have Sex With Men Engaging in Transactional Sexual Encounters.

PubMed

Viswanath, Humsini; Wilkerson, J Michael; Breckenridge, Ellen; Selwyn, Beatrice J

2017-01-02

Social support and life chaos have been inversely associated with increased risk of HIV infection. The purpose of this study was to explore among a sample of HIV-negative methamphetamine-using men who have sex with men (MSM) the association between engaging in transactional sex, life chaos, and low social support. HIV-negative methamphetamine-using MSM completed an online questionnaire between July and October 2012 about recent substance use and sexual behavior. Bivariate and multivariate tests were used to obtain statistically significant associations between demographic characteristics, engaging in transactional sex, life chaos, and the participants' perception of their social support. Of the 325 participants, 23.7% reported engaging in transactional sex, 45.2% reported high life chaos, and 53.5% reported low perceived social support. Participants who engaged in transactional sex were more likely to have high life chaos than participants who did not (aOR = 1.70, 95% CI = [1.01, 2.84]); transactional sex was not associated with social support. Participants with high life chaos were more out about their sexual orientation (aOR = 2.29, 95% CI = [1.18, 4.42]) and more likely to perceive they had low social support (aOR = 3.78, 95% CI = [2.31, 6.22]) than participants with low life chaos. Non-Latinos perceived they had less social support than Latinos (aOR = 0.48, 95% CI = [0.25, 0.92]). Methamphetamine-using MSM engaging in transactional sex experience more life chaos than those who do not engage in transactional sex. Outness, perceived social support, and ethnicity are associated with life chaos.

Chaos, Hubbub, and Order Scale and Health Risk Behaviors in Adolescents in Los Angeles.

PubMed

Chatterjee, Avik; Gillman, Matthew W; Wong, Mitchell D

2015-12-01

To determine the relationship between household chaos and substance use, sexual activity, and violence-related risk behaviors in adolescents. We analyzed cross-sectional data among 929 high-school students in Los Angeles who completed a 90-minute interview that assessed health behaviors and household chaos with the 14-question Chaos, Hubbub, and Order Scale (CHAOS). Using the generalized estimating equation and adjusting for personal, parental, and family covariates, we examined associations of CHAOS score with substance use, sexual activity, and violent behavior outcome variables. We also examined the role of depression and school engagement as mediators. Mean (SD) age of the 929 students was 16.4 (1.3) years, 516 (55%) were female, and 780 (84%) were Latino. After adjustment, compared with students with CHAOS score 0, those students with the greatest scores (5-14) had ORs of 3.1 (95% CI 1.1-8.7) for smoking, 2.6 (95% CI 1.6-4.4) for drinking, 6.1 (95% CI 1.8-21) for substance use at school, and 1.9 (95% CI 1.1-3.3) for fighting in the past 12 months. Associations between CHAOS score and sexual risk and other violent behaviors were not significant. Depression and school engagement attenuated the associations. In this group of adolescents, greatest CHAOS score was associated with increased odds of risky health behaviors, with depression and school engagement as potential mediators. In the future, CHAOS score could be measured to assess risk for such behaviors or be a target for intervention to reduce chances of engaging in these behaviors. Copyright © 2015 Elsevier Inc. All rights reserved.

Periodic and chaotic psychological stress variations as predicted by a social support buffered response model

NASA Astrophysics Data System (ADS)

Field, Richard J.; Gallas, Jason A. C.; Schuldberg, David

2017-08-01

Recent work has introduced social dynamic models of people's stress-related processes, some including amelioration of stress symptoms by support from others. The effects of support may be ;direct;, depending only on the level of support, or ;buffering;, depending on the product of the level of support and level of stress. We focus here on the nonlinear buffering term and use a model involving three variables (and 12 control parameters), including stress as perceived by the individual, physical and psychological symptoms, and currently active social support. This model is quantified by a set of three nonlinear differential equations governing its stationary-state stability, temporal evolution (sometimes oscillatory), and how each variable affects the others. Chaos may appear with periodic forcing of an environmental stress parameter. Here we explore this model carefully as the strength and amplitude of this forcing, and an important psychological parameter relating to self-kindling in the stress response, are varied. Three significant observations are made: 1. There exist many complex but orderly regions of periodicity and chaos, 2. there are nested regions of increasing number of peaks per cycle that may cascade to chaos, and 3. there are areas where more than one state, e.g., a period-2 oscillation and chaos, coexist for the same parameters; which one is reached depends on initial conditions.

Control or Chaos: Centralized Military Management

DTIC Science & Technology

1966-04-08

for effective coordination, only the beginnings of such a science has been developed.* 1-Harold Koontz and Cyril O’Donnell, Principles of Management . p...control of military strategy by the political element of government.) 46 13. Koontz, Harold, and O’Donnell, Cyril. Principles of Management . 2d ed

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 dynamics in the Leslie-Gower type of the food chain system with multiple delays

NASA Astrophysics Data System (ADS)

Guo, Lei; Song, Zi-Gen; Xu, Jian

2014-08-01

In this paper, we present a Leslie-Gower type of food chain system composed of three species, which are resource, consumer, and predator, respectively. The digestion time delays corresponding to consumer-eat-resource and predator-eat-consumer are introduced for more realistic consideration. It is called the resource digestion delay (RDD) and consumer digestion delay (CDD) for simplicity. Analyzing the corresponding characteristic equation, the stabilities of the boundary and interior equilibrium points are studied. The food chain system exhibits the species coexistence for the small values of digestion delays. Large RDD/CDD may destabilize the species coexistence and induce the system dynamic into recurrent bloom or system collapse. Further, the present of multiple delays can control species population into the stable coexistence. To investigate the effect of time delays on the recurrent bloom of species population, the Hopf bifurcation and periodic solution are investigated in detail in terms of the central manifold reduction and normal form method. Finally, numerical simulations are performed to display some complex dynamics, which include multiple periodic solution and chaos motion for the different values of system parameters. The system dynamic behavior evolves into the chaos motion by employing the period-doubling bifurcation.

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.

Relativistic quantum chaos-An emergent interdisciplinary field.

PubMed

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Photonic generation of polarization-resolved wideband chaos with time-delay concealment in three-cascaded vertical-cavity surface-emitting lasers.

PubMed

Liu, Huijie; Li, Nianqiang; Zhao, Qingchun

2015-05-10

Optical chaos generated by chaotic lasers has been widely used in several important applications, such as chaos-based communications and high-speed random-number generators. However, these applications are susceptible to degradation by the presence of time-delay (TD) signature identified from the chaotic output. Here we propose to achieve the concealment of TD signature, along with the enhancement of chaos bandwidth, in three-cascaded vertical-cavity surface-emitting lasers (VCSELs). The cascaded system is composed of an external-cavity master VCSEL, a solitary intermediate VCSEL, and a solitary slave VCSEL. Through mapping the evolutions of TD signature and chaos bandwidth in the parameter space of the injection strength and frequency detuning, photonic generation of polarization-resolved wideband chaos with TD concealment is numerically demonstrated for wide regions of the injection parameters.

Death and revival of chaos.

PubMed

Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás

2016-12-01

We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.

Chaos and the (un)predictability of evolution in a changing environment.

PubMed

Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

2018-02-01

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Confirmatory Factor Analysis of the Malay Version of the Confusion, Hubbub and Order Scale (CHAOS-6) among Myocardial Infarction Survivors in a Malaysian Cardiac Healthcare Facility.

PubMed

Ganasegeran, Kurubaran; Selvaraj, Kamaraj; Rashid, Abdul

2017-08-01

The six item Confusion, Hubbub and Order Scale (CHAOS-6) has been validated as a reliable tool to measure levels of household disorder. We aimed to investigate the goodness of fit and reliability of a new Malay version of the CHAOS-6. The original English version of the CHAOS-6 underwent forward-backward translation into the Malay language. The finalised Malay version was administered to 105 myocardial infarction survivors in a Malaysian cardiac health facility. We performed confirmatory factor analyses (CFAs) using structural equation modelling. A path diagram and fit statistics were yielded to determine the Malay version's validity. Composite reliability was tested to determine the scale's reliability. All 105 myocardial infarction survivors participated in the study. The CFA yielded a six-item, one-factor model with excellent fit statistics. Composite reliability for the single factor CHAOS-6 was 0.65, confirming that the scale is reliable for Malay speakers. The Malay version of the CHAOS-6 was reliable and showed the best fit statistics for our study sample. We thus offer a simple, brief, validated, reliable and novel instrument to measure chaos, the Skala Kecelaruan, Keriuhan & Tertib Terubahsuai (CHAOS-6) , for the Malaysian population.

Detection of "noisy" chaos in a time series

NASA Technical Reports Server (NTRS)

Chon, K. H.; Kanters, J. K.; Cohen, R. J.; Holstein-Rathlou, N. H.

1997-01-01

Time series from biological system often displays fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". The output from most biological systems is probably the result of both the internal dynamics of the systems, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

An Analysis of Polynomial Chaos Approximations for Modeling Single-Fluid-Phase Flow in Porous Medium Systems

PubMed Central

Rupert, C.P.; Miller, C.T.

2008-01-01

We examine a variety of polynomial-chaos-motivated approximations to a stochastic form of a steady state groundwater flow model. We consider approaches for truncating the infinite dimensional problem and producing decoupled systems. We discuss conditions under which such decoupling is possible and show that to generalize the known decoupling by numerical cubature, it would be necessary to find new multivariate cubature rules. Finally, we use the acceleration of Monte Carlo to compare the quality of polynomial models obtained for all approaches and find that in general the methods considered are more efficient than Monte Carlo for the relatively small domains considered in this work. A curse of dimensionality in the series expansion of the log-normal stochastic random field used to represent hydraulic conductivity provides a significant impediment to efficient approximations for large domains for all methods considered in this work, other than the Monte Carlo method. PMID:18836519

Using the concept of pseudo amino acid composition to predict resistance gene against Xanthomonas oryzae pv. oryzae in rice: an approach from chaos games representation.

PubMed

Jingbo, Xia; Silan, Zhang; Feng, Shi; Huijuan, Xiong; Xuehai, Hu; Xiaohui, Niu; Zhi, Li

2011-09-07

To evaluate the possibility of an unknown protein to be a resistant gene against Xanthomonas oryzae pv. oryzae, a different mode of pseudo amino acid composition (PseAAC) is proposed to formulate the protein samples by integrating the amino acid composition, as well as the Chaos games representation (CGR) method. Some numerical comparisons of triangle, quadrangle and 12-vertex polygon CGR are carried to evaluate the efficiency of using these fractal figures in classifiers. The numerical results show that among the three polygon methods, triangle method owns a good fractal visualization and performs the best in the classifier construction. By using triangle + 12-vertex polygon CGR as the mathematical feature, the classifier achieves 98.13% in Jackknife test and MCC achieves 0.8462. Copyright © 2011 Elsevier Ltd. All rights reserved.

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.

Chaos vibration of pinion and rack steering trapezoidal mechanism containing two clearances

NASA Astrophysics Data System (ADS)

Wei, Daogao; Wang, Yu; Jiang, Tong; Zheng, Sifa; Zhao, Wenjing; Pan, Zhijie

2017-08-01

The multi-clearances of breaking type steering trapezoidal mechanism joints influences vehicle steering stability. Hence, to ascertain the influence of clearance value on steering stability, this paper takes the steering mechanism of a certain vehicle type as a prototype that can be simplified into a planar six-bar linkage, then establishes the system dynamic differential equations after considering the two clearances of tie rods and the steering knuckle arms. The influence of the clearance parameters on the movement stability of the steering mechanism is studied using a numerical computation method. Results show that when the two clearances are equal, the planar movement of the tie rods changes from period-doubling to chaos as the clearances increase. When the two clearances are 0.25 mm and 1.5 mm respectively, the planar movements of the two side tie rods come into chaos, causing the steering stability to deteriorate. Moreover, with the increase of clearances, turning moment fluctuates more intensively and the peak value increases.

Detection and control of combustion instability based on the concept of dynamical system theory.

PubMed

Gotoda, Hiroshi; Shinoda, Yuta; Kobayashi, Masaki; Okuno, Yuta; Tachibana, Shigeru

2014-02-01

We propose an online method of detecting combustion instability based on the concept of dynamical system theory, including the characterization of the dynamic behavior of combustion instability. As an important case study relevant to combustion instability encountered in fundamental and practical combustion systems, we deal with the combustion dynamics close to lean blowout (LBO) in a premixed gas-turbine model combustor. The relatively regular pressure fluctuations generated by thermoacoustic oscillations transit to low-dimensional intermittent chaos owing to the intermittent appearance of burst with decreasing equivalence ratio. The translation error, which is characterized by quantifying the degree of parallelism of trajectories in the phase space, can be used as a control variable to prevent LBO.

