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1

A unified theory of chaos linking nonlinear dynamics and statistical physics

A fundamental issue in nonlinear dynamics and statistical physics is how to distinguish chaotic from stochastic fluctuations in short experimental recordings. This dilemma underlies many complex systems models from stochastic gene expression or stock exchange to quantum chaos. Traditionally, deterministic chaos is characterized by "sensitive dependence on initial conditions" as indicated by a positive Lyapunov exponent. However, ambiguity arises when applying this criterion to real-world data that are corrupted by measurement noise or perturbed nonautonomously by exogenous deterministic or stochastic inputs. Here, we show that a positive Lyapunov exponent is surprisingly neither necessary nor sufficient proof of deterministic chaos, and that a nonlinear dynamical system under deterministic or stochastic forcing may exhibit multiple forms of nonautonomous chaos assessable by a noise titration assay. These findings lay the foundation for reliable analysis of low-dimensional chaos for complex systems modeling and prediction of a wide variety of physical, biological, and socioeconomic data.

Chi-Sang Poon; Cheng Li; Guo-Qiang Wu

2010-04-08

2

Scaling of chaos in strongly nonlinear lattices.

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. PMID:24985455

Mulansky, Mario

2014-06-01

3

Detecting nonlinearity and chaos in epidemic data

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 of 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.

Ellner, S.; Gallant, A.R. [North Carolina State Univ., Raleigh, NC (United States). Dept. of Statistics; Theiler, J. [Santa Fe Inst., NM (United States)]|[Los Alamos National Lab., NM (United States)

1993-08-01

4

Specifying the links between household chaos and preschool children's development

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 instability, lack of routine, and television usually on. Chaos was measured at

Anne Martin; Rachel A. Razza; Jeanne Brooks-Gunn

2012-01-01

5

Specifying the links between household chaos and preschool children's development

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 instability, lack of routine, and television usually on. Chaos was measured at

Anne Martin; Rachel A. Razza; Jeanne Brooks-Gunn

2011-01-01

6

NSDL National Science Digital Library

In this experiment, we will discover: 1. how very simple systems can exhibit complex behavior under certain conditions, 2. the richness of the mathematical and physical structure of dynamical systems, 3. how an arbitrarily small change in the input can change the long-term conduct of a dynamical system drastically, 4. how to construct and interpret phase portraits and Poincare Maps for different kinds of responses of a system, 5. the mystery of Fiegenbaum constant and what makes chaos a universal underlying structure of the complexity exhibited by nonlinear dynamical systems, 6. a beautiful and artistic aspect of science in the form of attractors and fractals.

Alam, Junaid; Anwar, Muhammad S.

2012-03-15

7

Some Nonlinear Equations with Double Solutions: Soliton and Chaos

The fundamental characteristics of soliton and chaos in nonlinear equation are completely different. But all nonlinear equations with a soliton solution may derive chaos. While only some equations with a chaos solution have a soliton. The conditions of the two solutions are different. When some parameters are certain constants, the soliton is derived; while these parameters vary in a certain region, the bifurcation-chaos appears. It connects a chaotic control probably. The double solutions correspond possibly to the wave-particle duality in quantum theory, and connect the double solution theory of the nonlinear wave mechanics. Some nonlinear equations possess soliton and chaos, whose new meanings are discussed briefly in mathematics, physics and particle theory.

Yi-Fang Chang

2007-12-03

8

Short Communication Chaos and transient chaos in an experimental nonlinear pendulum

Pendulum is a mechanical device that instigates either technological or scientific studies, being associated with the measure of time, stabilization devices as well as ballistic applications. Nonlinear characteristic of the pendulum attracts a lot of attention being used to describe different phenomena related to oscillations, bifurcation and chaos. The main purpose of this contribution is the analysis of chaos in

Aline Souza de Paula; Marcelo Amorim Savi

9

Specifying the Links between Household Chaos and Preschool Children's Development

ERIC Educational Resources Information Center

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…

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

2012-01-01

10

Specifying the Links Between Household Chaos and Preschool Children's Development.

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

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

2012-10-01

11

Chaos and Nonlinear Dynamics in a Quantum Artificial Economy

Chaos and nonlinear economic dynamics are addressed for a quantum coupled map lattice model of an artificial economy, with quantized supply and demand equilibrium conditions. The measure theoretic properties and the patterns that emerge in both the economic business volume dynamics' diagrams as well as in the quantum mean field averages are addressed and conclusions are drawn in regards to the application of quantum chaos theory to address signatures of chaotic dynamics in relevant discrete economic state variables.

Carlos Pedro Gonçalves

2012-02-29

12

Classical and Quantum Chaos of Nonlinear Driven Systems

A comparison of the classical and quantum dynamics of several nonlinear systems is made. We are particularly interested in what happens in the quantum systems when the classical systems become chaotic. After a brief review of some important aspects of classical chaos in Hamiltonian systems, including the KAM theorem and Chirikov's resonance overlap criterion, we present results obtained from the

Michael Edward Goggin

1988-01-01

13

Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos Irving R. Epstein*

Nonlinear Chemical Dynamics: Oscillations, Patterns, and Chaos Irving R. Epstein* Department observations of chemical oscillations date back at least to the early nineteenth century,1 and the discovery sustained oscillations, and Bray5 had, albeit serendipitously, discovered the first homogeneous chemical

Showalter, Kenneth

14

Nonlinear Perspectives on Family Process: Chaos and Catastrophe Theories.

ERIC Educational Resources Information Center

This paper explores the principal features of nonlinear dynamical systems and applies the theory to parents' acceptance of a child adopted at an older age. Although family systems theories tend to be weak in addressing family change, chaos theory and catastrophe theory allow consideration of sudden, discontinuous change. If stable, the family may…

Ward, Margaret; Koopmans, Matthijs

15

12.006J / 18.353J Nonlinear Dynamics I: Chaos, Fall 2005

Introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. Forced and parametric oscillators. Phase space. Periodic, quasiperiodic, and aperiodic flows. Sensitivity to initial ...

Rothman, Daniel H.

16

Nonlinear dynamics and chaos: Geometrical methods for engineers and scientists

NASA Astrophysics Data System (ADS)

The fundamental principles of nonlinear dynamics are introduced, and a number of applications to specific physical and engineering problems are examined. Topics presented include nonlinear phenomena in damped and undamped, forced and unforced oscillators; point attractors and limit cycles in autonomous systems; periodic attractors in driven oscillators; chaotic attractors in forced oscillators; stability and bifurcations of equilibria and cycles; and iterated maps as dynamical systems. Consideration is given to the geometry of recurrence, the Lorenz system, Roessler's band, bifurcation geometry, the subharmonic resonances of an offshore structure, chaotic motions of an impacting system, the particle accelerator and Hamiltonian dynamics, and experimental observations of order and chaos.

Thompson, J. M. T.; Stewart, H. B.

17

Classical and Quantum Chaos of Nonlinear Driven Systems.

NASA Astrophysics Data System (ADS)

A comparison of the classical and quantum dynamics of several nonlinear systems is made. We are particularly interested in what happens in the quantum systems when the classical systems become chaotic. After a brief review of some important aspects of classical chaos in Hamiltonian systems, including the KAM theorem and Chirikov's resonance overlap criterion, we present results obtained from the study of the periodically kicked classical pendulum, the periodically and quasiperiodically kicked quantum pendulum, the quasiperiodically kicked two-state system, and the periodically and quasiperiodically driven classical and quantum Morse oscillator. We find that certain aspects of classical chaos are found in quantum systems. In particular we find decaying correlations of the state vector, broadband power spectra of the state vector, and diffuse energy growth in quasiperiodically kicked quantum systems. In addition we find that classical resonance overlap is a good indicator of the threshold field strength for dissociation for both the classical and quantum Morse oscillator and that the classical and quantum thresholds are in good agreement except near higher order classical resonances and quantum multiphoton transitions. We conclude that while quantum chaos may not exist in terms of exponential sensitivity of the state vector to initial conditions quantum systems can reflect in some ways the chaos of the corresponding classical system.

Goggin, Michael Edward

18

Chaos, creativity, and substance abuse: the nonlinear dynamics of choice.