Detection and control of combustion instability based on the concept of dynamical system theory

NASA Astrophysics Data System (ADS)

Gotoda, Hiroshi; Shinoda, Yuta; Kobayashi, Masaki; Okuno, Yuta; Tachibana, Shigeru

2014-02-01

We propose an online method of detecting combustion instability based on the concept of dynamical system theory, including the characterization of the dynamic behavior of combustion instability. As an important case study relevant to combustion instability encountered in fundamental and practical combustion systems, we deal with the combustion dynamics close to lean blowout (LBO) in a premixed gas-turbine model combustor. The relatively regular pressure fluctuations generated by thermoacoustic oscillations transit to low-dimensional intermittent chaos owing to the intermittent appearance of burst with decreasing equivalence ratio. The translation error, which is characterized by quantifying the degree of parallelism of trajectories in the phase space, can be used as a control variable to prevent LBO.

Network-induced chaos in integrate-and-fire neuronal ensembles.

PubMed

Zhou, Douglas; Rangan, Aaditya V; Sun, Yi; Cai, David

2009-09-01

It has been shown that a single standard linear integrate-and-fire (IF) neuron under a general time-dependent stimulus cannot possess chaotic dynamics despite the firing-reset discontinuity. Here we address the issue of whether conductance-based, pulsed-coupled network interactions can induce chaos in an IF neuronal ensemble. Using numerical methods, we demonstrate that all-to-all, homogeneously pulse-coupled IF neuronal networks can indeed give rise to chaotic dynamics under an external periodic current drive. We also provide a precise characterization of the largest Lyapunov exponent for these high dimensional nonsmooth dynamical systems. In addition, we present a stable and accurate numerical algorithm for evaluating the largest Lyapunov exponent, which can overcome difficulties encountered by traditional methods for these nonsmooth dynamical systems with degeneracy induced by, e.g., refractoriness of neurons.

A weighted ℓ{sub 1}-minimization approach for sparse polynomial chaos expansions

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

Peng, Ji; Hampton, Jerrad; Doostan, Alireza, E-mail: alireza.doostan@colorado.edu

2014-06-15

This work proposes a method for sparse polynomial chaos (PC) approximation of high-dimensional stochastic functions based on non-adapted random sampling. We modify the standard ℓ{sub 1}-minimization algorithm, originally proposed in the context of compressive sampling, using a priori information about the decay of the PC coefficients, when available, and refer to the resulting algorithm as weightedℓ{sub 1}-minimization. We provide conditions under which we may guarantee recovery using this weighted scheme. Numerical tests are used to compare the weighted and non-weighted methods for the recovery of solutions to two differential equations with high-dimensional random inputs: a boundary value problem with amore » random elliptic operator and a 2-D thermally driven cavity flow with random boundary condition.« less

Polynomial Chaos decomposition applied to stochastic dosimetry: study of the influence of the magnetic field orientation on the pregnant woman exposure at 50 Hz.

PubMed

Liorni, I; Parazzini, M; Fiocchi, S; Guadagnin, V; Ravazzani, P

2014-01-01

Polynomial Chaos (PC) is a decomposition method used to build a meta-model, which approximates the unknown response of a model. In this paper the PC method is applied to the stochastic dosimetry to assess the variability of human exposure due to the change of the orientation of the B-field vector respect to the human body. In detail, the analysis of the pregnant woman exposure at 7 months of gestational age is carried out, to build-up a statistical meta-model of the induced electric field for each fetal tissue and in the fetal whole-body by means of the PC expansion as a function of the B-field orientation, considering a uniform exposure at 50 Hz.

Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi-Pasta-Ulam lattices by the Generalized Alignment Index method

NASA Astrophysics Data System (ADS)

Skokos, C.; Bountis, T.; Antonopoulos, C.

2008-12-01

The recently introduced GALI method is used for rapidly detecting chaos, determining the dimensionality of regular motion and predicting slow diffusion in multi-dimensional Hamiltonian systems. We propose an efficient computation of the GALIk indices, which represent volume elements of k randomly chosen deviation vectors from a given orbit, based on the Singular Value Decomposition (SVD) algorithm. We obtain theoretically and verify numerically asymptotic estimates of GALIs long-time behavior in the case of regular orbits lying on low-dimensional tori. The GALIk indices are applied to rapidly detect chaotic oscillations, identify low-dimensional tori of Fermi-Pasta-Ulam (FPU) lattices at low energies and predict weak diffusion away from quasiperiodic motion, long before it is actually observed in the oscillations.

Early Exposure to Environmental Chaos and Children's Physical and Mental Health.

PubMed

Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

Environmental chaos has been proposed as a central influence impeding children's health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children's physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children's functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children's functioning.

Early Exposure to Environmental Chaos and Children’s Physical and Mental Health

PubMed Central

Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

2015-01-01

Environmental chaos has been proposed as a central influence impeding children’s health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children’s physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children’s functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children’s functioning. PMID:25844016

Does chaos theory have major implications for philosophy of medicine?

PubMed

Holm, S

2002-12-01

In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the concept of disease and the concept of causation. This paper gives a brief introduction to the concepts underlying chaos theory and non-linear dynamics. It is then shown that chaos theory has only very minimal implications for the analysis of the concept of disease and the concept of causation, mainly because the mathematics of chaotic processes entail that these processes are fully deterministic. The practical unpredictability of chaotic processes, caused by their extreme sensitivity to initial conditions, may raise practical problems in diagnosis, prognosis, and treatment, but it raises no major theoretical problems. The relation between chaos theory and the problem of free will is discussed, and it is shown that chaos theory may remove the problem of predictability of decisions, but does not solve the problem of free will. Chaos theory may thus be very important for our understanding of physiological processes, and specific disease entities, without having any major implications for philosophy of medicine.

Fractal Patterns and Chaos Games

ERIC Educational Resources Information Center

Devaney, Robert L.

2004-01-01

Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

The joy of transient chaos.

PubMed

Tél, Tamás

2015-09-01

We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.

Rank one chaos in a class of planar systems with heteroclinic cycle.

PubMed

Chen, Fengjuan; Han, Maoan

2009-12-01

In this paper, we study rank one chaos in a class of planar systems with heteroclinic cycle. We first find a stable limit cycle inside the heteroclinic cycle. We then add an external periodic forcing to create rank one chaos. We follow a step-by-step procedure guided by the theory of rank one chaos to find experimental evidence of strange attractors with Sinai, Ruelle, and Bowen measures.

Li-Yorke Chaos in Hybrid Systems on a Time Scale

NASA Astrophysics Data System (ADS)

Akhmet, Marat; Fen, Mehmet Onur

2015-12-01

By using the reduction technique to impulsive differential equations [Akhmet & Turan, 2006], we rigorously prove the presence of chaos in dynamic equations on time scales (DETS). The results of the present study are based on the Li-Yorke definition of chaos. This is the first time in the literature that chaos is obtained for DETS. An illustrative example is presented by means of a Duffing equation on a time scale.

Chaos and Forecasting - Proceedings of the Royal Society Discussion Meeting

NASA Astrophysics Data System (ADS)

Tong, Howell

1995-04-01

The Table of Contents for the full book PDF is as follows: * Preface * Orthogonal Projection, Embedding Dimension and Sample Size in Chaotic Time Series from a Statistical Perspective * A Theory of Correlation Dimension for Stationary Time Series * On Prediction and Chaos in Stochastic Systems * Locally Optimized Prediction of Nonlinear Systems: Stochastic and Deterministic * A Poisson Distribution for the BDS Test Statistic for Independence in a Time Series * Chaos and Nonlinear Forecastability in Economics and Finance * Paradigm Change in Prediction * Predicting Nonuniform Chaotic Attractors in an Enzyme Reaction * Chaos in Geophysical Fluids * Chaotic Modulation of the Solar Cycle * Fractal Nature in Earthquake Phenomena and its Simple Models * Singular Vectors and the Predictability of Weather and Climate * Prediction as a Criterion for Classifying Natural Time Series * Measuring and Characterising Spatial Patterns, Dynamics and Chaos in Spatially-Extended Dynamical Systems and Ecologies * Non-Linear Forecasting and Chaos in Ecology and Epidemiology: Measles as a Case Study

How does the Xenopus laevis embryonic cell cycle avoid spatial chaos?

PubMed Central

Gelens, Lendert; Huang, Kerwyn Casey; Ferrell, James E.

2015-01-01

Summary Theoretical studies have shown that a deterministic biochemical oscillator can become chaotic when operating over a sufficiently large volume, and have suggested that the Xenopus laevis cell cycle oscillator operates close to such a chaotic regime. To experimentally test this hypothesis, we decreased the speed of the post-fertilization calcium wave, which had been predicted to generate chaos. However, cell divisions were found to develop normally and eggs developed into normal tadpoles. Motivated by these experiments, we carried out modeling studies to understand the prerequisites for the predicted spatial chaos. We showed that this type of spatial chaos requires oscillatory reaction dynamics with short pulse duration, and postulated that the mitotic exit in Xenopus laevis is likely slow enough to avoid chaos. In systems with shorter pulses, chaos may be an important hazard, as in cardiac arrhythmias, or a useful feature, as in the pigmentation of certain mollusk shells. PMID:26212326

Western Eos Chaos on Mars: A Potential Site for Future Landing and Returning Samples

NASA Astrophysics Data System (ADS)

Asif Iqbal Kakkassery; Rajesh, V. J.

2018-04-01

Introducing Eos Chaos as a potential area for collecting samples. Eos Chaos contains a number of aqueous minerals. We have detected zoisite — a least reported low-grade metamorphic mineral from this area.

Sub-optimal control of unsteady boundary layer separation and optimal control of Saltzman-Lorenz model

NASA Astrophysics Data System (ADS)

Sardesai, Chetan R.

The primary objective of this research is to explore the application of optimal control theory in nonlinear, unsteady, fluid dynamical settings. Two problems are considered: (1) control of unsteady boundary-layer separation, and (2) control of the Saltzman-Lorenz model. The unsteady boundary-layer equations are nonlinear partial differential equations that govern the eruptive events that arise when an adverse pressure gradient acts on a boundary layer at high Reynolds numbers. The Saltzman-Lorenz model consists of a coupled set of three nonlinear ordinary differential equations that govern the time-dependent coefficients in truncated Fourier expansions of Rayleigh-Renard convection and exhibit deterministic chaos. Variational methods are used to derive the nonlinear optimal control formulations based on cost functionals that define the control objective through a performance measure and a penalty function that penalizes the cost of control. The resulting formulation consists of the nonlinear state equations, which must be integrated forward in time, and the nonlinear control (adjoint) equations, which are integrated backward in time. Such coupled forward-backward time integrations are computationally demanding; therefore, the full optimal control problem for the Saltzman-Lorenz model is carried out, while the more complex unsteady boundary-layer case is solved using a sub-optimal approach. The latter is a quasi-steady technique in which the unsteady boundary-layer equations are integrated forward in time, and the steady control equation is solved at each time step. Both sub-optimal control of the unsteady boundary-layer equations and optimal control of the Saltzman-Lorenz model are found to be successful in meeting the control objectives for each problem. In the case of boundary-layer separation, the control results indicate that it is necessary to eliminate the recirculation region that is a precursor to the unsteady boundary-layer eruptions. In the case of the Saltzman-Lorenz model, it is possible to control the system about either of the two unstable equilibrium points representing clockwise and counterclockwise rotation of the convection roles in a parameter regime for which the uncontrolled solution would exhibit deterministic chaos.

Complexity and Productivity Differentiation Models of Metallogenic Indicator Elements in Rocks and Supergene Media Around Daijiazhuang Pb-Zn Deposit in Dangchang County, Gansu Province

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

He, Jin-zhong, E-mail: viewsino@163.com; Yao, Shu-zhen; Zhang, Zhong-ping

2013-03-15

With the help of complexity indices, we quantitatively studied multifractals, frequency distributions, and linear and nonlinear characteristics of geochemical data for exploration of the Daijiazhuang Pb-Zn deposit. Furthermore, we derived productivity differentiation models of elements from thermodynamics and self-organized criticality of metallogenic systems. With respect to frequency distributions and multifractals, only Zn in rocks and most elements except Sb in secondary media, which had been derived mainly from weathering and alluviation, exhibit nonlinear distributions. The relations of productivity to concentrations of metallogenic elements and paragenic elements in rocks and those of elements strongly leached in secondary media can be seenmore » as linear addition of exponential functions with a characteristic weak chaos. The relations of associated elements such as Mo, Sb, and Hg in rocks and other elements in secondary media can be expressed as an exponential function, and the relations of one-phase self-organized geological or metallogenic processes can be represented by a power function, each representing secondary chaos or strong chaos. For secondary media, exploration data of most elements should be processed using nonlinear mathematical methods or should be transformed to linear distributions before processing using linear mathematical methods.« less

The Induction of Chaos in Electronic Circuits Final Report-October 1, 2001

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

R.M.Wheat, Jr.