Artists create their work in conditions of disequilibrium, states of creative chaos that may appear turbulent but are capable of bringing forth new order. By absorbing information from the environment and discharging it negentropically as new work, artists can be modeled as dissipative systems. A characteristic of chaotic systems is a heightened sensitivity to stimuli, which can generate either positive experiences or negative ones that can lead some artists to substance abuse and misguided searches for a creative chaos. Alcohol and drug use along with inadequately addressed co-occurring emotional disorders interfere with artists' quest for the nonlinearity of creativity. Instead, metaphorically modeled by a limit cycle of addiction and then a spiral to disorder, the joys of a creative chaos become an elusive chimera for them rather than a fulfilling experience. Untreated mental illness and addiction to substances have shortened the lives of artists such as Vincent Van Gogh, Frida Kahlo, Henri de Toulouse-Lautrec, and Jackson Pollock, all of whom committed suicide. In contrast Edvard Munch and John Callahan, who chose to address their emotional problems and substance abuse, continued to live and remain creative. Choosing to access previously avoided moments of pain can activate the nonlinear power of self-transformation. PMID:21382261

Zausner, Tobi

2011-04-01

19

Order and chaos in polarized nonlinear optics

Methods for investigating temporal complexity in Hamiltonian systems are applied to the dynamics of a polarized optical laser beam propagating as a travelling wave in a medium with cubically nonlinear polarizability (i.e., a Kerr medium). The theory of Hamiltonian systems with symmetry is used to study the geometry of phase space for the optical problem, transforming from C{sup 2} to S{sup 2} {times} (J,{theta}), where (J,{theta}) is a symplectic action-angle pair. The bifurcations of the phase portraits of the Hamiltonian motion on S{sup 2} are classified and shown graphically. These bifurcations create various saddle connections on S{sup 2} as either J (the beam intensity), or the optical parameters of the medium are varied. After this bifurcation analysis, the Melnikov method is used to demonstrate analytically that the saddle connections break and intersect transversely in a Poincare map under spatially periodic perturbations of the optical parameters of the medium. These transverse intersections in the Poincare map imply intermittent polarization switching with extreme sensitivity to initial conditions characterized by a Smale horseshoe construction for the travelling waves of a polarized optical laser pulse. The resulting chaotic behavior in the form of sensitive dependence on initial conditions may have implications for the control and predictability of nonlinear optical polarization switching in birefringent media. 19 refs., 2 figs., 1 tab.

Holm, D.D.

1990-01-01

20

Overlapping of nonlinear resonances and the problem of quantum chaos.

The motion of a nonlinearly oscillating particle under the influence of a periodic sequence of short impulses is investigated. We analyze the Schrödinger equation for the universal Hamiltonian. It is shown that the quantum criterion of overlapping of resonances is of the form lambdaK>or=1, where K is the classical coefficient of stochasticity and lambda is the functional defined with the use of Mathieu functions. The area of the maximal values of lambda is determined. The idea about the emerging of quantum chaos due to the adiabatic motion along the curves of Mathieu characteristics at multiple passages through the points of branching is advanced. PMID:14525093

Ugulava, A; Chotorlishvili, L; Nickoladze, K

2003-08-01

21

Nonlinearly-enhanced energy transport in many dimensional quantum chaos

By employing a nonlinear quantum kicked rotor model, we investigate the transport of energy in multidimensional quantum chaos. This problem has profound implications in many fields of science ranging from Anderson localization to time reversal of classical and quantum waves. We begin our analysis with a series of parallel numerical simulations, whose results show an unexpected and anomalous behavior. We tackle the problem by a fully analytical approach characterized by Lie groups and solitons theory, demonstrating the existence of a universal, nonlinearly-enhanced diffusion of the energy in the system, which is entirely sustained by soliton waves. Numerical simulations, performed with different models, show a perfect agreement with universal predictions. A realistic experiment is discussed in two dimensional dipolar Bose-Einstein-Condensates (BEC). Besides the obvious implications at the fundamental level, our results show that solitons can form the building block for the realization of new systems for the enhanced transport of matter. PMID:23912934

Brambila, D. S.; Fratalocchi, A.

2013-01-01

22

Two types of chaos in non-linear mechanics

NASA Technical Reports Server (NTRS)

The two types of chaos, weak and strong, associated with the Liapunov and Hadamard instabilities respectively, are analyzed. The geometrical representation of weak chaos is considered, and criteria of this chaos are formulated using the geometrical interpretation of dynamics. Weak chaos in inertial motion of two-bar linkage is discussed. The analysis of strong chaos is restricted to a review of results published elsewhere.

Zak, M.

1985-01-01

23

Integrability and chaos in nonlinearly coupled optical beams

This paper presents a study, using dynamical systems methods, of the equations describing the polarization behavior of two nonlinearly coupled optical beams counterpropagating in a nonlinear medium. In the travelling-wave regime assumption, this system possesses a Lie-Poisson structure on the manifold C{sup 2} {times} C{sup 2}. In the case where the medium is assumed to be isotropic, this system exhibits invariance under the Hamiltonian action of two copies of the rotation group, S{sup 1}, and actually reduces to a lower-dimensional system on the two-sphere, S{sup 2}. We study the dynamics on the reduced space and examine the structure of the phase portrait by determining the fixed points and infinite-period homoclinic and heteroclinic orbits; we concentrate on presenting some exotic behaviour that occurs when some parameters are varied, and we also show special solutions associated with some of the above-mentioned orbits. Last, we demonstrate the existence of complex dynamics when the system is subject to certain classes of Hamiltonian perturbations. To this end, we make use of the Melnikov method to analytically show the occurrence of either horseshoe chaos, or Arnold diffusion. 19 refs.

David, D.

1989-01-01

24

BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns

NASA Astrophysics Data System (ADS)

When the editorial office of Journal of Physics A: Mathematical and General of the Institute of Physics Publishing asked me to review a book on nonlinear dynamics I experienced an undeniable apprehension. Indeed, the domain is a rapidly expanding one and writing a book aiming at a certain degree of completeness looks like an almost impossible task. My uneasiness abated somewhat when I saw the names of the authors, two well-known specialists of the nonlinear domain, but it was only when I held the book in my hands that I felt really reassured. The book is not just a review of the recent (and less so) findings on nonlinear systems. It is also a textbook. The authors set out to provide a detailed, step by step, introduction to the domain of nonlinearity and its various subdomains: chaos, integrability and pattern formation (although this last topic is treated with far less detail than the other two). The public they have in mind is obviously that of university students, graduate or undergraduate, who are interested in nonlinear phenomena. I suspect that a non-negligible portion of readers will be people who have to teach topics which figure among those included in the book: they will find this monograph an excellent companion to their course. The book is written in a pedagogical way, with a profusion of examples, detailed explanations and clear diagrams. The point of view is that of a physicist, which to my eyes is a major advantage. The mathematical formulation remains simple and perfectly intelligible. Thus the reader is not bogged down by fancy mathematical formalism, which would have discouraged the less experienced ones. A host of exercises accompanies every chapter. This will give the novice the occasion to develop his/her problem-solving skills and acquire competence in the use of nonlinear techniques. Some exercises are quite straightforward, like `verify the relation 14.81'. Others are less so, such as `prepare a write-up on a) frequency-locking and b) devil's staircase'. I do not quite grasp the usefulness of such project-like exercises. Projects must be assigned by the person who indeed teaches the course. There are things that I really like a lot in this book. For instance, the section on `chaos in nonlinear electronic circuits' is particularly interesting. It offers a simple and rather inexpensive way to visualize chaos in the laboratory. The closing section of the book devoted to technological applications of nonlinear dynamics is also quite useful. The fact that the treatment remains rather elementary, based on review articles and monographs rather than research articles, adds to the intelligibility of the chapter, which will certainly prove stimulating to many a student. Of course, not everything can be perfect, and a 600-page book is bound to have some weak points. I find the treatment of quantum chaos rather sketchy and that of chaotic scattering even more so. Also, while the authors are aware of the importance of complex time in integrability, they do not attempt an explanation of the fundamental puzzle: `why, while the physical time is par excellence real, do we need a complex time in order to study the long-time behaviour of dynamical systems?'. Also the book devotes just four pages to integrable discrete systems. Given the tremendous development of this domain over the past decade, this short presentation is not doing justice to the subject. (However as the present reviewer is editing Springer Lecture Notes in Physics on precisely `Integrable Discrete Systems', to appear in early 2004, he would be the last one to complain about the absence of more details on the matter in the present book.) To sum it up, the monograph of Lakshmanan and Rajasekar is a book written by physicists and for physicists. It will be of interest to both the experienced practitioner and to the uninitiated. Its main quality resides in its thorough, pedagogical approach to the matter. Moreover the relaxed, not too formal, style makes for easy reading. Given that I am writing this review just a few days before Christmas I cannot hel

Grammaticos, B.

2004-02-01

25

Nonlinear Dynamics In Quantum Physics -- Quantum Chaos and Quantum Instantons

We discuss the recently proposed quantum action - its interpretation, its motivation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos.

H. Kröger

2003-02-21

26

Nonlinear Oscillations, Noise and Chaos in Neural Delayed Feedback.

NASA Astrophysics Data System (ADS)

Bifurcations and complex oscillations in the human pupil light reflex (PLR) are studied. Autonomous pupil area oscillations are produced by substituting electronically controllable nonlinear feedback for the normal negative feedback of this reflex. A physiologically sound theoretical framework in which to study pupillary oscillations is developed. The model, framed as a delay-differential equation (DDE), agrees quantitatively with the simpler periodic behaviors and qualitatively with the complex behaviors. Much of the aperiodicity in the data can be ascribed to noise and transients rather than to chaos. The critical behavior of the PLR at oscillation onset is different with piecewise constant rather than smooth negative feedback. In the former, relative fluctuations in period are larger than those in amplitude, and vice versa in the latter. Properties of the time solutions and densities of a stochastic DDE are used to explain this experimental result. The Hopf bifurcation in this system is postponed by both additive and multiplicative colored noise. Theoretical insight into the behavior of stationary densities of DDE's and the origin of the postponement is given, and implications for analyzing bifurcations in neural delayed feedback systems are discussed.

Longtin, Andre

27

On the local nature and scaling of chaos in weakly nonlinear disordered chains

The dynamics of a disordered nonlinear chain can be either regular or chaotic with a certain probability. The chaotic behavior is often associated with the destruction of Anderson localization by the nonlinearity. In the presentwork it is argued that at weak nonlinearity chaos is nucleated locally on rare resonant segments of the chain. Based on this picture, the probability of chaos is evaluated analytically. The same probability is also evaluated by direct numerical sampling of disorder realizations and quantitative agreement between the two results is found.

D. M. Basko

2012-06-06

28

NASA Technical Reports Server (NTRS)

Three measures of nonlinear chaos (fractal dimension, Approximate Entropy (ApEn), and Lyapunov exponents) were studied as potential measures of cardiovascular condition. It is suggested that these measures have potential in the assessment of cardiovascular condition in environments of normal cardiovascular stress (normal gravity on the Earth surface), cardiovascular deconditioning (microgravity of space), and increased cardiovascular stress (lower body negative pressure (LBNP) treatments).

Hooker, John C.

1991-01-01

29

Chaos for a Microelectromechanical Oscillator Governed by the Nonlinear Mathieu Equation

A variety of microelectromechanical (MEM) oscillators is governed by a version of the Mathieu equation that harbors both linear and cubic nonlinear time-varying stiffness terms. In this paper, chaotic behavior is predicted and shown to occur in this class of MEM device. Specifically, by using Melnikov's method, an inequality that describes the region of parameter space where chaos lives is

Barry E. DeMartini; Holly E. Butterfield; Jeff Moehlis; Kimberly L. Turner

2007-01-01

30

Household chaos moderates the link between maternal attribution bias and parenting

Objective Parents who attribute child misbehavior to children's intentions and dismiss situational factors tend to show more hostility and less warmth in their parenting behavior, and are at greater risk for maltreatment. We extended this literature by investigating the role of household chaos as a moderator of the link between maternal attribution biases and parenting behaviors. Design The current sample included 160 mothers of 3- to7-year-old children. Mothers provided reports on their attribution biases and household chaos levels. Maternal negativity and positivity were measured using self-reports and observers’ ratings. Results The links between attribution bias and parenting behavior were stronger in more chaotic environments, with the moderating effect of chaos being particularly strong for internal attribution bias. Conclusions The findings point to the importance of social cognitive biases in the etiology of maternal behavior in family contexts that lack order and predictability. PMID:24358017

Wang, Z.; Deater-Deckard, K.; Bell, M.A.

2013-01-01

31

NONLINEAR DYNAMICS IN QUANTUM PHYSICS - QUANTUM CHAOS AND QUANTUM INSTANTONS

We discuss the recently proposed quantum action - its interpretation, its moti- vation, its mathematical properties and its use in physics: quantum mechanical tunneling, quantum instantons and quantum chaos. 1. Introduction. Modern physics returns to some of its origins dating back to the first part of the last century. Examples are entanglement, according to Schrodinger the most peculiar property occuring

Helmut Kroger

32

Bifurcation and chaos in a perturbed soliton equation with higher-order nonlinearity

NASA Astrophysics Data System (ADS)

The influence of a soliton system under external perturbation is considered. We take the compound Korteweg-de Vries-Burgers-type equation with nonlinear terms of any order as an example, and investigate numerically the chaotic behavior of the system with periodic forcing. It is shown that dynamical chaos can occur when we appropriately choose system parameters. Abundant bifurcation structures and different routes to chaos, such as period doubling, intermittent bifurcation and crisis, are found by applying bifurcation diagrams, Poincaré maps and phase portraits. To characterize the chaotic behavior of this system, a spectrum of Lyapunov exponents and Lyapunov dimensions of attractors are also employed.

Yu, Jun; Zhang, Rongbo; Jin, Guojuan

2011-12-01

33

Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos

Different types of structural and aerodynamic nonlinearities commonly encountered in aeronautical engineering are discussed. The equations of motion of a two-dimensional airfoil oscillating in pitch and plunge are derived for a structural nonlinearity using subsonic aerodynamics theory. Three classical nonlinearities, namely, cubic, freeplay and hysteresis are investigated in some detail. The governing equations are reduced to a set of ordinary

B. H. K. Lee; S. J. Price; Y. S. Wong

1999-01-01

34

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

NASA Astrophysics Data System (ADS)

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.

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

2014-09-01

35

Controlling chaos of nonlinear domain-wall motion

NASA Astrophysics Data System (ADS)

The two-step Ott-Grebogi-Yorke (OGY) method and the prediction OGY method for controlling chaos of magnetic domain-wall motion are proposed to improve the long settling time in the original OGY method. In the two-step OGY method, a magnetic domain wall is first moved on a periodic orbit and the OGY method is used when the orbit approaches a saddle point. In the prediction OGY method, the motion of the domain wall is predicted before the OGY method is applied. An attractor in the state space can be reconstructed by using the time series of the domain-wall motion. The near future can be predicted even in the chaotic system, because the short time developments of the neighborhood system of a predictee in the attractor are not so different from each other. The settling time of the improved OGY methods is 1/5-1/30 times as long as that of the original OGY method.

Okuno, H.; Sakata, T.; Takeda, H.

1999-04-01

36

Study on the chaos anti-control technology in nonlinear vibration isolation system

NASA Astrophysics Data System (ADS)

The nonlinear vibration isolation system (NVIS) works in a chaotic state when its parameters are in chaotic range. Under single-frequency harmonic excitation, the system exhibits chaotic behavior with broad band frequency. This idea can be used to control the line spectra water-born noise of the underwater vehicle, and to improve its capability of concealment. In order to ensure that the system works in the chaotic state effectively, a new chaos anti-control method is presented in this paper. Firstly, the NVIS model with feedback is provided, and the periodic-doubling bifurcation characteristic is analyzed. Simulation results show that the system has multiple dynamical behaviors with different parameters. Finally, an experiment on the basis of self-design rig is carried out, and the acceleration signal is measured. Combined with the chaos identification technology, it proves that the system works in a chaotic state at some special parameter range.

Liu, Shu-Yong; Yu, Xiang; Zhu, Shi-Jian

2008-03-01

37

Identification and control of chaos in nonlinear gear dynamic systems using Melnikov analysis

NASA Astrophysics Data System (ADS)

In this paper, the Melnikov analysis is extended to develop a practical model of gear system to control and eliminate the chaotic behavior. To this end, a nonlinear dynamic model of a spur gear pair with backlash, time-varying stiffness and static transmission error is established. Based on the Melnikov analysis the global homoclinic bifurcation and transition to chaos in this model are predicted. Then non-feedback control method is used to eliminate the chaos by applying an additional control excitation. The regions of the parameter space for the control excitation are obtained analytically. The accuracy of the theoretical predictions and also the performance of the proposed control system are verified by the comparison with the numerical simulations. The simulation results show effectiveness of the proposed control system and present some useful information to analyze and control the gear dynamical systems.

Farshidianfar, A.; Saghafi, A.