2003-04-01

This project, now known by the name ''Chaos in Electronic Circuits,'' was originally tasked as a two-year project to examine various ''fault'' or ''non-normal'' operational states of common electronic circuits with some focus on determining the feasibility of exploiting these states. Efforts over the two-year duration of this project have been dominated by the study of the chaotic behavior of electronic circuits. These efforts have included setting up laboratory space and hardware for conducting laboratory tests and experiments, acquiring and developing computer simulation and analysis capabilities, conducting literature surveys, developing test circuitry and computer models to exercise and test ourmore » capabilities, and experimenting with and studying the use of RF injection as a means of inducing chaotic behavior in electronics. An extensive array of nonlinear time series analysis tools have been developed and integrated into a package named ''After Acquisition'' (AA), including capabilities such as Delayed Coordinate Embedding Mapping (DCEM), Time Resolved (3-D) Fourier Transform, and several other phase space re-creation methods. Many computer models have been developed for Spice and for the ATP (Alternative Transients Program), modeling the several working circuits that have been developed for use in the laboratory. And finally, methods of induction of chaos in electronic circuits have been explored.« less

Deterministic chaos in an ytterbium-doped mode-locked fiber laser

NASA Astrophysics Data System (ADS)

Mélo, Lucas B. A.; Palacios, Guillermo F. R.; Carelli, Pedro V.; Acioli, Lúcio H.; Rios Leite, José R.; de Miranda, Marcio H. G.

2018-05-01

We experimentally study the nonlinear dynamics of a femtosecond ytterbium doped mode-locked fiber laser. With the laser operating in the pulsed regime a route to chaos is presented, starting from stable mode-locking, period two, period four, chaos and period three regimes. Return maps and bifurcation diagrams were extracted from time series for each regime. The analysis of the time series with the laser operating in the quasi mode-locked regime presents deterministic chaos described by an unidimensional Rossler map. A positive Lyapunov exponent $\\lambda = 0.14$ confirms the deterministic chaos of the system. We suggest an explanation about the observed map by relating gain saturation and intra-cavity loss.

Chaos in charged AdS black hole extended phase space

NASA Astrophysics Data System (ADS)

Chabab, M.; El Moumni, H.; Iraoui, S.; Masmar, K.; Zhizeh, S.

2018-06-01

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare-Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

Least squares polynomial chaos expansion: A review of sampling strategies

NASA Astrophysics Data System (ADS)

Hadigol, Mohammad; Doostan, Alireza

2018-04-01

As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling methods, such as Monte Carlo, Latin hypercube, quasi-Monte Carlo, optimal design of experiments (ODE), Gaussian quadratures, as well as more recent techniques, such as coherence-optimal and randomized quadratures are discussed. We also propose a hybrid sampling method, dubbed alphabetic-coherence-optimal, that employs the so-called alphabetic optimality criteria used in the context of ODE in conjunction with coherence-optimal samples. A comparison between the empirical performance of the selected sampling methods applied to three numerical examples, including high-order PCE's, high-dimensional problems, and low oversampling ratios, is presented to provide a road map for practitioners seeking the most suitable sampling technique for a problem at hand. We observed that the alphabetic-coherence-optimal technique outperforms other sampling methods, specially when high-order ODE are employed and/or the oversampling ratio is low.

Discovery of Dozy Chaos and Discovery of Quanta: Analogy Being in Science and Perhaps in Human Progress

NASA Astrophysics Data System (ADS)

Egorov, Vladimir V.

The concept of a dozy chaos in the theory of quantum transitions and its applications are discussed in a historical context. Conjectured that dozy chaos is of primary importance to the dynamic self-organization of any living organism and concentrated in its brain. A hypothesis of the physical origin of cancer is put forward. Surmised that dozy chaos is the physical origin of life and driving force of its evolution.

Chaos Theory and James Joyce's "ulysses": Leopold Bloom as a Human COMPLEX@SYSTEM^

NASA Astrophysics Data System (ADS)

Mackey, Peter Francis

1995-01-01

These four ideas apply as much to our lives as to the life of Leopold Bloom: (1) A trivial decision can wholly change a life. (2) A chance encounter can dramatically alter life's course. (3) A contingent nexus exists between consciousness and environment. (4) A structure of meaning helps us interpret life's chaos. These ideas also relate to a contemporary science called by some "chaos theory." The connection between Ulysses and chaos theory enhances our understanding of Bloom's day; it also suggests that this novel may be about the real process of life itself. The first chapter explains how Joyce's own essays and comments to friends compel attention to the links between Ulysses and chaos theory. His scientific contemporaries anticipated chaos theory, and their ideas seem to have rubbed off on him. We see this in his sense of trivial things and chance, his modernistic organizational impulses, and the contingent nature of Bloom's experience. The second chapter studies what chaos theory and Joyce's ideas tell us about "Ithaca," the episode which particularly implicates our processes of interpreting this text as well as life itself as we face their chaos. The third chapter examines Bloom's close feel for the aboriginal world, a contingency that clarifies his vulnerability to trivial changes. The fourth chapter studies how Bloom's stream of consciousness unfolds--from his chance encounters with trivial things. Beneath this stream's seeming chaos, Bloom's distinct personality endures, similar to how Joyce's schemas give Ulysses an imbedded, underlying order. The fifth chapter examines how trivial perturbations, such as Lyons' misunderstanding about "Throwaway," produce small crises for Bloom, exacerbating his seeming impotence before his lonely "fate.". The final chapter analyzes Bloom's views that fate and chance dictate his life. His views provide an opportunity to explore the implications chaos theory has for our understanding of free will and determinism. Ultimately, despite ungovernable fate and chance, Bloom asserts his will with Stephen and Molly, proving that he will live on, attempting to create his own destiny, wresting hope from the "chaos" of his experience.

Detection of Gray Crystalline Hematite in the Aureum and Iani Chaos Layered Terrains

NASA Astrophysics Data System (ADS)

Glotch, T. D.; Rogers, D.; Christensen, P. R.

2005-12-01

Using the TES and THEMIS datasets, small hematite-rich deposits have been discovered in Aureum and Iani Chaos. The newly discovered hematite-rich deposits share several similarities with the deposit in Aram Chaos [1], including the occurrence of hematite in a friable layered unit, and the presence of a light-toned caprock. The presence of these units over a distance of several hundred kilometers in the equatorial latitudes of Mars may point to a preferred global mechanism for hematite formation. However, it is unclear how, if at all, these units are related to the hematite- and sulfate-rich unit in Meridiani Planum, which is substantially larger and older (by as much as 1 Ga) than the layered units seen in the equatorial chaotic terrains. Though the caprock units in Aram Chaos and Aureum Chaos are similar, the corresponding unit in Iani Chaos is morphologically different, exhibiting less of a cliff-forming erosional pattern. The hematite-rich units in Aram and Aureum Chaos lie stratigraphically below the light-toned caprock units. In Iani Chaos, the hematite deposit is coincident with the light-toned unit. Data returned from the Mars Express OMEGA instrument have shown the presence of hydrated sulfates in the hematite-rich units associated with Aram and Iani Chaos, although to date, no sulfate detection has been reported in Aureum Chaos [2]. The sequence of caprock and hematite units in Aram, Aureum, and Iani Chaos probably did not form coincidentally as part of an extensive regional layer, but instead formed by similar, but not identical, processes in their respective chaotic terrains. The presence of these units in chaotic terrains, which have been hypothesized to form by subsidence after the release of subsurface water, indicate that these units may have been deposited in an aqueous environment. By analogy to Meridiani Planum, later subsurface aqueous activity in the region of the chaotic terrains may have provided the necessary diagenetic conditions for the formation of hematite within the layered units. [1] Glotch and Christensen, J. Geophys. Res., in press. [2] Gendrin et al., 2005, Science, 307 p. 1587-1590

How to control chaotic behaviour and population size with proportional feedback

NASA Astrophysics Data System (ADS)

Liz, Eduardo

2010-01-01

We study the control of chaos in one-dimensional discrete maps as they often occur in modelling population dynamics. For managing the population, we seek to suppress any possible chaotic behavior, leading the system to a stable equilibrium. In this Letter, we make a rigorous analysis of the proportional feedback method under certain conditions fulfilled by a wide family of maps. We show that it is possible to stabilize the chaotic dynamics towards a globally stable positive equilibrium, that can be chosen among a broad range of possible values. In particular, the size of the population can be enhanced by control in form of population reduction. This paradoxical phenomenon is known as the hydra effect, and it has important implications in the design of strategies in such areas as fishing, pest management, and conservation biology.

Early Adjustment, Gender Differences, and Classroom Organizational Climate in First Grade

ERIC Educational Resources Information Center

Ponitz, Claire Cameron; Rimm-Kaufman, Sara E.; Brock, Laura L.

2009-01-01

We examined gender differences in the first-grade transition, exploring child and classroom contributions to self-control and achievement in a rural sample. Teachers (n = 36) reported on children's (n = 172) initial adjustment difficulty and end-of-year self-control. Observed classroom organization and teacher-reported classroom chaos measured…

Devising and Attaining National Health Objectives: A Case Study in Policy Formulation Using Asthma Targets in Healthy People 2000

DTIC Science & Technology

1991-05-06

Phys- (loosely) Quantum Chaos Theory entific Paradigm ics - atomistic move- ments Value Claims transmutes values value isolated into Values incorporat...infant care 3. immunizations 4. sexually transmissible disease services 5. high blood pressure control 6. toxic agent control 7. occupational safety and

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.

The Application of Chaos Theory to the Career-Plateaued Worker.

ERIC Educational Resources Information Center

Duffy, Jean Ann

2000-01-01

Applies some of the principles of chaos theory to career-plateaued workers on the basis of a case study. Concludes that chaos theory provides career practitioners a useful application for working with this type of client. (Author/JDM)

An introduction to chaotic and random time series analysis

NASA Technical Reports Server (NTRS)

Scargle, Jeffrey D.

1989-01-01

The origin of chaotic behavior and the relation of chaos to randomness are explained. Two mathematical results are described: (1) a representation theorem guarantees the existence of a specific time-domain model for chaos and addresses the relation between chaotic, random, and strictly deterministic processes; (2) a theorem assures that information on the behavior of a physical system in its complete state space can be extracted from time-series data on a single observable. Focus is placed on an important connection between the dynamical state space and an observable time series. These two results lead to a practical deconvolution technique combining standard random process modeling methods with new embedded techniques.

Chaos of radiative heat-loss-induced flame front instability.

PubMed

Kinugawa, Hikaru; Ueda, Kazuhiro; Gotoda, Hiroshi

2016-03-01

We are intensively studying the chaos via the period-doubling bifurcation cascade in radiative heat-loss-induced flame front instability by analytical methods based on dynamical systems theory and complex networks. Significant changes in flame front dynamics in the chaotic region, which cannot be seen in the bifurcation diagrams, were successfully extracted from recurrence quantification analysis and nonlinear forecasting and from the network entropy. The temporal dynamics of the fuel concentration in the well-developed chaotic region is much more complicated than that of the flame front temperature. It exhibits self-affinity as a result of the scale-free structure in the constructed visibility graph.

Bifurcations and chaos in a parametrically damped two-well Duffing oscillator subjected to symmetric periodic pulses.

PubMed

Chacón, R; Martínez García-Hoz, A

1999-06-01

We study a parametrically damped two-well Duffing oscillator, subjected to a periodic string of symmetric pulses. The order-chaos threshold when altering solely the width of the pulses is investigated theoretically through Melnikov analysis. We show analytically and numerically that most of the results appear independent of the particular wave form of the pulses provided that the transmitted impulse is the same. By using this property, the stability boundaries of the stationary solutions are determined to first approximation by means of an elliptic harmonic balance method. Finally, the bifurcation behavior at the stability boundaries is determined numerically.

Chaos-based CAZAC scheme for secure transmission in OFDM-PON

NASA Astrophysics Data System (ADS)

Fu, Xiaosong; Bi, Meihua; Zhou, Xuefang; Yang, Guowei; Lu, Yang; Hu, Miao

2018-01-01

To effectively resist malicious eavesdropping and performance deterioration, a novel chaos-based secure transmission scheme is proposed to enhance the physical layer security and reduce peak-to-average power ratio (PAPR) in orthogonal frequency division multiplexing passive optical network (OFDM-PON). By the randomly extracting operation of common CAZAC values, the specially-designed constant amplitude zero autocorrelation (CAZAC) is created for system encryption and PAPR reduction enhancing the transmission security. This method is verified in {10-Gb/s encrypted OFDM-PON with 20-km fiber transmission. Results show that, compared to common OFDM-PON, our scheme achieves {3-dB PAPR reduction and {1-dB receiver sensitivity improvement.

Observation of Hamiltonian chaos and its control in wave particle interaction

NASA Astrophysics Data System (ADS)

Doveil, F.; Macor, A.; Aïssi, A.

2007-12-01

Wave-particle interactions are central in plasma physics. They can be studied in a traveling wave tube (TWT) to avoid intrinsic plasma noise. This led to detailed experimental analysis of the self-consistent interaction between unstable waves and an either cold or warm beam. More recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The nonlinear synchronization of particles by a single wave responsible for Landau damping is observed. The resonant velocity domain associated with a single wave is also observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a 'devil's staircase' behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons from escaping from a given velocity region as well as its robustness are successfully tested. The underlying concepts extend far beyond the field of electron devices and plasma physics.

Nonlinear Time Series Analysis of Nodulation Factor Induced Calcium Oscillations: Evidence for Deterministic Chaos?

PubMed Central

Hazledine, Saul; Sun, Jongho; Wysham, Derin; Downie, J. Allan; Oldroyd, Giles E. D.; Morris, Richard J.