2014-10-01

38

Research Highlights: > In a one-dimensional disordered chain of oscillators all normal modes are localized. > Nonlinearity leads to chaotic dynamics. > Chaos is concentrated on rare chaotic spots. > Chaotic spots drive energy exchange between oscillators. > Macroscopic transport coefficients are obtained. - Abstract: The subject of this study is the long-time equilibration dynamics of a strongly disordered one-dimensional chain of coupled weakly anharmonic classical oscillators. It is shown that chaos in this system has a very particular spatial structure: it can be viewed as a dilute gas of chaotic spots. Each chaotic spot corresponds to a stochastic pump which drives the Arnold diffusion of the oscillators surrounding it, thus leading to their relaxation and thermalization. The most important mechanism of equilibration at long distances is provided by random migration of the chaotic spots along the chain, which bears analogy with variable-range hopping of electrons in strongly disordered solids. The corresponding macroscopic transport equations are obtained.

Basko, D.M., E-mail: denis.basko@grenoble.cnrs.fr [Laboratoire de Physique et Modelisation des Milieux Condenses, Universite de Grenoble 1 and CNRS, BP166, 38042 Grenoble (France)

2011-07-15

39

Chaos in fractional-order autonomous nonlinear systems

We numerically investigate chaotic behavior in autonomous nonlinear models of fractional order. Linear transfer function approximations of the fractional integrator block are calculated for a set of fractional orders in (0,1], based on frequency domain arguments, and the resulting equivalent models are studied. Two chaotic models are considered in this study; an electronic chaotic oscillator, and a mechanical chaotic “jerk”

Wajdi M. Ahmad; J. C. Sprott

2003-01-01

40

Chaos and Nonlinear Dynamics: Application to Financial Markets

After the stock market crash of October 19, 1987, interest in nonlinear dynamics, especially deterministic chaotic dynamics, has increased in both the financial press and the academic literature. This has come about because the frequency of large moves in stock markets is greater than would be expected under a normal distribution. There are a number of possible explanations. A popular

David A. Hsieh

1990-01-01

41

Nonlinear chaos in temperature time series: Part I: Case studies

In this work we present 3 case studies of local temperature time series obtained from stations in Europe and Israel. The nonlinear nature of the series is presented along with model based forecasting. Data is nonlinearly filtered using high dimensional projection and analysis is performed on the filtered data. A lorenz type model of 3 first order ODEs is then fitted. Forecasts are shown for periods of 100 days ahead, outperforming any existing forecast method known today. While other models fail at forecasting periods above 11 days, ours shows remarkable stability 100 days ahead. Thus finally a local dynamical system if found for local temperature forecasting not requiring solution of Navier-Stokes equations. Thus saving computational costs.

Rosenstein, Yaron

2012-01-01

42

Pattern selection and instability in nonlinear wave equation: an aspect of soliton and chaos

Pattern selection problems are found in a variety of phenomena. Fluid dynamical systems and nonlinear diffusion phenomena give typical examples of pattern formation problems in dissipative systems. In some cases the dissipation reduces the effective dimension of the system, and this fact leads to several strikingly universal behaviors which were initially found in simple model systems with a few degrees of freedom. Nonlinear wave equations themselves, however, describes systems without dissipation in which the situation is more complicated. In spite of this complexity, many completely integrable systems are known in nonlinear wave equations, where neither ergodicity nor chaos is expected. With addition of small perturbation to completely integrable systems, one can see the growth of instability and the role of coherent structures in the pattern selection problem. Two aspects are briefly discussed in the following sections.

Imada, M.

1985-01-01

43

Turbulent Fluid Motion 6: Turbulence, Nonlinear Dynamics, and Deterministic Chaos

NASA Technical Reports Server (NTRS)

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The turbulence is sustained by a nonrandom time-independent external force. The solutions, on the average, separate exponentially with time, having a positive Liapunov exponent. Thus, the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number (or strength of the forcing) is reduced. Several qualitatively different flows are noted. These are, respectively, fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, we classify only the fully chaotic flows as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows, although having positive Liapunov exponents, have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, as generally understood, is both time-dependent and aperiodic.

Deissler, Robert G.

1996-01-01

44

MZ twinning: chance or determinism? An essay in nonlinear dynamics (chaos).

Classically, researchers considered monozygotic twinning (MZT) a random phenomenon. This paper tests the hypothesis with the aid of nonlinear dynamics techniques. The latter can tell true randomness from chance-like variation. Chaos, the endpoint of the threshold state of a nonlinear deterministic system, can mimic constrained randomness. From a practical standpoint, recognizing chaos in a time series data set means that the paradigmatic multifactorial model of causation is essentially ruled out. Specifically, time series of MZ, DZ, and single maternities were analysed. First, spectral analysis was used to uncover periodicities embedded in the series. Second, a singular value decomposition was undertaken to reduce noise from the series. Third, phase space attractors were drawn up that describe the 'asymptotic' trajectory of the system at any time. Results suggested that DZ, MZ, and single maternities shared a similar 32-year periodicity. Owing to two interwoven similar periodicities, the single-maternity cycle kinetics proved to be faster than that of DZ's. The MZ series was the only one to display secondary interacting harmonics, thus eliciting a rather unusual trajectory in the bidimensional phase space. The MZ time points were not spread in a haphazard fashion; on the contrary, a fine structure was present that did not reduce to a limit cycle such as the one characterizing the DZ- or the single-maternity trajectory. It was concluded that a complex nonlinear dynamic underlies MZ twinning. Therefore, calling for extrinsic causes to account for what appears to be random variation overtime would be pointless. MZ twinning should rather be traced to a limited number of intrinsic and deterministic interacting system components. The most likely candidates are presented and discussed. PMID:7985991

Philippe, P

1994-01-01

45

Nonlinear Dynamics and Chaos of Microcantilever-Based TM-AFMs with Squeeze Film Damping Effects

In Atomic force microscope (AFM) examination of a vibrating microcantilever, the nonlinear tip-sample interaction would greatly influence the dynamics of the cantilever. In this paper, the nonlinear dynamics and chaos of a tip-sample dynamic system being run in the tapping mode (TM) were investigated by considering the effects of hydrodynamic loading and squeeze film damping. The microcantilever was modeled as a spring-mass-damping system and the interaction between the tip and the sample was described by the Lennard-Jones (LJ) potential. The fundamental frequency and quality factor were calculated from the transient oscillations of the microcantilever vibrating in air. Numerical simulations were carried out to study the coupled nonlinear dynamic system using the bifurcation diagram, Poincaré maps, largest Lyapunov exponent, phase portraits and time histories. Results indicated the occurrence of periodic and chaotic motions and provided a comprehensive understanding of the hydrodynamic loading of microcantilevers. It was demonstrated that the coupled dynamic system will experience complex nonlinear oscillation as the system parameters change and the effect of squeeze film damping is not negligible on the micro-scale. PMID:22412340

Zhang, Wen-Ming; Meng, Guang; Zhou, Jian-Bin; Chen, Jie-Yu

2009-01-01

46

Nonlinear Dynamics, Psychology, and Life Sciences, Vol.8, No.1, January, 2004. Â© 2004 Society for Chaos Theory in Psychology & Life Sciences Book Review Chaos and Time-Series Analysis. By Julien Clinton for representation in state space. The chapter finishes with an explanation of the various numerical methods

Sprott, Julien Clinton

47

The paper discusses the main ideas of the chaos theory and presents mainly the importance of the nonlinearities in the mathematical models. Chaos and order are apparently two opposite terms. The fact that in chaos can be found a certain precise symmetry (Feigenbaum numbers) is even more surprising. As an illustration of the ubiquity of chaos, three models among many other existing models that have chaotic features are presented here: the nonlinear feedback profit model, one model for the simulation of the exchange rate and one application of the chaos theory in the capital markets.

Sorin Vlad; Paul Pascu; Nicolae Morariu

2010-01-20

48

Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 15, No. 1, pp. 129-136. Â© 2011 Society for Chaos Theory in Psychology & Life Sciences. The Art and Science of Foam Bubbles R. P. Taylor 1 of Nonlinear Dynamics, Psychology, and Life Sciences. Denis Weaire, Stefan Hutzler, Wiebke Drenckhan form

Taylor, Richard

49

Nonlinear microwave absorption in weak-link Josephson junctions

NASA Astrophysics Data System (ADS)

A model, based on the resistively shunted junction theory, is developed and used to study microwave absorption in weak-link Josephson junctions in high-Tc superconductors. Both linear and nonlinear cases of microwave absorption in Josephson junctions are analyzed. A comparison of the model with microwave absorption loop theory is presented along with a general condition for the applicability of both models. The nonlinear case was solved numerically and the threshold points of sharp microwave absorption are presented. At these points, a 2? phase quantization takes place within each microwave cycle, leading to an onset of a sharp rise of absorption. Existence of the 2? dynamic quantization is the key to the interpretation of nonlinear microwave absorption data. The nonlinear microwave absorption model is extended to the study of nonuniformly coupled junctions, and a general statement for the applicability of such a model is presented.

Xie, L. M.; Wosik, J.; Wolfe, J. C.

1996-12-01

50

It is found that chirped elliptically polarised cnoidal waves can propagate and aperiodic regimes, resembling polarisation chaos, can emerge in an isotropic medium with local and nonlocal components of cubic nonlinearity and second-order frequency dispersion. In the particular case of the formation of the waveguides of the same profile for two circularly polarised components of the light field relevant analytical solutions are derived and the frequencies of chirped components are shown to vary in concord with periodic changes of their intensities. In this case, the nature of the changes in the polarisation state during the light wave propagation depends on the values of nonlinear phase shifts of circularly polarised components of the field during the period and is sensitive to changes in the initial conditions. (nonlinear optical phenomena)

Makarov, Vladimir A; Petnikova, V M; Potravkin, N N; Shuvalov, Vladimir V

2012-12-31

51

A Self-Check System for Mental Health Care based on Nonlinear and Chaos Analysis

NASA Astrophysics Data System (ADS)

We applied nonlinear and chaos analysis to fingertip pulse wave data. The largest Lyapunov exponent, a measure of the "divergence" of the trajectory of the attractor in phase space, was found to be a useful index of mental health in humans, particularly for the early detection of dementia and depressive psychosis, and for monitoring mental changes in healthy persons. Most of the methods used for assessing mental health are subjective. A few of existing objective methods, such as those using EEG and ECG, for example, are not simple to use and expansive. Therefore, we developed an easy-to-use economical device, a PC mouse with an integrated sensor for measuring the pulse waves, and its required software, to make the measurements. After about 1 min of measurement, the Lyapunov exponent is calculated and displayed as a graph on the PC. An advantage of this system is that the measurements can be made very easily, and hence mental health can be assessed during operating a PC using the pulse wave mouse. Moreover, the measured data can be saved according to the time and date, so diurnal changes and changes over longer time periods can be monitored as a time series and history. At the time the pulse waves are measured, we ask the subject about his or her physical health and mood, and use their responses, along with the Lyapunov exponents, as factors causing variation in the divergence. The changes in the Lyapunov exponent are displayed on the PC as constellation graphs, which we developed to facilitate simpler self-diagnosis and problem resolution.

Oyama-Higa, Mayumi; Miao, Tiejun; Cheng, Huaichang; Tang, Yuan Guang

2007-11-01

52

The theoretical and experimental status of chaos in nonlinear optics and laser physics will be reviewed. Attention will then be focused on the possibility of chaotic behavior in individual atoms and molecules driven by intense radiation fields. 46 refs., 7 figs.

Milonni, P.W.

1989-01-01

53

The presence of physical systems whose characteristics change in a seemingly erratic manner gives rise to the study of chaotic systems. The characteristics of these systems are due to their hypersensitivity to changes in initial conditions. In order to understand chaotic systems, some sort of simulation and visualization is pertinent. Consequently, in this work, we have simulated and graphically visualized chaos in a driven nonlinear pendulum as a means of introducing chaotic systems. The visualized results obtained which highlight the hypersensitivity of the pendulum to initial conditions can be used to effectively introduce the physics of chaotic system. The simulation and visualization programme is written in Python codes.

Louis Ehwerhemuepha; Godfrey E. Akpojotor

2013-06-05

54

In Chaos 19, 013102 (2009), the author proposed generalized projective synchronization for time delay systems using nonlinear observer and obtained sufficient condition to ensure projective synchronization for modulated time varying delay. There are concerns with the obtained conditions as the result was applicable only to trivial case of time varying delay ?[over dot](1)(t)=d?(1)(t)/dt<1. In this paper, we note the drawbacks of the proposed sufficient condition. The new improved sufficient condition for ensuring the projective synchronization of time varying delayed systems is presented. The proposed new criteria have been verified by adopting the Ikeda system. PMID:23020506

Theesar, S Jeeva Sathya; Balasubramaniam, P; Banerjee, Santo

2012-09-01

55

NASA Astrophysics Data System (ADS)

Chaos is usually attributed only to nonlinear systems. Yet it was recently shown that chaotic waveforms can be synthesized by linear superposition of randomly polarized basis functions. The basis function contains a growing oscillation that terminates in a large pulse. We show that this function is easily realized when viewed backward in time as a pulse followed by ringing decay. Consequently, a linear filter driven by random pulses outputs a waveform that, when viewed backward in time, exhibits essential qualities of chaos, i.e. determinism and a positive Lyapunov exponent. This phenomenon suggests that chaos may be connected to physical theories whose framework is not that of a deterministic dynamical system. We demonstrate that synthesizing chaos requires a balance between the topological entropy of the random source and the dissipation in the filter. Surprisingly, using different encodings of the random source, the same filter can produce both Lorenz-like and R"ossler-like waveforms. The different encodings can be viewed as grammar restrictions on a more general encoding that produces a chaotic superset encompassing the Lorenz and R"ossler paradigms of nonlinear dynamics. Thus, the language of deterministic chaos provides a useful description for a class of signals not generated by a deterministic system.

Blakely, Jonathan; Corron, Ned; Hayes, Scott; Pethel, Shawn

2007-03-01

56

Chaos and bifurcation in Power Electronics Medical Instruments Implications

Practical uses of chaos Quantum chaos? Collective Phenomena Coupled harmonic oscillators Solid-state physics Nonequilibrium statistical mechanics Nonlinear solid-state physics (semiconductors) Josephson arrays Heart cell

Gajic, Zoran

57

An investigation of the routes to chaos for complex nonlinear dynamical systems

NASA Astrophysics Data System (ADS)

This dissertation presents a study of how the routes to chaos change as system complexity is increased. Increasing complexity is achieved by increasing the number of degrees of freedom, increasing system coupling strength, distributing system excitation, and varying the excitation phasing for many dynamical models described by a set of ordinary differential equations. An additional goal is to identify any potential universalities associated with the breakdown of the quasi-periodic torus that leads to chaos. The investigation is conducted by coupling a series of Duffing oscillators together and observing the change in the system's routes to chaos along with the change in the quantitative aspects of the system's chaotic regions. The same analysis is conducted on a more specific model describing captive flight missile vibration. The numerical algorithms utilized in the time, frequency, and phase space domains are the Lyapunov spectrum, the power spectrum, and the Poincare section, respectively. Although the classic Duffing system is known to widely exhibit period doubling, as Duffing oscillators are coupled together the period doubling route disappears. This is the case for the 3, 4, 5 and 6 oscillator models. In these higher dimensional systems, initial period doubling cascades are interrupted by crisis. The strict universal features of the period doubling route to chaos discovered in one dimensional maps are not adhered to in these higher dimensional systems described by continuous time differential equations. As system complexity is increased, period doubling disappears while crisis and quasi-periodicity emerge. A new phenomenon is discovered relating to the breakdown of the quasi-periodic torus. First, it has been shown that quasiperiodicity, which is not present in the Duffing or the 2 oscillator model, emerges as the dominant behavior in the higher dimensional oscillator models. Stable 3 frequency motion on a 2 torus is commonplace. It has been shown that for the symmetrical systems all torii that lead to chaos must pass through a period 3 times the period of the forcing period. It is a necessary and sufficient condition that the torus passes through an n = 3 periodic window before chaos emerges. For the nonsymmetric 3 and 5 oscillator systems, it has been shown that the torus is destroyed by an n = 2 periodic window before chaos emerges. For the linearly coupled two oscillator system, the methods of introducing complexity by distributing the input force preclude chaotic activity. As the strength of the coupling stiffness is increased to cubic order, the crisis route to chaos is dominant. The period doubling route that was present in the linearly coupled case disappears. The low dimensional rigid body missile model displays interrupted period doubling bifurcations while the higher dimensional rigid body missile model exclusively experiences the crisis bifurcation event. The introduction of system flexibility using modal superposition does not move the chaotic regions within the control parameter domain. As additional modes are introduced, the intensity of the chaos increases; thus the divergence rate of the trajectories is increased. The only route to chaos present in the higher dimensional flexible systems is crisis. Therefore, as system complexity is increased in the missile models, the crisis route to chaos dominates.