2009-01-01

Legume plants form beneficial symbiotic interactions with nitrogen fixing bacteria (called rhizobia), with the rhizobia being accommodated in unique structures on the roots of the host plant. The legume/rhizobial symbiosis is responsible for a significant proportion of the global biologically available nitrogen. The initiation of this symbiosis is governed by a characteristic calcium oscillation within the plant root hair cells and this signal is activated by the rhizobia. Recent analyses on calcium time series data have suggested that stochastic effects have a large role to play in defining the nature of the oscillations. The use of multiple nonlinear time series techniques, however, suggests an alternative interpretation, namely deterministic chaos. We provide an extensive, nonlinear time series analysis on the nature of this calcium oscillation response. We build up evidence through a series of techniques that test for determinism, quantify linear and nonlinear components, and measure the local divergence of the system. Chaos is common in nature and it seems plausible that properties of chaotic dynamics might be exploited by biological systems to control processes within the cell. Systems possessing chaotic control mechanisms are more robust in the sense that the enhanced flexibility allows more rapid response to environmental changes with less energetic costs. The desired behaviour could be most efficiently targeted in this manner, supporting some intriguing speculations about nonlinear mechanisms in biological signaling. PMID:19675679

Chaos and the Double Function of Communication

NASA Astrophysics Data System (ADS)

Aula, P. S.

Since at least the needle model age, communication researchers have systematically sought means to explain, control and predict communication behavior between people. For many reasons, the accuracy of constructed models and the studies based upon them has not risen very high. It can be claimed that the reasons for the inaccuracy of communication models, and thus the poor predictability of everyday action, originate from the processes' innate chaos, apparent beneath their behavior. This leads to the argument that communication systems, which appear stable and have precisely identical starting points and identical operating environments, can nevertheless behave in an exceptional and completely different manner, despite the fact that their behavior is ruled or directed by the same rules or laws.

Frequency-locked chaotic opto-RF oscillator.

PubMed

Thorette, Aurélien; Romanelli, Marco; Brunel, Marc; Vallet, Marc

2016-06-15

A driven opto-RF oscillator, consisting of a dual-frequency laser (DFL) submitted to frequency-shifted feedback, is experimentally and numerically studied in a chaotic regime. Precise control of the reinjection strength and detuning permits isolation of a parameter region of bounded-phase chaos, where the opto-RF oscillator is frequency-locked to the master oscillator, in spite of chaotic phase and intensity oscillations. Robust experimental evidence of this synchronization regime is found, and phase noise spectra allow us to compare phase-locking and bounded-phase chaos regimes. In particular, it is found that the long-term phase stability of the master oscillator is well transferred to the opto-RF oscillator, even in the chaotic regime.

Chaos in a neural network circuit

NASA Astrophysics Data System (ADS)

Kepler, Thomas B.; Datt, Sumeet; Meyer, Robert B.; Abott, L. F.

1990-12-01

We have constructed a neural network circuit of four clipped, high-grain, integrating operational amplifiers coupled to each other through an array of digitally programmable resistor ladders (MDACs). In addition to fixed-point and cyclic behavior, the circuit exhibits chaotic behavior with complex strange attractors which are approached through period doubling, intermittent attractor expansion and/or quasiperiodic pathways. Couplings between the nonlinear circuit elements are controlled by a computer which can automatically search through the space of couplings for interesting phenomena. We report some initial statistical results relating the behavior of the network to properties of its coupling matrix. Through these results and further research the circuit should help resolve fundamental issues concerning chaos in neural networks.

Transition to spatiotemporal chaos in a two-dimensional hydrodynamic system.

PubMed

Pirat, Christophe; Naso, Aurore; Meunier, Jean-Louis; Maïssa, Philippe; Mathis, Christian

2005-04-08

We study the transition to spatiotemporal chaos in a two-dimensional hydrodynamic experiment where liquid columns take place in the gravity induced instability of a liquid film. The film is formed below a plane grid which is used as a porous media and is continuously supplied with a controlled flow rate. This system can be either ordered (on a hexagonal structure) or disordered depending on the flow rate. We observe, for the first time in an initially structured state, a subcritical transition to spatiotemporal disorder which arises through spatiotemporal intermittency. Statistics of numbers, creations, and fusions of columns are investigated. We exhibit a critical behavior close to the directed percolation one.

A bound on chaos

DOE PAGES

Maldacena, Juan; Shenker, Stephen H.; Stanford, Douglas

2016-08-17

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ L ≤ 2πk B T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

Applying the Network Simulation Method for testing chaos in a resistively and capacitively shunted Josephson junction model

NASA Astrophysics Data System (ADS)

Bellver, Fernando Gimeno; Garratón, Manuel Caravaca; Soto Meca, Antonio; López, Juan Antonio Vera; Guirao, Juan L. G.; Fernández-Martínez, Manuel

In this paper, we explore the chaotic behavior of resistively and capacitively shunted Josephson junctions via the so-called Network Simulation Method. Such a numerical approach establishes a formal equivalence among physical transport processes and electrical networks, and hence, it can be applied to efficiently deal with a wide range of differential systems. The generality underlying that electrical equivalence allows to apply the circuit theory to several scientific and technological problems. In this work, the Fast Fourier Transform has been applied for chaos detection purposes and the calculations have been carried out in PSpice, an electrical circuit software. Overall, it holds that such a numerical approach leads to quickly computationally solve Josephson differential models. An empirical application regarding the study of the Josephson model completes the paper.

Bifurcations and Chaos of AN Immersed Cantilever Beam in a Fluid and Carrying AN Intermediate Mass

NASA Astrophysics Data System (ADS)

AL-QAISIA, A. A.; HAMDAN, M. N.

2002-06-01

The concern of this work is the local stability and period-doubling bifurcations of the response to a transverse harmonic excitation of a slender cantilever beam partially immersed in a fluid and carrying an intermediate lumped mass. The unimodal form of the non-linear dynamic model describing the beam-mass in-plane large-amplitude flexural vibration, which accounts for axial inertia, non-linear curvature and inextensibility condition, developed in Al-Qaisia et al. (2000Shock and Vibration7 , 179-194), is analyzed and studied for the resonance responses of the first three modes of vibration, using two-term harmonic balance method. Then a consistent second order stability analysis of the associated linearized variational equation is carried out using approximate methods to predict the zones of symmetry breaking leading to period-doubling bifurcation and chaos on the resonance response curves. The results of the present work are verified for selected physical system parameters by numerical simulations using methods of the qualitative theory, and good agreement was obtained between the analytical and numerical results. Also, analytical prediction of the period-doubling bifurcation and chaos boundaries obtained using a period-doubling bifurcation criterion proposed in Al-Qaisia and Hamdan (2001 Journal of Sound and Vibration244, 453-479) are compared with those of computer simulations. In addition, results of the effect of fluid density, fluid depth, mass ratio, mass position and damping on the period-doubling bifurcation diagrams are studies and presented.

Aram and Iani Chaos

NASA Technical Reports Server (NTRS)

2003-01-01

MGS MOC Release No. MOC2-344, 28 April 2003

This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image mosaic was constructed from data acquired by the MOC red wide angle camera. The large, circular feature in the upper left is Aram Chaos, an ancient impact crater filled with layered sedimentary rock that was later disrupted and eroded to form a blocky, 'chaotic' appearance. To the southeast of Aram Chaos, in the lower right of this picture, is Iani Chaos. The light-toned patches amid the large blocks of Iani Chaos are known from higher-resolution MOC images to be layered, sedimentary rock outcrops. The picture center is near 0.5oN, 20oW. Sunlight illuminates the scene from the left/upper left.

Building CHAOS: An Operating System for Livermore Linux Clusters

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

Garlick, J E; Dunlap, C M

2003-02-21

The Livermore Computing (LC) Linux Integration and Development Project (the Linux Project) produces and supports the Clustered High Availability Operating System (CHAOS), a cluster operating environment based on Red Hat Linux. Each CHAOS release begins with a set of requirements and ends with a formally tested, packaged, and documented release suitable for use on LC's production Linux clusters. One characteristic of CHAOS is that component software packages come from different sources under varying degrees of project control. Some are developed by the Linux Project, some are developed by other LC projects, some are external open source projects, and some aremore » commercial software packages. A challenge to the Linux Project is to adhere to release schedules and testing disciplines in a diverse, highly decentralized development environment. Communication channels are maintained for externally developed packages in order to obtain support, influence development decisions, and coordinate/understand release schedules. The Linux Project embraces open source by releasing locally developed packages under open source license, by collaborating with open source projects where mutually beneficial, and by preferring open source over proprietary software. Project members generally use open source development tools. The Linux Project requires system administrators and developers to work together to resolve problems that arise in production. This tight coupling of production and development is a key strategy for making a product that directly addresses LC's production requirements. It is another challenge to balance support and development activities in such a way that one does not overwhelm the other.« less

Chaos: A Topic for Interdisciplinary Education in Physics

ERIC Educational Resources Information Center

Bae, Saebyok

2009-01-01

Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…

Chaos based encryption system for encrypting electroencephalogram signals.

PubMed

Lin, Chin-Feng; Shih, Shun-Han; Zhu, Jin-De

2014-05-01

In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity.

PubMed

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

Mesoscopic chaos mediated by Drude electron-hole plasma in silicon optomechanical oscillators

PubMed Central

Wu, Jiagui; Huang, Shu-Wei; Huang, Yongjun; Zhou, Hao; Yang, Jinghui; Liu, Jia-Ming; Yu, Mingbin; Lo, Guoqiang; Kwong, Dim-Lee; Duan, Shukai; Wei Wong, Chee

2017-01-01

Chaos has revolutionized the field of nonlinear science and stimulated foundational studies from neural networks, extreme event statistics, to physics of electron transport. Recent studies in cavity optomechanics provide a new platform to uncover quintessential architectures of chaos generation and the underlying physics. Here, we report the generation of dynamical chaos in silicon-based monolithic optomechanical oscillators, enabled by the strong and coupled nonlinearities of two-photon absorption induced Drude electron–hole plasma. Deterministic chaotic oscillation is achieved, and statistical and entropic characterization quantifies the chaos complexity at 60 fJ intracavity energies. The correlation dimension D2 is determined at 1.67 for the chaotic attractor, along with a maximal Lyapunov exponent rate of about 2.94 times the fundamental optomechanical oscillation for fast adjacent trajectory divergence. Nonlinear dynamical maps demonstrate the subharmonics, bifurcations and stable regimes, along with distinct transitional routes into chaos. This provides a CMOS-compatible and scalable architecture for understanding complex dynamics on the mesoscopic scale. PMID:28598426

Effect of the centrifugal force on domain chaos in Rayleigh-Bénard convection.

PubMed

Becker, Nathan; Scheel, J D; Cross, M C; Ahlers, Guenter

2006-06-01

Experiments and simulations from a variety of sample sizes indicated that the centrifugal force significantly affects the domain-chaos state observed in rotating Rayleigh-Bénard convection-patterns. In a large-aspect-ratio sample, we observed a hybrid state consisting of domain chaos close to the sample center, surrounded by an annulus of nearly stationary nearly radial rolls populated by occasional defects reminiscent of undulation chaos. Although the Coriolis force is responsible for domain chaos, by comparing experiment and simulation we show that the centrifugal force is responsible for the radial rolls. Furthermore, simulations of the Boussinesq equations for smaller aspect ratios neglecting the centrifugal force yielded a domain precession-frequency f approximately epsilon(mu) with mu approximately equal to 1 as predicted by the amplitude-equation model for domain chaos, but contradicted by previous experiment. Additionally the simulations gave a domain size that was larger than in the experiment. When the centrifugal force was included in the simulation, mu and the domain size were consistent with experiment.

HIV-Related Stress and Life Chaos Mediate the Association Between Poverty and Medication Adherence Among People Living with HIV/AIDS.

PubMed

Kalichman, Seth C; Kalichman, Moira O

2016-12-01

HIV treatment depends on high-levels of antiretroviral therapy (ART) adherence, which is severely impeded by poverty. Men and women living with HIV infection (N = 92) completed computerized interviews of demographic and health characteristics, poverty markers, stressful life events, and life chaos, as well as unannounced pill counts to determine prospective medication adherence and medical record chart abstractions for HIV viral load. Poverty markers were associated with both stressors and chaos, and the direct effects of all three factors predicted ART non-adherence. The multiple mediation model showed that accounting for stressors and chaos resulted in a non-significant association between poverty markers and ART adherence. The indirect effect of poverty markers on adherence through life chaos was significant, whereas the indirect effect of poverty markers on adherence through stressors was not significant. Factors that render HIV-related stress and create chaos offer intervention targets that are more amenable to change than poverty itself.

Multi-Gbit/s optical phase chaos communications using a time-delayed optoelectronic oscillator with a three-wave interferometer nonlinearity

NASA Astrophysics Data System (ADS)

Oden, Jérémy; Lavrov, Roman; Chembo, Yanne K.; Larger, Laurent

2017-11-01

We propose a chaos communication scheme based on a chaotic optical phase carrier generated with an optoelectronic oscillator with nonlinear time-delay feedback. The system includes a dedicated non-local nonlinearity, which is a customized three-wave imbalanced interferometer. This particular feature increases the complexity of the chaotic waveform and thus the security of the transmitted information, as these interferometers are characterized by four independent parameters which are part of the secret key for the chaos encryption scheme. We first analyze the route to chaos in the system, and evidence a sequence of period doubling bifurcations from the steady-state to fully developed chaos. Then, in the chaotic regime, we study the synchronization between the emitter and the receiver, and achieve chaotic carrier cancellation with a signal-to-noise ratio up to 20 dB. We finally demonstrate error-free chaos communications at a data rate of 3 Gbit/s.