Benner, Jeffrey William

58

NSDL National Science Digital Library

This site features a chapter from an online textbook that covers chaos theory from a mathematical perspective. The topic of this chapter is a simple logistic equation; a formula for approximating the evolution of an animal population over time. The entire book can also be linked from this site.

Elert, Glenn; Hypertextbook

59

International Journal of Bifurcation and Chaos (IJBC)

NSDL National Science Digital Library

The International Journal of Bifurcation and Chaos is "widely regarded as the leading journal in the exciting field of chaos and nonlinear science." Feature articles from previous issues are available online as free samples, along with papers and letters, as long as you provide your name and email address. They also offer to send free emails with updates on the current issues's table of contents. Access to the full journal is available only by paid subscription. Links to information on related books and journals are also provided.

60

An investigation of the routes to chaos for complex nonlinear dynamical systems

This dissertation presents a study of how the routes to chaos change as system complexity is increased. Increasing complexity is achieved by increasing the number of degrees of freedom, increasing system coupling strength, distributing system excitation, and varying the excitation phasing for many dynamical models described by a set of ordinary differential equations. An additional goal is to identify any

Jeffrey William Benner

1997-01-01

61

Major open problems in chaos theory and nonlinear Y. Charles Li

. an effective description of chaos and turbulence, 2. rough dependence on initial data, 3. arrow of time, 4 on initial data, arrow of time, enrichment paradox, pesticide paradox, plankton paradox. c 2013 (copyright dependence on initial data. The initiation (onset) of turbulence is much trickier [16] [11] than

Li, Charles

62

preparing an interface to be evaluated, conducting the actual evaluation, and interpreting the resultsFrom Chaos to Cooperation: Teaching Analytic Evaluation with LINK-UP Jason Chong Lee, Sirong Lin, C analytic evaluations, a popular evaluation method that can be conducted rapidly and inexpensively. With our

McCrickard, Scott

63

NASA Astrophysics Data System (ADS)

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

Akpojotor, Godfrey; Ehwerhemuepha, Louis; Amromanoh, Ogheneriobororue

2013-03-01

64

Selected Topics in Nonlinear Wave Phenomena: Diffusive Solitons, Singular Surfaces, and Wave Chaos

We explore some recent topics of interest in the field of nonlinear wave phenomena. We do so in the context of problems arising in acoustic\\/second-sound (e.g., thermal waves) propagation in certain nonlinear media; reaction-diffusion theory, e.g., population and chemical dynamics; and systems described by equations of the nonlinear Klein--Gordon type (e.g., the sine--Gordon equation). We investigate the corresponding governing equations

Pedro Jordan; Ashok Puri

2009-01-01

65

NSDL National Science Digital Library

This site, from the University of Toronto, provides an overview of chaos theory and concisely explains the characteristics of chaotic systems. The bifurcation of a rabbit population, with the transition to chaos, is presented with several graphs. There are links to various animations and a list of other examples.

Harrison, David M.

2008-06-03

66

Schizophrenia is characterized by disturbed sleep architecture. It has been thought that sleep abnormalities may underlie information processing deficits associated with this disorder. Nonlinear analyses of sleep data can provide valuable information on sleep characteristics that may be relevant to the functions of sleep. This study examined the predictability and nonlinear complexity of sleep EEG time series in two EEG

Matcheri S. Keshavan; J. David Cashmere; Jean Miewald; Vikram Kumar Yeragani

2004-01-01

67

Selected Topics in Nonlinear Wave Phenomena: Diffusive Solitons, Singular Surfaces, and Wave Chaos

NASA Astrophysics Data System (ADS)

We explore some recent topics of interest in the field of nonlinear wave phenomena. We do so in the context of problems arising in acoustic/second-sound (e.g., thermal waves) propagation in certain nonlinear media; reaction-diffusion theory, e.g., population and chemical dynamics; and systems described by equations of the nonlinear Klein--Gordon type (e.g., the sine--Gordon equation). We investigate the corresponding governing equations with an emphasis on shock, solitary/traveling, and chaotic wave phenomena. Employing both analytical and numerical techniques, this study is carried out with the purpose of gaining a better understanding of the physical systems represented in the mathematical models. Finally, other applications of this research are noted and discussed, time permitting.

Jordan, Pedro; Puri, Ashok

2009-11-01

68

Nonlinear vibration and radiation from a panel with transition to chaos induced by acoustic waves

NASA Technical Reports Server (NTRS)

The dynamic response of an aircraft panel forced at resonance and off-resonance by plane acoustic waves at normal incidence is investigated experimentally and numerically. Linear, nonlinear (period doubling) and chaotic responses are obtained by increasing the sound pressure level of the excitation. The response time history is sensitive to the input level and to the frequency of excitation. The change in response behavior is due to a change in input conditions, triggered either naturally or by modulation of the bandwidth of the incident waves. Off-resonance, bifurcation is diffused and difficult to maintain, thus the panel response drifts into a linear behavior. The acoustic pressure emanated by the panel is either linear or nonlinear as is the vibration response. The nonlinear effects accumulate during the propagation with distance. Results are also obtained on the control of the panel response using damping tape on aluminum panel and using a graphite epoxy panel having the same size and weight. Good agreement is obtained between the experimental and numerical results.

Maestrello, Lucio; Frendi, Abdelkader; Brown, Donald E.

1992-01-01

69

Linking Nonlinearity and Non-Gaussianity of Planetary Wave Behavior by the Fokker-Planck Equation

To link prominent nonlinearities in the dynamics of 500-hPa geopotential heights to non-Gaussian features in their probability density, a nonlinear stochastic model of atmospheric planetary wave behavior is developed. An analysis of geopotential heights generated by extended integrations of a GCM suggests that a stochastic model and its associated Fokker-Planck equation call for a nonlinear drift and multiplicative noise. All

Judith Berner

2005-01-01

70

Quantum-mechanical research on nonlinear resonance and the problem of quantum chaos.

The quantum-mechanical investigation of nonlinear resonance in terms of approximation to moderate nonlinearity is reduced to the investigation of eigenfunctions and eigenvalues of the Mathieu-Schrodinger equation. The eigenstates of the Mathieu-Schrodinger equation are nondegenerate in a certain area of pumping amplitude values in the neighborhood of the classical separatrix. Outside this area, the system finds itself in a degenerate state for both small and large pumping amplitude values. Degenerate energy terms arise as a result of merging and branching of pairs of nondegenerate energy terms. Equations are obtained for finding the merging points of energy terms. These equations are solved by numerical methods. The main objective of this paper is to establish a quantum analog of the classical stochastic layer formed in the separatrix area. With this end in view, we consider a nonstationary quantum-mechanical problem of perturbation of the state of the Mathieu-Schrodinger equation. It is shown that in passing through the branching point the system may pass from the pure state to the mixed one. At multiple passages through branching points there develops the irreversible process of "creeping" of the system to quantum states. In that case, the observed population of a certain number of levels can be considered, in our opinion, to be a quantum analog of the stochastic layer. The number of populated levels is defined by a perturbation amplitude. PMID:15447577

Ugulava, A; Chotorlishvili, L; Nickoladze, K

2004-08-01

71

Nonlinear System Control Using Functional-link-based Neuro-fuzzy Networks

This study presents a functional-link-based neuro-fuzzy network (FLNFN) structure for nonlinear system control. The proposed\\u000a FLNFN model uses a functional link neural network (FLNN) to the consequent part of the fuzzy rules. This study uses orthogonal\\u000a polynomials and linearly independent functions in a functional expansion of the FLNN. Thus, the consequent part of the proposed\\u000a FLNFN model is a nonlinear

Chin-Teng Lin; Cheng-Hung Chen; Cheng-Jian Lin

72

Fiber dispersion induced nonlinearity in fiber-optic links with multimode laser diodes

In analog RF fiber-optic (FO) links with directly modulated multimode laser diodes (LD's), nonlinear distortions of the received modulation signal occur due to fiber dispersion. Using a simple analytical two mode model, we show that the mutual compensation of strong nonlinearities between particular modes breaks down at high-modulation frequencies. The effect can be observed even in 1300-nm links with single-mode

S. Hunziker; W. Baechtold

1997-01-01

73

Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos

We propose a general strategy for determining the minimal finite amplitude isturbance to trigger transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth opt...

Pringle, Chris C T; Kerswell, Rich R

2011-01-01

74

NASA Astrophysics Data System (ADS)

In this paper, we consider an environmental interface as a complex system, in which difference equations for calculating the environmental interface temperature and deeper soil layer temperature are represented by the coupled maps. First equation has its background in the energy balance equation while the second one in the prognostic equation for deeper soil layer temperature, commonly used in land surface parametrization schemes. Nonlinear dynamical consideration of this coupled system includes: (i) examination of period one fixed point and (ii) bifurcation analysis. Focusing part of analysis is calculation of the Lyapunov exponent for a specific range of values of system parameters and discussion about domain of stability for this coupled system. Finally, we calculate Kolmogorov complexity of time series generated from the coupled system.

Mimi?, Gordan; Mihailovi?, Dragutin T.; Budin?evi?, Mirko

2013-10-01

75

Most of the recent literature on chaos and nonlinear dynamics is written either for popular science magazine readers or for advanced mathematicians. This paper gives a broad introduction to this interesting and rapidly ...

Bradley, Elizabeth

1990-12-01

76

A Functional-Link-Based Neurofuzzy Network for Nonlinear System Control

This study presents a functional-link-based neuro- fuzzy network (FLNFN) structure for nonlinear system control. The proposed FLNFN model uses a functional link neural network (FLNN) to the consequent part of the fuzzy rules. This study uses orthogonal polynomials and linearly independent functions in a functional expansion of the FLNN. Thus, the consequent part of the proposed FLNFN model is a

Cheng-hung Chen; Cheng-jian Lin; Chin-teng Lin

2008-01-01

77

Coherence and chaos in condensed matter

This paper discusses the following topics: nonlinearity in condensed matter; coherence and chaos in spatially extended condensed matter systems; nonlinearity and magnetism; and solitons and conducting polymers. 52 refs., 7 figs. (LSP)

Bishop, A.R.

1989-01-01

78

Deterministic polarization chaos from a laser diode

Fifty years after the invention of the laser diode and fourty years after the report of the butterfly effect - i.e. the unpredictability of deterministic chaos, it is said that a laser diode behaves like a damped nonlinear oscillator. Hence no chaos can be generated unless with additional forcing or parameter modulation. Here we report the first counter-example of a free-running laser diode generating chaos. The underlying physics is a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time-series and show theoretically the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles at first sight a noise-driven mode hopping but shows opposite statistical properties. Our findings open up new research areas that combine the high speed performances of microcavity lasers with controllable and integrated sources of optical chaos.

Martin Virte; Krassimir Panajotov; Hugo Thienpont; Marc Sciamanna

2014-07-22

79

NSDL National Science Digital Library

The Ejs Duffing Chaos model computes the solutions to the non-linear Duffing equation, which reads, x'' + 2 γ x' - x (1 - xÂ²) = f cos( ω t), where each prime denotes a time derivative. The simulation displays two solutions with different initial positions and a plot of phase. The evolution parameters can be changed via textboxes. You can modify this simulation if you have Ejs installed by right-clicking within the plot and selecting âOpen Ejs Modelâ from the pop-up menu item. Ejs Duffing Chaos model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ehu_chaos_Duffing_chaos.jar file will run the program if Java is installed. Ejs is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models. Additional Ejs models for non-linear dynamics and chaos are available. They can be found by searching ComPADRE for Open Source Physics, OSP, or Ejs.

Aguirregabiria, Juan

2008-08-18

80

by delay in a linearly controlled system Outline Sketch of modelled setup t Chaos Bifurcation analysis oscillations t t Perfect stabilization System has symmetric chaotic at- tractor, visualized by a long-time for delay differential equations, bifurcation theory for finite-dimensional dynamical systems, numerical

Mumby, Peter J.

81

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

NASA Technical Reports Server (NTRS)

The paper develops a general theory for finite rubber viscoelasticity, and specifies it in the form, convenient for solving problems important for rubber, tire and space industries. Based on the quasi-linear approach of non-equilibrium thermodynamics, a general nonlinear theory has been developed for arbitrary nonisothermal deformations of viscoelastic solids. In this theory, the constitutive equations are presented as the sum of known equilibrium (rubber elastic) and non-equilibrium (liquid polymer viscoelastic) terms. These equations are then simplified using several modeling arguments. Stability constraints for the proposed constitutive equations are also discussed. It is shown that only strong ellipticity criteria are applicable for assessing stability of the equations governing viscoelastic solids.

Freed, Alan D.; Leonov, Arkady I.; Gray, Hugh R. (Technical Monitor)

2002-01-01

82

Nonlinear oceanic-atmospheric oscil-lations have been linked to hydro-

, such as the Pacific Decadal Oscillation (PDO), Atlan- tic Multidecadal Oscillation (AMO), North Atlantic Oscillation conditions associated with phases of the AMO and North Atlantic Oscil- lation (NAO) in conjunction139 Nonlinear oceanic-atmospheric oscil- lations have been linked to hydro- logical conditions

83

Chaos in driven Alfven systems

NASA Technical Reports Server (NTRS)

The chaos in a one-dimensional system, which would be nonlinear stationary Alfven waves in the absence of an external driver, is characterized. The evolution equations are numerically integrated for the transverse wave magnetic field amplitude and phase using the derivative nonlinear Schroedinger equation (DNLS), including resistive wave damping and a long-wavelength monochromatic, circularly polarized driver. A Poincare map analysis shows that, for the nondissipative (Hamiltonian) case, the solutions near the phase space (soliton) separatrices of this system become chaotic as the driver amplitude increases, and 'strong' chaos appears when the driver amplitude is large. The dissipative system exhibits a wealth of dynamical behavior, including quasiperiodic orbits, period-doubling bifurcations leading to chaos, sudden transitions to chaos, and several types of strange attractors.

Hada, T.; Kennel, C. F.; Buti, B.; Mjolhus, E.

1990-01-01

84

for Chaos Theory in Psychology & Life Sciences.2 3 Spatiotemporal Chaos in Easter Island Ecology4 5 J. C proposed spatiotemporal8 model for the ecology of Easter Island admits periodic and chaotic attractors,9 that is ubiquitous in such12 systems.13 Key Words: chaos, Easter Island, ecology, population dynamics, Turing14

Sprott, Julien Clinton

85

Quantum Correlations, Chaos and Information

NASA Astrophysics Data System (ADS)

Quantum chaos is the study of quantum systems whose classical description is chaotic. How does chaos manifest itself in the quantum world? In this spirit, we study the dynamical generation of entanglement as a signature of chaos in a system of periodically kicked coupled-tops, where chaos and entanglement arise from the same physical mechanism. The long-time entanglement as a function of the position of an initially localized wave packet very closely correlates with the classical phase space surface of section - it is nearly uniform in the chaotic sea, and reproduces the detailed structure of the regular islands. The uniform value in the chaotic sea is explained by the random state conjecture. As classically chaotic dynamics take localized distributions in phase space to random distributions, quantized versions take localized coherent states to pseudo-random states in Hilbert space. Such random states are highly entangled, with an average value near that of the maximally entangled state. For a map with global chaos, we derive that value based on new analytic results for the entropy of random states. For a mixed phase space, we use the Percival conjecture to identify a "chaotic subspace" of the Hilbert space. The typical entanglement, averaged over the unitarily invariant Haar measure in this subspace, agrees with the long-time averaged entanglement for initial states in the chaotic sea. In all cases the dynamically generated entanglement is that of a random complex vector, even though the system is time-reversal invariant, and the Floquet operator is a member of the circular orthogonal ensemble. Continuing on our journey to find the footprints of chaos in the quantum world, we explore quantum signatures of classical chaos by studying the rate of information gain in quantum tomography. The measurement record is obtained as a sequence of expectation values of a Hermitian operator evolving under repeated application of the Floquet operator of the quantum kicked top on a large ensemble of identical systems. We find an increase in the rate of information gain and hence higher fidelities in the process when the Floquet maps employed increase in chaoticity. We make predictions for the information gain using random matrix theory in the fully chaotic regime and show a remarkable agreement between the two. Finally we discuss how this approach can be used in general as a benchmark for information gain in an experimental implementation based on nonlinear dynamics of atomic spins measured weakly by the Faraday rotation of a laser probe. The last part of this thesis is devoted to the study of the nature of quantum correlations themselves. Quantum correlations are at the heart of the weirdness of quantum mechanics and at the same time serve as a resource for the potential benefits quantum information processing might provide. For example, Einstein described quantum entanglement as "spooky action at a distance". However, even entanglement does not fully capture the complete quantum character of a system. Quantum discord aims to fill this gap and captures essentially all the quantum correlations in a quantum state. There is a considerable interest in the research community about quantum discord, since there is evidence showing this very quantity as responsible for the exponential speed up of a certain class of quantum algorithms over classical ones. Now, an important question arises: Is discord just a mathematical construct or does it have a definable physical role in information processing? This thesis provides a link between quantum discord and an actual physical task involving communication between two parties. We present an operational interpretation of quantum discord based on the quantum state merging protocol. Quantum discord is the markup in the cost of quantum communication in the process of quantum state merging, if one discards relevant prior information. We further derive a quantitative relation between the yield of the fully quantum Slepian-Wolf protocol in the presence of noise and the quantum discord of