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

Shwehdi, M.H.; Khan, A.Z.

Building automation technology is rapidly developing towards more reliable communication systems, devices that control electronic equipments. These equipment if controlled leads to efficient energy management, and savings on the monthly electricity bill. Power Line communication (PLC) has been one of the dreams of the electronics industry for decades, especially for building automation. It is the purpose of this paper to demonstrate communication methods among electronic control devices through an AC power line carrier within the buildings for more efficient energy control. The paper outlines methods of communication over a powerline, namely the X-10 and CE bus. It also introduces themore » spread spectrum technology as to increase speed to 100--150 times faster than the X-10 system. The powerline carrier has tremendous applications in the field of building automation. The paper presents an attempt to realize a smart house concept, so called, in which all home electronic devices from a coffee maker to a water heater microwave to chaos robots will be utilized by an intelligent network whenever one wishes to do so. The designed system may be applied very profitably to help in energy management for both customer and utility.« less

The operation of large computer-controlled manufacturing systems

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

Upton, D.M.

1988-01-01

This work examines methods for operation of large computer-controlled manufacturing systems, with more than 50 or so disparate CNC machines in congregation. The central theme is the development of a distributed control system, which requires minimal central supervision, and allows manufacturing system re-configuration without extensive control software re-writes. Provision is made for machines to learn from their experience and provide estimates of the time necessary to effect various tasks. Routing is opportunistic, with varying degrees of myopia depending on the prevailing situation. Necessary curtailments of opportunism are built in to the system, in order to provide a society of machinesmore » that operate in unison rather than in chaos. Negotiation and contention resolution are carried out using a UHF radio communications network, along with processing capability on both pallets and tools. Graceful and robust error recovery is facilitated by ensuring adequate pessimistic consideration of failure modes at each stage in the scheme. Theoretical models are developed and an examination is made of fundamental characteristics of auction-based scheduling methods.« less

Fractal mechanisms in the electrophysiology of the heart

NASA Technical Reports Server (NTRS)

Goldberger, A. L.

1992-01-01

The mathematical concept of fractals provides insights into complex anatomic branching structures that lack a characteristic (single) length scale, and certain complex physiologic processes, such as heart rate regulation, that lack a single time scale. Heart rate control is perturbed by alterations in neuro-autonomic function in a number of important clinical syndromes, including sudden cardiac death, congestive failure, cocaine intoxication, fetal distress, space sickness and physiologic aging. These conditions are associated with a loss of the normal fractal complexity of interbeat interval dynamics. Such changes, which may not be detectable using conventional statistics, can be quantified using new methods derived from "chaos theory.".

Genome chaos: survival strategy during crisis.

PubMed

Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H

2014-01-01

Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment.

Teaching as Chaos

ERIC Educational Resources Information Center

Moseley, Bryan; Dustin, Daniel

2008-01-01

In this article, the authors advance a metaphor born of chaos theory that views the college classroom as a complex dynamical system. The authors reason further that "teaching as chaos" provides a more accurate representation of the teaching-learning process than the existing linear scientific metaphors on which traditional learning assessments are…

Developing Quality Preschool Movement Programs: CHAOS and KinderPlay

ERIC Educational Resources Information Center

Robert, Darren L.; Yongue, Bill

2004-01-01

This article presents two models for creating new developmentally appropriate preschool movement programs: CHAOS (Children Helping Adults Open Senses) at Eastern Connecticut State University and "KinderPlay" at Florida International University. CHAOS and KinderPlay utilize skill themes and movement concepts as their focus and incorporate…

Efficient uncertainty quantification in fully-integrated surface and subsurface hydrologic simulations

NASA Astrophysics Data System (ADS)

Miller, K. L.; Berg, S. J.; Davison, J. H.; Sudicky, E. A.; Forsyth, P. A.

2018-01-01

Although high performance computers and advanced numerical methods have made the application of fully-integrated surface and subsurface flow and transport models such as HydroGeoSphere common place, run times for large complex basin models can still be on the order of days to weeks, thus, limiting the usefulness of traditional workhorse algorithms for uncertainty quantification (UQ) such as Latin Hypercube simulation (LHS) or Monte Carlo simulation (MCS), which generally require thousands of simulations to achieve an acceptable level of accuracy. In this paper we investigate non-intrusive polynomial chaos for uncertainty quantification, which in contrast to random sampling methods (e.g., LHS and MCS), represents a model response of interest as a weighted sum of polynomials over the random inputs. Once a chaos expansion has been constructed, approximating the mean, covariance, probability density function, cumulative distribution function, and other common statistics as well as local and global sensitivity measures is straightforward and computationally inexpensive, thus making PCE an attractive UQ method for hydrologic models with long run times. Our polynomial chaos implementation was validated through comparison with analytical solutions as well as solutions obtained via LHS for simple numerical problems. It was then used to quantify parametric uncertainty in a series of numerical problems with increasing complexity, including a two-dimensional fully-saturated, steady flow and transient transport problem with six uncertain parameters and one quantity of interest; a one-dimensional variably-saturated column test involving transient flow and transport, four uncertain parameters, and two quantities of interest at 101 spatial locations and five different times each (1010 total); and a three-dimensional fully-integrated surface and subsurface flow and transport problem for a small test catchment involving seven uncertain parameters and three quantities of interest at 241 different times each. Numerical experiments show that polynomial chaos is an effective and robust method for quantifying uncertainty in fully-integrated hydrologic simulations, which provides a rich set of features and is computationally efficient. Our approach has the potential for significant speedup over existing sampling based methods when the number of uncertain model parameters is modest ( ≤ 20). To our knowledge, this is the first implementation of the algorithm in a comprehensive, fully-integrated, physically-based three-dimensional hydrosystem model.

Pathways to Problem Behaviors: Chaotic Homes, Parent and Child Effortful Control, and Parenting

ERIC Educational Resources Information Center

Valiente, Carlos; Lemery-Chalfant, Kathryn; Reiser, Mark

2007-01-01

Guided by Belsky's and Eisenberg, Cumberland, and Spinrad's heuristic models, we tested a process model with hypothesized paths from parents' effortful control (EC) and family chaos to indices of parenting to children's EC, and finally children's externalizing problem behavior. Parents reported on all constructs and children (N = 188; M age = 9.55…

Generalized chaos synchronization theorems for bidirectional differential equations and discrete systems with applications

NASA Astrophysics Data System (ADS)

Ji, Ye; Liu, Ting; Min, Lequan

2008-05-01

Two constructive generalized chaos synchronization (GCS) theorems for bidirectional differential equations and discrete systems are introduced. Using the two theorems, one can construct new chaos systems to make the system variables be in GCS. Five examples are presented to illustrate the effectiveness of the theoretical results.

Chaos Theory: Implications for Nonlinear Dynamics in Counseling.

ERIC Educational Resources Information Center

Stickel, Sue A.

The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…

The "Chaos" Pattern in Piaget's Theory of Cognitive Development.

ERIC Educational Resources Information Center

Lindsay, Jean S.

Piaget's theory of the cognitive development of the child is related to the recently developed non-linear "chaos" model. The term "chaos" refers to the tendency of dynamical, non-linear systems toward irregular, sometimes unpredictable, deterministic behavior. Piaget identified this same pattern in his model of cognitive…

Specifying the Links between Household Chaos and Preschool Children's Development

ERIC Educational Resources Information Center

Martin, Anne; Razza, Rachel A.; Brooks-Gunn, Jeanne

2012-01-01

Household chaos has been linked to poorer cognitive, behavioural, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family…

Chaos, Complexity, Learning, and the Learning Organization: Towards a Chaordic Enterprise

ERIC Educational Resources Information Center

van Eijnatten, Frans M.; Putnik, Goran D.

2004-01-01

In order to set the stage for this special issue, the prime concepts are defined: i.e. "chaos," "complexity," "learning" (individual and organizational), "learning organization," and "chaordic enterprise". Also, several chaos-and-complexity-related definitions of learning and learning organizations are provided. Next, the guest editors' main…

Counseling Chaos: Techniques for Practitioners

ERIC Educational Resources Information Center

Pryor, Robert G. L.; Bright, Jim E. H.

2006-01-01

The chaos theory of careers draws together a number of themes in current theory and research. This article applies some of these themes to career counseling. The chaos theory of careers is outlined, and a conceptual framework for understanding assessment and counseling issues that focuses on convergent and emergent qualities is presented. Three…

Aram Chaos: A Long Lived Subsurface Aqueous Environment with Strong Water Resource Potential for Human Missions on Mars

NASA Astrophysics Data System (ADS)

Sibille, L.; Mueller, R. P.; Niles, P. B.; Glotch, T.; Archer, P. D.; Bell, M. S.

2015-10-01

Aram Chaos is a 280-km-wide near-circular structure near the outflow channel Ares Vallis and Aureum Chaos. It is a compelling landing site for human explorers featuring multiple science ROIs with a compelling resource ROI with polyhydrated sulfates.

Quantum chaos in nuclear physics

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

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu

A definition of classical and quantum chaos on the basis of the Liouville–Arnold theorem is proposed. According to this definition, a chaotic quantum system that has N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) that are determined by the symmetry of the Hamiltonian for the system being considered. Quantitative measures of quantum chaos are established. In the classical limit, they go over to the Lyapunov exponent or the classical stability parameter. The use of quantum-chaos parameters in nuclear physics is demonstrated.

Self-organization of chaos in mythology from a scientific point of view

NASA Astrophysics Data System (ADS)

Melker, Alexander I.

2007-04-01

In this contribution ancient Greek myths describing world's creation are analyzed as if they were a scientific paper. The 'paper' divided into the following parts: initial and boundary conditions, self-organization of chaos, world lines of self-organization, conclusion. It is shown that the self-organization of chaos consists of several stages during which two motive forces (attractive and repulsive) are generated, and totally disordered chaos transforms into partially ordered. It is found that there are five world lines of self-organization: water, light, cosmos-weather, water-fire, and State evolution.

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.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

NASA Astrophysics Data System (ADS)

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.

2018-06-01

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet.

PubMed

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E; Sols, Fernando; Carr, Lincoln D

2018-06-08

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Quantum chaos in the Heisenberg spin chain: The effect of Dzyaloshinskii-Moriya interaction.

PubMed

Vahedi, J; Ashouri, A; Mahdavifar, S

2016-10-01

Using one-dimensional spin-1/2 systems as prototypes of quantum many-body systems, we study the emergence of quantum chaos. The main purpose of this work is to answer the following question: how the spin-orbit interaction, as a pure quantum interaction, may lead to the onset of quantum chaos? We consider the three integrable spin-1/2 systems: the Ising, the XX, and the XXZ limits and analyze whether quantum chaos develops or not after the addition of the Dzyaloshinskii-Moriya interaction. We find that depending on the strength of the anisotropy parameter, the answer is positive for the XXZ and Ising models, whereas no such evidence is observed for the XX model. We also discuss the relationship between quantum chaos and thermalization.

Time-delay signature of chaos in 1550 nm VCSELs with variable-polarization FBG feedback.

PubMed

Li, Yan; Wu, Zheng-Mao; Zhong, Zhu-Qiang; Yang, Xian-Jie; Mao, Song; Xia, Guang-Qiong

2014-08-11

Based on the framework of spin-flip model (SFM), the output characteristics of a 1550 nm vertical-cavity surface-emitting laser (VCSEL) subject to variable-polarization fiber Bragg grating (FBG) feedback (VPFBGF) have been investigated. With the aid of the self-correlation function (SF) and the permutation entropy (PE) function, the time-delay signature (TDS) of chaos in the VPFBGF-VCSEL is evaluated, and then the influences of the operation parameters on the TDS of chaos are analyzed. The results show that the TDS of chaos can be suppressed efficiently through selecting suitable coupling coefficient and feedback rate of the FBG, and is weaker than that of chaos generated by traditional variable-polarization mirror feedback VCSELs (VPMF-VCSELs) or polarization-preserved FBG feedback VCSELs (PPFBGF-VCSELs).

Experimental Induction of Genome Chaos.

PubMed

Ye, Christine J; Liu, Guo; Heng, Henry H

2018-01-01

Genome chaos, or karyotype chaos, represents a powerful survival strategy for somatic cells under high levels of stress/selection. Since the genome context, not the gene content, encodes the genomic blueprint of the cell, stress-induced rapid and massive reorganization of genome topology functions as a very important mechanism for genome (karyotype) evolution. In recent years, the phenomenon of genome chaos has been confirmed by various sequencing efforts, and many different terms have been coined to describe different subtypes of the chaotic genome including "chromothripsis," "chromoplexy," and "structural mutations." To advance this exciting field, we need an effective experimental system to induce and characterize the karyotype reorganization process. In this chapter, an experimental protocol to induce chaotic genomes is described, following a brief discussion of the mechanism and implication of genome chaos in cancer evolution.

The Simple Map for a Single-null Divertor Tokamak: How to Look for Self-Similarity in Chaos

NASA Astrophysics Data System (ADS)

Nguyen, Christina; Ali, Halima; Punjabi, Alkesh

2000-10-01

The movement of magnetic field lines inside a single-null divertor tokamak can be described by the Simple Map^1. The Simple Map in the Poincaré Surface of Section is given by the equations: X_1=X_0-KY_0(1-Y_0) and Y_1=Y_0+KX_1. In these equations, K remains constant at 0.60. However, the values for X0 and Y0 are changed. These values are changed so that we can zoom into chaos. Chaos lies between the region (0,0.997) and (0,1). In chaos, there lies order. As we zoom into chaos, we again find chaos and order that looks like the original good surfaces and chaos. This phenomenon is called self-similarity. Self-similarity can occur for an infinite number of times if one magnifies into the chaotic region. For this work, we write a program in a computer language called Fortran 77 and Gnuplot. This work is supported by US DOE OFES. Ms. Christina Nguyen is a HU CFRT Summer Fusion High School Workshop Scholar from Andrew Hill High School in California. She is supported by NASA SHARP Plus Program. 1. Punjabi A, Verma A and Boozer A, Phys Rev Lett 69 3322 (1992) and J Plasma Phys 52 91 (1994)

Combined peak-to-average power ratio reduction and physical layer security enhancement in optical orthogonal frequency division multiplexing visible-light communication systems

NASA Astrophysics Data System (ADS)

Wang, Zhongpeng; Chen, Shoufa

2016-07-01

A physical encryption scheme for discrete Hartley transform (DHT) precoded orthogonal frequency division multiplexing (OFDM) visible-light communication (VLC) systems using frequency domain chaos scrambling is proposed. In the scheme, the chaos scrambling, which is generated by a modified logistic mapping, is utilized to enhance the physical layer of security, and the DHT precoding is employed to reduce of OFDM signal for OFDM-based VLC. The influence of chaos scrambling on peak-to-average power ratio (PAPR) and bit error rate (BER) of systems is studied. The experimental simulation results prove the efficiency of the proposed encryption method for DHT-precoded, OFDM-based VLC systems. Furthermore, the influence of the proposed encryption to the PAPR and BER of systems is evaluated. The experimental results show that the proposed security scheme can protect the DHT-precoded, OFDM-based VLC from eavesdroppers, while keeping the good BER performance of DHT-precoded systems. The BER performance of the encrypted and DHT-precoded system is almost the same as that of the conventional DHT-precoded system without encryption.

Reliability-based trajectory optimization using nonintrusive polynomial chaos for Mars entry mission

NASA Astrophysics Data System (ADS)

Huang, Yuechen; Li, Haiyang

2018-06-01

This paper presents the reliability-based sequential optimization (RBSO) method to settle the trajectory optimization problem with parametric uncertainties in entry dynamics for Mars entry mission. First, the deterministic entry trajectory optimization model is reviewed, and then the reliability-based optimization model is formulated. In addition, the modified sequential optimization method, in which the nonintrusive polynomial chaos expansion (PCE) method and the most probable point (MPP) searching method are employed, is proposed to solve the reliability-based optimization problem efficiently. The nonintrusive PCE method contributes to the transformation between the stochastic optimization (SO) and the deterministic optimization (DO) and to the approximation of trajectory solution efficiently. The MPP method, which is used for assessing the reliability of constraints satisfaction only up to the necessary level, is employed to further improve the computational efficiency. The cycle including SO, reliability assessment and constraints update is repeated in the RBSO until the reliability requirements of constraints satisfaction are satisfied. Finally, the RBSO is compared with the traditional DO and the traditional sequential optimization based on Monte Carlo (MC) simulation in a specific Mars entry mission to demonstrate the effectiveness and the efficiency of the proposed method.

Binary image encryption in a joint transform correlator scheme by aid of run-length encoding and QR code

NASA Astrophysics Data System (ADS)

Qin, Yi; Wang, Zhipeng; Wang, Hongjuan; Gong, Qiong

2018-07-01

We propose a binary image encryption method in joint transform correlator (JTC) by aid of the run-length encoding (RLE) and Quick Response (QR) code, which enables lossless retrieval of the primary image. The binary image is encoded with RLE to obtain the highly compressed data, and then the compressed binary image is further scrambled using a chaos-based method. The compressed and scrambled binary image is then transformed into one QR code that will be finally encrypted in JTC. The proposed method successfully, for the first time to our best knowledge, encodes a binary image into a QR code with the identical size of it, and therefore may probe a new way for extending the application of QR code in optical security. Moreover, the preprocessing operations, including RLE, chaos scrambling and the QR code translation, append an additional security level on JTC. We present digital results that confirm our approach.

A polynomial chaos approach to the analysis of vehicle dynamics under uncertainty

NASA Astrophysics Data System (ADS)

Kewlani, Gaurav; Crawford, Justin; Iagnemma, Karl

2012-05-01

The ability of ground vehicles to quickly and accurately analyse their dynamic response to a given input is critical to their safety and efficient autonomous operation. In field conditions, significant uncertainty is associated with terrain and/or vehicle parameter estimates, and this uncertainty must be considered in the analysis of vehicle motion dynamics. Here, polynomial chaos approaches that explicitly consider parametric uncertainty during modelling of vehicle dynamics are presented. They are shown to be computationally more efficient than the standard Monte Carlo scheme, and experimental results compared with the simulation results performed on ANVEL (a vehicle simulator) indicate that the method can be utilised for efficient and accurate prediction of vehicle motion in realistic scenarios.

Ikeda-like chaos on a dynamically filtered supercontinuum light source

NASA Astrophysics Data System (ADS)

Chembo, Yanne K.; Jacquot, Maxime; Dudley, John M.; Larger, Laurent

2016-08-01

We demonstrate temporal chaos in a color-selection mechanism from the visible spectrum of a supercontinuum light source. The color-selection mechanism is governed by an acousto-optoelectronic nonlinear delayed-feedback scheme modeled by an Ikeda-like equation. Initially motivated by the design of a broad audience live demonstrator in the framework of the International Year of Light 2015, the setup also provides a different experimental tool to investigate the dynamical complexity of delayed-feedback dynamics. Deterministic hyperchaos is analyzed here from the experimental time series. A projection method identifies the delay parameter, for which the chaotic strange attractor originally evolving in an infinite-dimensional phase space can be revealed in a two-dimensional subspace.

Experimental evidence of intermittent chaos in a glow discharge plasma without external forcing and its numerical modelling

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

Ghosh, S., E-mail: sabuj.ghosh@saha.ac.in; Kumar Shaw, Pankaj; Sekar Iyengar, A. N.

Intermittent chaos was observed in a glow discharge plasma as the system evolved from regular type of relaxation oscillations (of larger amplitude) to an irregular type of oscillations (of smaller amplitude) as the discharge voltage was increased. Floating potential fluctuations were analyzed by different statistical and spectral methods. Features like a gradual change in the normal variance of the interpeak time intervals, a dip in the skewness, and a hump in the kurtosis with variation in the control parameter have been seen, which are strongly indicative of intermittent behavior in the system. Detailed analysis also suggests that the intrinsic noisemore » level in the experiment increases with the increasing discharge voltage. An attempt has been made to model the experimental observations by a second order nonlinear ordinary differential equation derived from the fluid equations for an unmagnetized plasma. Though the experiment had no external forcing, it was conjectured that the intrinsic noise in the experiment could be playing a vital role in the dynamics of the system. Hence, a constant bias and noise as forcing terms were included in the model. Results from the theoretical model are in close qualitative agreement with the experimental results.« less

Synchronization and information processing by an on-off coupling

NASA Astrophysics Data System (ADS)

Wei, G. W.; Zhao, Shan

2002-05-01

This paper proposes an on-off coupling process for chaos synchronization and information processing. An in depth analysis for the net effect of a conventional coupling is performed. The stability of the process is studied. We show that the proposed controlled coupling process can locally minimize the smoothness and the fidelity of dynamical data. A digital filter expression for the on-off coupling process is derived and a connection is made to the Hanning filter. The utility and robustness of the proposed approach is demonstrated by chaos synchronization in Duffing oscillators, the spatiotemporal synchronization of noisy nonlinear oscillators, the estimation of the trend of a time series, and restoration of the contaminated solution of the nonlinear Schrödinger equation.

Chaotic Dynamics in the Planar Gravitational Many-Body Problem with Rigid Body Rotations

NASA Astrophysics Data System (ADS)

Kwiecinski, James A.; Kovacs, Attila; Krause, Andrew L.; Planella, Ferran Brosa; van Gorder, Robert A.

The discovery of Pluto’s small moons in the last decade has brought attention to the dynamics of the dwarf planet’s satellites. With such systems in mind, we study a planar N-body system in which all the bodies are point masses, except for a single rigid body. We then present a reduced model consisting of a planar N-body problem with the rigid body treated as a 1D continuum (i.e. the body is treated as a rod with an arbitrary mass distribution). Such a model provides a good approximation to highly asymmetric geometries, such as the recently observed interstellar asteroid ‘Oumuamua, but is also amenable to analysis. We analytically demonstrate the existence of homoclinic chaos in the case where one of the orbits is nearly circular by way of the Melnikov method, and give numerical evidence for chaos when the orbits are more complicated. We show that the extent of chaos in parameter space is strongly tied to the deviations from a purely circular orbit. These results suggest that chaos is ubiquitous in many-body problems when one or more of the rigid bodies exhibits nonspherical and highly asymmetric geometries. The excitation of chaotic rotations does not appear to require tidal dissipation, obliquity variation, or orbital resonance. Such dynamics give a possible explanation for routes to chaotic dynamics observed in N-body systems such as the Pluto system where some of the bodies are highly nonspherical.

Practice Environments and Job Satisfaction in Patient-Centered Medical Homes

PubMed Central

Alidina, Shehnaz; Rosenthal, Meredith B.; Schneider, Eric C.; Singer, Sara J.; Friedberg, Mark W.

2014-01-01

PURPOSE We undertook a study to evaluate the effects of medical home transformation on job satisfaction in the primary care setting. METHODS We collected primary data from 20 primary care practices participating in medical home pilot projects in Rhode Island and Colorado from 2009 to 2011. We surveyed clinicians and staff about the quality of their practice environments (eg, office chaos, communication, difficulties in providing safe, high-quality care) and job satisfaction at baseline and 30 months, and about stress, burnout, and intention to leave at 30 months. We interviewed practice leaders about the impact of pilot project participation. We assessed longitudinal changes in the practice environment and job satisfaction and, in the final pilot year, examined cross-sectional associations between the practice environment and job satisfaction, stress, burnout, and intention to leave. RESULTS Between baseline and 30 months, job satisfaction improved in Rhode Island (P =.03) but not in Colorado. For both pilot projects, reported difficulties in providing safe, high-quality care decreased (P <.001), but emphasis on quality and the level of office chaos did not change significantly. In cross-sectional analyses, fewer difficulties in providing safe, high-quality care and more open communication were associated with greater job satisfaction. Greater office chaos and an emphasis on electronic information were associated with greater stress and burnout. CONCLUSIONS Medical home transformations that emphasize quality and open communication while minimizing office chaos may offer the best chances of improving job satisfaction. PMID:25024241

Urban chaos and replacement dynamics in nature and society

NASA Astrophysics Data System (ADS)

Chen, Yanguang

2014-11-01

Replacements resulting from competition are ubiquitous phenomena in both nature and society. The evolution of a self-organized system is always a physical process substituting one type of components for another type of components. A logistic model of replacement dynamics has been proposed in terms of technical innovation and urbanization, but it fails to arouse widespread attention in the academia. This paper is devoted to laying the foundations of general replacement principle by using analogy and induction. The empirical base of this study is urban replacement, including urbanization and urban growth. The sigmoid functions can be employed to model various processes of replacement. Many mathematical methods such as allometric scaling and head/tail breaks can be applied to analyzing the processes and patterns of replacement. Among varied sigmoid functions, the logistic function is the basic and the simplest model of replacement dynamics. A new finding is that replacement can be associated with chaos in a nonlinear system, e.g., urban chaos is just a part of replacement dynamics. The aim of developing replacement theory is at understanding complex interaction and conversion. This theory provides a new way of looking at urbanization, technological innovation and diffusion, Volterra-Lotka’s predator-prey interaction, man-land relation, and dynastic changes resulting from peasant uprising, and all that. Especially, the periodic oscillations and chaos of replacement dynamics can be used to explain and predict the catastrophic occurrences in the physical and human systems.

Control of generation regimes of ring chip laser under the action of the stationary magnetic field

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

Aulova, T V; Kravtsov, Nikolai V; Lariontsev, E G

2013-05-31

We consider realisation of different generation regimes in an autonomous ring chip laser, which is a rather complicated problem. We offer and demonstrate a simple and effective method for controlling the radiation dynamics of a ring Nd:YAG chip laser when it is subjected to a stationary magnetic field producing both frequency and substantial amplitude nonreciprocities. The amplitude and frequency nonreciprocities of a ring cavity, arising under the action of this magnetic field, change when the magnet is moved with respect to the active element of the chip laser. Some self-modulation and stationary generation regimes as well as the regime ofmore » beatings and dynamic chaos regime are experimentally realised. Temporal and spectral characteristics of radiation are studied and conditions for the appearance of the generation regime are found. (control of laser radiation parameters)« less

75 FR 53013 - Culturally Significant Objects Imported for Exhibition Determinations: “Chaos and Classicism: Art...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-08-30

... DEPARTMENT OF STATE [Public Notice 7137] Culturally Significant Objects Imported for Exhibition Determinations: ``Chaos and Classicism: Art in France, Italy, and Germany, 1918-1936'' SUMMARY: Notice is hereby... hereby determine that the objects to be included in the exhibition ``Chaos and Classicism: Art in France...

Role of DNA Replication Defects in Breast Cancer

DTIC Science & Technology

2010-10-01

effect is that C3H-Mcm4Chaos3/Chaos3 mice are developmentally normal, but Mcm4Chaos3/- animals die in utero or neonatally [Shima, 2007]. To further...3e). This increase in the ratio of reticulocytes (erythrocyte precursors) to mature RBCs is characteristic of anemia . Hemizygosity for Mcm3

Applying Chaos Theory to Lesson Planning and Delivery

ERIC Educational Resources Information Center

Cvetek, Slavko

2008-01-01

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

The Chaos Theory of Careers: A User's Guide

ERIC Educational Resources Information Center

Bright, Jim E. H.; Pryor, Robert G. L.

2005-01-01

The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…

Chaos Theory as a Planning Tool for Community-Based Educational Experiences for Health Students.

ERIC Educational Resources Information Center

Velde, Beth P.; Greer, Annette G.; Lynch, Deirdre C.; Escott-Stump, Sylvia

2002-01-01

Chaos theory, which attempts to understand underlying order where none is apparent, was applied to an interdisciplinary rural health training program for health professionals. Similar programs should anticipate systemic flux between order and chaos and pay attention to information flow, degree of diversity, richness of connectivity, contained…

Chaos Theory and Post Modernism

ERIC Educational Resources Information Center

Snell, Joel

2009-01-01

Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…

"Chaos Rules" Revisited

ERIC Educational Resources Information Center

Murphy, David

2011-01-01

About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…

Chaotic micromixer utilizing electro-osmosis and induced charge electro-osmosis in eccentric annulus

NASA Astrophysics Data System (ADS)

Feng, Huicheng; Wong, Teck Neng; Che, Zhizhao; Marcos

2016-06-01

Efficient mixing is of significant importance in numerous chemical and biomedical applications but difficult to realize rapidly in microgeometries due to the lack of turbulence. We propose to enhance mixing by introducing Lagrangian chaos through electro-osmosis (EO) or induced charge electro-osmosis (ICEO) in an eccentric annulus. The analysis reveals that the created Lagrangian chaos can achieve a homogeneous mixing much more rapidly than either the pure EO or the pure ICEO. Our systematic investigations on the key parameters, ranging from the eccentricity, the alternating time period, the number of flow patterns in one time period, to the specific flow patterns utilized for the Lagrangian chaos creation, present that the Lagrangian chaos is considerably robust. The system can obtain a good mixing effect with wide ranges of eccentricity, alternating time period, and specific flow patterns utilized for the Lagrangian chaos creation as long as the number of flow patterns in one time period is two. As the electric field increases, the time consumption for homogenous mixing is reduced more remarkably for the Lagrangian chaos of the ICEO than that of the EO.

Suppression of chaos at slow variables by rapidly mixing fast dynamics

NASA Astrophysics Data System (ADS)

Abramov, R.

2012-04-01

One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger mixing system would result in general increase of chaos at the slow variables.

On the design of henon and logistic map-based random number generator

NASA Astrophysics Data System (ADS)

Magfirawaty; Suryadi, M. T.; Ramli, Kalamullah

2017-10-01

The key sequence is one of the main elements in the cryptosystem. True Random Number Generators (TRNG) method is one of the approaches to generating the key sequence. The randomness source of the TRNG divided into three main groups, i.e. electrical noise based, jitter based and chaos based. The chaos based utilizes a non-linear dynamic system (continuous time or discrete time) as an entropy source. In this study, a new design of TRNG based on discrete time chaotic system is proposed, which is then simulated in LabVIEW. The principle of the design consists of combining 2D and 1D chaotic systems. A mathematical model is implemented for numerical simulations. We used comparator process as a harvester method to obtain the series of random bits. Without any post processing, the proposed design generated random bit sequence with high entropy value and passed all NIST 800.22 statistical tests.

Relativistic quantum chaos—An emergent interdisciplinary field

NASA Astrophysics Data System (ADS)

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics—all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Philosophical perspectives on quantum chaos: Models and interpretations

NASA Astrophysics Data System (ADS)

Bokulich, Alisa Nicole

2001-09-01

The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and theoretical pluralism, are inadequate. The fruitful ways in which models have been used in quantum chaos research point to the need for a new framework for addressing intertheoretic relations that focuses on models rather than laws.

Margaret Wheatley on Leadership for Change.

ERIC Educational Resources Information Center

Steinberger, Elizabeth Donohoe

1995-01-01

Wheatley's 1992 bestseller, "Leadership and the New Science," argues that across scientific disciplines, our rational, systematic quest for order, control, stability, and predictability are yielding to a deeper appreciation for chaos, complexity, uncertainty, and change. In this interview, Wheatley shows how breakthroughs in biology,…

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.

Defining chaos.

PubMed

Hunt, Brian R; Ott, Edward

2015-09-01

In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy," and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.

Manifestation of resonance-related chaos in coupled Josephson junctions

NASA Astrophysics Data System (ADS)

Shukrinov, Yu. M.; Hamdipour, M.; Kolahchi, M. R.; Botha, A. E.; Suzuki, M.

2012-11-01

Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase-charge and charge-charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current-voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.

Characterizing the heterogeneity of triple-negative breast cancers using microdissected normal ductal epithelium and RNA-sequencing

PubMed Central

Radovich, Milan; Clare, Susan E.; Atale, Rutuja; Pardo, Ivanesa; Hancock, Bradley A.; Solzak, Jeffrey P.; Kassem, Nawal; Mathieson, Theresa; Storniolo, Anna Maria V.; Rufenbarger, Connie; Lillemoe, Heather A.; Blosser, Rachel J.; Choi, Mi Ran; Sauder, Candice A.; Doxey, Diane; Henry, Jill E.; Hilligoss, Eric E.; Sakarya, Onur; Hyland, Fiona C.; Hickenbotham, Matthew; Zhu, Jin; Glasscock, Jarret; Badve, Sunil; Ivan, Mircea; Liu, Yunlong; Sledge, George W.; Schneider, Bryan P.

2014-01-01

Triple-negative breast cancers (TNBCs) are a heterogeneous set of tumors defined by an absence of actionable therapeutic targets (ER−,PR−,HER2−). Microdissected normal ductal epithelium from healthy volunteers represents a novel comparator to reveal insights into TNBC heterogeneity and to inform drug development. Using RNA-sequencing data from our institution and The Cancer Genome Atlas (TCGA) we compared the transcriptomes of 94 TNBCs, 20 microdissected normal breast tissues from healthy volunteers from the Susan G. Komen for the Cure Tissue Bank, and 10 histologically normal tissues adjacent to tumor. Pathway analysis comparing TNBCs to optimized normal controls of microdissected normal epithelium versus classic controls composed of adjacent normal tissue revealed distinct molecular signatures. Differential gene expression of TNBC compared with normal comparators demonstrated important findings for TNBC-specific clinical trials testing targeted agents; lack of over-expression for negative studies and over-expression in studies with drug activity. Next, by comparing each individual TNBC to the set of microdissected normals, we demonstrate that TNBC heterogeneity is attributable to transcriptional chaos, is associated with non-silent DNA mutational load, and explains transcriptional heterogeneity in addition to known molecular subtypes. Finally, chaos analysis identified 146 core genes dysregulated in >90% of TNBCs revealing an over-expressed central network. In conclusion, Use of microdissected normal ductal epithelium from healthy volunteers enables an optimized approach for studying TNBC and uncovers biological heterogeneity mediated by transcriptional chaos. PMID:24292813

Characterizing the heterogeneity of triple-negative breast cancers using microdissected normal ductal epithelium and RNA-sequencing.

PubMed

Radovich, Milan; Clare, Susan E; Atale, Rutuja; Pardo, Ivanesa; Hancock, Bradley A; Solzak, Jeffrey P; Kassem, Nawal; Mathieson, Theresa; Storniolo, Anna Maria V; Rufenbarger, Connie; Lillemoe, Heather A; Blosser, Rachel J; Choi, Mi Ran; Sauder, Candice A; Doxey, Diane; Henry, Jill E; Hilligoss, Eric E; Sakarya, Onur; Hyland, Fiona C; Hickenbotham, Matthew; Zhu, Jin; Glasscock, Jarret; Badve, Sunil; Ivan, Mircea; Liu, Yunlong; Sledge, George W; Schneider, Bryan P

2014-01-01

Triple-negative breast cancers (TNBCs) are a heterogeneous set of tumors defined by an absence of actionable therapeutic targets (ER, PR, and HER-2). Microdissected normal ductal epithelium from healthy volunteers represents a novel comparator to reveal insights into TNBC heterogeneity and to inform drug development. Using RNA-sequencing data from our institution and The Cancer Genome Atlas (TCGA) we compared the transcriptomes of 94 TNBCs, 20 microdissected normal breast tissues from healthy volunteers from the Susan G. Komen for the Cure Tissue Bank, and 10 histologically normal tissues adjacent to tumor. Pathway analysis comparing TNBCs to optimized normal controls of microdissected normal epithelium versus classic controls composed of adjacent normal tissue revealed distinct molecular signatures. Differential gene expression of TNBC compared with normal comparators demonstrated important findings for TNBC-specific clinical trials testing targeted agents; lack of over-expression for negative studies and over-expression in studies with drug activity. Next, by comparing each individual TNBC to the set of microdissected normals, we demonstrate that TNBC heterogeneity is attributable to transcriptional chaos, is associated with non-silent DNA mutational load, and explains transcriptional heterogeneity in addition to known molecular subtypes. Finally, chaos analysis identified 146 core genes dysregulated in >90 % of TNBCs revealing an over-expressed central network. In conclusion, use of microdissected normal ductal epithelium from healthy volunteers enables an optimized approach for studying TNBC and uncovers biological heterogeneity mediated by transcriptional chaos.

Chaos in World Politics: A Reflection

NASA Astrophysics Data System (ADS)

Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.

Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.

Intrusive Method for Uncertainty Quantification in a Multiphase Flow Solver

NASA Astrophysics Data System (ADS)

Turnquist, Brian; Owkes, Mark

2016-11-01

Uncertainty quantification (UQ) is a necessary, interesting, and often neglected aspect of fluid flow simulations. To determine the significance of uncertain initial and boundary conditions, a multiphase flow solver is being created which extends a single phase, intrusive, polynomial chaos scheme into multiphase flows. Reliably estimating the impact of input uncertainty on design criteria can help identify and minimize unwanted variability in critical areas, and has the potential to help advance knowledge in atomizing jets, jet engines, pharmaceuticals, and food processing. Use of an intrusive polynomial chaos method has been shown to significantly reduce computational cost over non-intrusive collocation methods such as Monte-Carlo. This method requires transforming the model equations into a weak form through substitution of stochastic (random) variables. Ultimately, the model deploys a stochastic Navier Stokes equation, a stochastic conservative level set approach including reinitialization, as well as stochastic normals and curvature. By implementing these approaches together in one framework, basic problems may be investigated which shed light on model expansion, uncertainty theory, and fluid flow in general. NSF Grant Number 1511325.

A Route to Chaos after Bifurcation in a Two-section Semiconductor Laser Using Opto-electronic Delayed Feedback at Each In-current

NASA Astrophysics Data System (ADS)

Yan, Sen-lin

2014-12-01

We study dynamics in an opto-electronic delayed feedback two-section semiconductor laser. We predict theoretically that the system can result in bistability and bifurcation. We analyze numerically the route to chaos from stability to bifurcation by varying the delayed time, feedback strength and two in-currents. The system displays the four distinct types or modes of stable, periodic pulsed or self-pulsing, undamped oscillating or beating, and chaos. The frequency and intensity varying with the delayed time in the self-pulsation regions are discussed detailedly to find that the pulsing frequency is reduced with the long delayed time while the pulsing intensity is added. And the chaotic pulsing frequency is increased with the large in-current Ja. The laser relaxation oscillation frequency is decreased with the large in-current Jb. One in-current characterize dynamics in the laser to conduce to stable, periodic pulsed, beating and chaotic states by altering its values. The other in-current characterize dynamics in the chaotic laser to be controlled to a stable state after a road to quasi-period by adding the values.

Preliminary study of Alzheimer's Disease diagnosis based on brain electrical signals using wireless EEG

NASA Astrophysics Data System (ADS)

Handayani, N.; Akbar, Y.; Khotimah, S. N.; Haryanto, F.; Arif, I.; Taruno, W. P.

2016-03-01

This research aims to study brain's electrical signals recorded using EEG as a basis for the diagnosis of patients with Alzheimer's Disease (AD). The subjects consisted of patients with AD, and normal subjects are used as the control. Brain signals are recorded for 3 minutes in a relaxed condition and with eyes closed. The data is processed using power spectral analysis, brain mapping and chaos test to observe the level of complexity of EEG's data. The results show a shift in the power spectral in the low frequency band (delta and theta) in AD patients. The increase of delta and theta occurs in lobus frontal area and lobus parietal respectively. However, there is a decrease of alpha activity in AD patients where in the case of normal subjects with relaxed condition, brain alpha wave dominates the posterior area. This is confirmed by the results of brain mapping. While the results of chaos analysis show that the average value of MMLE is lower in AD patients than in normal subjects. The level of chaos associated with neural complexity in AD patients with lower neural complexity is due to neuronal damage caused by the beta amyloid plaques and tau protein in neurons.

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT

PubMed Central

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of “premature convergence,” that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment. PMID:29181020

The Weierstrassian movement patterns of snails

PubMed Central

Santini, Giacomo; Chelazzi, Guido; Focardi, Stefano

2017-01-01

Weierstrassian Lévy walks are the archetypical form of random walk that do not satisfy the central limit theorem and are instead characterized by scale invariance. They were originally regarded as a mathematical abstraction but subsequent theoretical studies showed that they can, in principle, at least, be generated by chaos. Recently, Weierstrassian Lévy walks have been found to provide accurate representations of the movement patterns of mussels (Mytilus edulis) and mud snails (Hydrobia ulvae) recorded in the laboratory under controlled conditions. Here, we tested whether Weierstrassian Lévy walks and chaos are present under natural conditions in intertidal limpets Patella vulgata and P. rustica, and found that both characteristics are pervasive. We thereby show that Weierstrassian Lévy walks may be fundamental to how molluscs experience and interact with the world across a wide range of ecological contexts. We also show in an easily accessible way how chaos can produce a wide variety of Weierstrassian Lévy walk movement patterns. Our findings support the Lévy flight foraging hypothesis that posits that because Lévy walks can optimize search efficiencies, natural selection should have led to adaptations for Lévy walks. PMID:28680656

Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT.

PubMed

Nie, Xiaohua; Wang, Wei; Nie, Haoyao

2017-01-01

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of "premature convergence," that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment.

Massively parallel rRNA gene sequencing exacerbates the potential for biased community diversity comparisons due to variable library sizes

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

Gihring, Thomas; Green, Stefan; Schadt, Christopher Warren

2011-01-01

Technologies for massively parallel sequencing are revolutionizing microbial ecology and are vastly increasing the scale of ribosomal RNA (rRNA) gene studies. Although pyrosequencing has increased the breadth and depth of possible rRNA gene sampling, one drawback is that the number of reads obtained per sample is difficult to control. Pyrosequencing libraries typically vary widely in the number of sequences per sample, even within individual studies, and there is a need to revisit the behaviour of richness estimators and diversity indices with variable gene sequence library sizes. Multiple reports and review papers have demonstrated the bias in non-parametric richness estimators (e.g.more » Chao1 and ACE) and diversity indices when using clone libraries. However, we found that biased community comparisons are accumulating in the literature. Here we demonstrate the effects of sample size on Chao1, ACE, CatchAll, Shannon, Chao-Shen and Simpson's estimations specifically using pyrosequencing libraries. The need to equalize the number of reads being compared across libraries is reiterated, and investigators are directed towards available tools for making unbiased diversity comparisons.« less

From chaos to control: winning the war.

PubMed

Wojciak, P J

1994-08-01

This article illustrates how a small manufacturing facility in the Midwest undertook the process of an MRP II implementation and ultimately gained class A status at a true make-or-break time in its history. The control that was gained throughout the entire process has helped create a winning environment and will continue to strengthen our position as we move toward world-class excellence.

Identification of minimal parameters for optimal suppression of chaos in dissipative driven systems.

PubMed

Martínez, Pedro J; Euzzor, Stefano; Gallas, Jason A C; Meucci, Riccardo; Chacón, Ricardo

2017-12-21

Taming chaos arising from dissipative non-autonomous nonlinear systems by applying additional harmonic excitations is a reliable and widely used procedure nowadays. But the suppressory effectiveness of generic non-harmonic periodic excitations continues to be a significant challenge both to our theoretical understanding and in practical applications. Here we show how the effectiveness of generic suppressory excitations is optimally enhanced when the impulse transmitted by them (time integral over two consecutive zeros) is judiciously controlled in a not obvious way. Specifically, the effective amplitude of the suppressory excitation is minimal when the impulse transmitted is maximum. Also, by lowering the impulse transmitted one obtains larger regularization areas in the initial phase difference-amplitude control plane, the price to be paid being the requirement of larger amplitudes. These two remarkable features, which constitute our definition of optimum control, are demonstrated experimentally by means of an analog version of a paradigmatic model, and confirmed numerically by simulations of such a damped driven system including the presence of noise. Our theoretical analysis shows that the controlling effect of varying the impulse is due to a subsequent variation of the energy transmitted by the suppressory excitation.

At the Edge of Chaos: A New Paradigm for Social Work?

ERIC Educational Resources Information Center

Hudson, Christopher G.

2000-01-01

Reviews key concepts and applications of chaos theory and the broader complex systems theory in the context of general systems theory and the search for a unified conceptual framework for social work. Concludes that chaos theory shows promise as a solution to many problems posed by the now dated general systems approach. (DB)

75 FR 20384 - ABB, Inc., Including On-Site Leased Workers From Spherion Staffing, Dividend Staffing, Mystaff...

Federal Register 2010, 2011, 2012, 2013, 2014

2010-04-19

...-Site Leased Workers From Spherion Staffing, Dividend Staffing, Mystaff, and Zero Chaos, Wichita Falls... from Spherion Staffing, Dividend Staffing, MyStaff, and Zero Chaos were employed on-site by the Wichita..., Dividend Staffing, MyStaff, and Zero Chaos working on-site at the Wichita Falls, Texas location of ABB, Inc...

Home Chaos: Sociodemographic, Parenting, Interactional, and Child Correlates

ERIC Educational Resources Information Center

Dumas, Jean E.; Nissley, Jenelle; Nordstrom, Alicia; Smith, Emilie Phillips; Prinz, Ronald J.; Levine, Douglas W.

2005-01-01

We conducted 2 studies to (a) establish the usefulness of the construct of home chaos, (b) investigate its correlates, and (c) determine the validity of the Confusion, Hubbub, and Order Scale (CHAOS) used to measure the construct in each study. Study 1 relied on a sample of European American preschoolers and their mothers and Study 2 on a sample…

Narrative and Chaos Acknowledging the Novelty of Lives-in-Time

ERIC Educational Resources Information Center

Randall, William L.

2007-01-01

In this paper I propose that interest in "narrative" within the human sciences is comparable to interest in "chaos" within the natural sciences. In their respective ways, theories on narrative and theories on chaos are aimed at appreciating the dynamics of complex, multi-dimensional systems which otherwise resist our attempts to predict, measure,…

Master Teachers: Making a Difference on the Edge of Chaos

ERIC Educational Resources Information Center

Chapin, Dexter

2008-01-01

The No Child Left Behind legislation, by legitimizing a stark, one-size-fits-all, industrial model of education, has denied the inherent complexity and richness of what teachers do. Discussing teaching in terms of Chaos Theory, Chapin explains that while excellent teaching may occur at the edge of chaos, it is not chaotic. There are patterns…

Chaotic Feedback Loops within Decision Making Groups: Towards an Integration of Chaos Theory and Cybernetics.

ERIC Educational Resources Information Center

Keaten, James A.

This paper offers a model that integrates chaos theory and cybernetics, which can be used to describe the structure of decision making within small groups. The paper begins with an overview of cybernetics and chaos. Definitional characteristics of cybernetics are reviewed along with salient constructs, such as goal-seeking, feedback, feedback…

Chaotic Bohmian trajectories for stationary states

NASA Astrophysics Data System (ADS)

Cesa, Alexandre; Martin, John; Struyve, Ward

2016-09-01

In Bohmian mechanics, the nodes of the wave function play an important role in the generation of chaos. However, so far, most of the attention has been on moving nodes; little is known about the possibility of chaos in the case of stationary nodes. We address this question by considering stationary states, which provide the simplest examples of wave functions with stationary nodes. We provide examples of stationary wave functions for which there is chaos, as demonstrated by numerical computations, for one particle moving in three spatial dimensions and for two and three entangled particles in two dimensions. Our conclusion is that the motion of the nodes is not necessary for the generation of chaos. What is important is the overall complexity of the wave function. That is, if the wave function, or rather its phase, has a complex spatial variation, it will lead to complex Bohmian trajectories and hence to chaos. Another aspect of our work concerns the average Lyapunov exponent, which quantifies the overall amount of chaos. Since it is very hard to evaluate the average Lyapunov exponent analytically, which is often computed numerically, it is useful to have simple quantities that agree well with the average Lyapunov exponent. We investigate possible correlations with quantities such as the participation ratio and different measures of entanglement, for different systems and different families of stationary wave functions. We find that these quantities often tend to correlate to the amount of chaos. However, the correlation is not perfect, because, in particular, these measures do not depend on the form of the basis states used to expand the wave function, while the amount of chaos does.

Europa's Great Lakes

NASA Astrophysics Data System (ADS)

Schmidt, B. E.; Blankenship, D. D.; Patterson, G. W.; Schenk, P. M.

2012-04-01

Unique to the surface of Europa, chaos terrain is diagnostic of the properties and dynamics of its icy shell. While models have suggested that partial melt within a thick shell or melt-through of a thin shell may form chaos, neither model has been able to definitively explain all observations of chaos terrain. However, we present a new model that suggests large melt lenses form within the shell and that water-ice interactions above and within these lenses drive the production of chaos. Our analysis of the geomorphology of Conamara Chaos and Thera Macula, was used to infer and test a four-stage lens-collapse chaos formation model: 1) Thermal plumes of warm, pure ice ascend through the shell melting the impure brittle ice above, producing a lake of briny water and surface down draw due to volume reduction. 2) Surface deflection and driving force from the plume below hydraulically seals the water in place. 3) Extension of the brittle ice lid generates fractures from below, allowing brines to enter and fluidize the ice matrix. 4) As the lens and now brash matrix refreeze, thermal expansion creates domes and raises the chaos feature above the background terrain. This new "lense-collapse" model indicates that chaos features form in the presence of a great deal of liquid water, and that large liquid water bodies exist within 3km of Europa's surface comparable in volume to the North American Great Lakes. The detection of shallow subsurface "lakes" implies that the ice shell is recycling rapidly and that Europa may be currently active. In this presentation, we will explore environments on Europa and their analogs on Earth, from collapsing Antarctic ice shelves to to subglacial volcanos in Iceland. I will present these new analyses, and describe how this new perspective informs the debate about Europa's habitability and future exploration.

Generation of flat wideband chaos with suppressed time delay signature by using optical time lens.

PubMed

Jiang, Ning; Wang, Chao; Xue, Chenpeng; Li, Guilan; Lin, Shuqing; Qiu, Kun

2017-06-26

We propose a flat wideband chaos generation scheme that shows excellent time delay signature suppression effect, by injecting the chaotic output of general external cavity semiconductor laser into an optical time lens module composed of a phase modulator and two dispersive units. The numerical results demonstrate that by properly setting the parameters of the driving signal of phase modulator and the accumulated dispersion of dispersive units, the relaxation oscillation in chaos can be eliminated, wideband chaos generation with an efficient bandwidth up to several tens of GHz can be achieved, and the RF spectrum of generated chaotic signal is nearly as flat as uniform distribution. Moreover, the periodicity of chaos induced by the external cavity modes can be simultaneously destructed by the optical time lens module, based on this the time delay signature can be completely suppressed.

Chaos and complexity by design

DOE PAGES

Roberts, Daniel A.; Yoshida, Beni

2017-04-20

We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame poten-tial,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We also show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. In addition, we prove that these 2k-point correlators for Pauli operators completely determine the k-foldmore » channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.« less

Chaos and wave propagation regimes

NASA Astrophysics Data System (ADS)

Colosi, John

2003-04-01

Ray chaos theory and parabolic equation numerical modeling were two thrusts of Fred Tappert's research that were perpetually in tension. Fred was interested in the problem of identifying wave propagation regimes, most notably the strong focusing caustic regime and its evolution into the saturation regime. On the one hand, chaos theory held the seed of the complexity Fred believed existed in ocean acoustic wavefields; on the other hand ocean acoustic ray chaos theory (which Fred helped to pioneer) was a disdainful approximation to the full wave treatments offered by parabolic equation calculations. Fred was convinced that the saturation limit could not be obtained using ray theory and therefore he examined a new field of inquiry: a blend of chaotic ray insight and full wave dynamics called wave chaos. This talk will discuss some of Fred's insights on this topic and how they relate to observations from basin scale acoustic transmissions.