Madhok, Vaibhav

86

Generalized Statistical Mechanics at the Onset of Chaos

Transitions to chaos in archetypal low-dimensional nonlinear maps offer real and precise model systems in which to assess proposed generalizations of statistical mechanics. The known association of chaotic dynamics with the structure of Boltzmann--Gibbs (BG) statistical mechanics has suggested the potential verification of these generalizations at the onset of chaos, when the only Lyapunov exponent vanishes and ergodic and mixing properties cease to hold. There are three well-known routes to chaos in these deterministic dissipative systems, period-doubling, quasi-periodicity and intermittency, which provide the setting in which to explore the limit of validity of the standard BG structure. It has been shown that there is a rich and intricate behavior for both the dynamics within and towards the attractors at the onset of chaos and that these two kinds of properties are linked via generalized statistical-mechanical expressions. Amongst the topics presented are: (i) permanently growing sensitivity fluctuations and their infinite family of generalized Pesin identities; (ii) the emergence of statistical-mechanical structures in the dynamics along the routes to chaos; (iii) dynamical hierarchies with modular organization; and (iv) limit distributions of sums of deterministic variables. The occurrence of generalized entropy properties in condensed-matter physical systems is illustrated by considering critical fluctuations, localization transition and glass formation. We complete our presentation with the description of the manifestations of the dynamics at the transitions to chaos in various kinds of complex systems, such as, frequency and size rank distributions and complex network images of time series. We discuss the results.

Alberto Robledo

2013-12-03

87

International Journal of Bifurcation Chaos, Vol. No.

, motivated numerical simulation of nonlinear dynamical systems in high dimensions the growing recent interestÂdimensional chaos also has been known hyperchaos [Kapitaniak Steeb, 1991; Kapitaniak, 1993; Kapitaniak Chua, 1994

Lai, Ying-Cheng

88

Comparative performance analysis of M-CPSK and M-QAM over nonlinear satellite links

NASA Astrophysics Data System (ADS)

The classical moment technique is introduced as an accurate and efficient analytical tool for an end-to-end analysis of digital nonlinear satellite links. The method uses computational techniques that compute the symbol error probability when only the moments of the interference random variables are available. Using the moment method, analyses are presented for the symbol error probabilities of M-CPSK and M-QAM (quadrature amplitude modulation) through a band-limited nonlinear channel with both up-link and down-link noise and cochannel interference (CCI) preceding and following the transponder. It is shown that 16-QAM can be employed to increase the capacity of a typical C-band satellite communication link over a 4-GHz transponder up to 100 Mb/s with a ground-based linearizer and up to 140 Mb/s with a linearizer onboard the satellite. The results obtained using the moment technique are validated through the exhaustive method and brute-force computer simulation.

Rafie, Manouchehr S.; Shanmugan, K. Sam

89

Impact of nonlinearity phenomenon FWM in DWDM optical link considering dispersive fiber

NASA Astrophysics Data System (ADS)

The increasing demand of network traffic requires new research centers; improve their communications networks, due to the excessive use of mobile and portable devices wanting to have greater access to the network by downloading interactive content quickly and effectively. For our case analyze optical network link through simulation results assuming a DWDM (Dense wavelength Division Multiplexing) optical link, considering the nonlinearity phenomenon FWM (Four Mixed Wavelength) in order to compare their performance, assuming transmission bit rates to 2.5 Gbps and 10 Gbps, using three primary wavelengths of 1450 nm, 1550 nm and 1650 nm for the transmission of information, whose separation is 100 GHz to generate 16 channels or user information. Tests were conducted to analyze optical amplifiers EDFAs link robustness at a maximum distance of 200 km and identify parameters OSNR, SNR and BER, for a robust and effective transmission

Puche, William S.; Amaya, Ferney O.; Sierra, Javier E.

2013-12-01

90

Bose-Einstein condensate(BEC) provides a nice stage when the nonlinearSchrödinger equation plays a vital role. We study the dynamics of multi-component repulsive BEC in 2 dimensions with harmonic traps by using the nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly we consider a driven two-component BEC with each component trapped in different vertical positions. The appropriate tuning of the oscillation frequency of the

Katsuhiro Nakamura

2007-01-01

91

Chaos Optimization Strategy on Fuzzy-immune-PID Control of the Turbine Governing System

Aiming at the non-linear links such as time lag, inertia, dead time and saturation within the steam turbine governing system, we designed a fuzzy-immune-PID control system based on a mutative scale chaos optimization method, the principium of immune feedback system and the theory of fuzzy control. The proposed algorithm was used in tuning-parameter design of the steam turbine governing system

Shuangxin Wang; Yan Jiang; Hui Yang

2006-01-01

92

A cross-linked electro-optic polymer for second order nonlinear optical applications

NASA Astrophysics Data System (ADS)

Electro-optic properties of a cross-linked second order nonlinear optical polymer were reported. This polymer was synthesized via the crosslinking reaction with cross linker Trimethylolmelamine by doping the chromophores into the cellulose diacetate system. The crosslinking temperature is 144°C. The electro-optic coefficient was measured to be 7.12 pm/v at 1550 nm after poling. The stability characteristic of electro-optic effects was studied by a combination of the electro-optic coefficient and dielectric relaxation measurements. Results show that the cross-linked electro-optic polymer system possesses an excellent long-time stability. The average relaxation time is as large as 5880 days and the relaxation was modeled by KWW equation. The dielectric analyses show that the temperature dependence of the relaxation time follows Arrhenius law.

Hong, Jianxun; Li, Chengjun; Zhou, Jianxin; Zhou, Limin; Chen, Shuiping; Chen, Wei

2008-11-01

93

It is well known that settling transparency-efficiency tradeoff is important to design nonlinear optical (NLO) materials. In this work, we constructed one-dimensional polymeric cyanoacetylene (NCCCH)n by hydrogen-bond-directed-linking to understand this tradeoff from molecular level. Results show that the first hyperpolarizability of (NCCCH)n (n=2-8) gradually increased with the increase of n, and what is more important is that the red-shifts, associated with the increase of n, were very little. It is proposed that these polymeric structures possess double-degenerated charge transitions, which contribute to the hyperpolarizability in an additive fashion, and that the coupled oscillators are gradually improved, which lead to the increase of the first hyperpolarizability. Therefore, we propose the hydrogen-bond-directed-linking idea is helpful to develop the potential high-performance NLO materials. PMID:25145287

Ma, Fang; Bai, Dong-Sheng; Xu, Hong-Liang

2014-09-01

94

Charged fine particles confined in an AC trap exhibit either periodic motion or irregular motion, depending on the frequency and amplitude of the AC electric field. This motion was analyzed using an idealized electric field model with a nonlinear term in the radial direction (r) and an angular (theta-dependent) term. The potential U(r,theta,z,t) generates a rotational diffusion of chaotic orbits,

Ryuji Ishizaki; Hiroki Hata; Tatsuo Shoji

2011-01-01

95

Reflective confocal laser scanning microscopy and nonlinear microscopy of cross-linked rabbit cornea

NASA Astrophysics Data System (ADS)

Cross-linking of the cornea with application of Ribovlavin and UV-A light is an evolving clinical treatment of the eye disease keratoconus. Despite the positive clinical track record of corneal cross-linking, the complex wound healing process after the treatment is still under investigation. In this study an animal model was used to clarify the state of wound healing 5 weeks after treatment. Cross-linked rabbit corneae were imaged with reflective confocal laser scanning and nonlinear microscopy, namely second harmonic imaging microscopy (SHIM) and two-photon excited autofluorescence. First results show that the NAD(P) H-autofluorescence of the corneal keratocytes and their scattering signal still show a signature of the treatment five weeks after the cross-linking procedure. The SHIM signals show the structural morphology of the fibrous collagen sheets in the stroma of the cornea. SHIM detected in the forward direction differs substantially from backward SHIM, but no signature of treatment was found in both detection channels of the SHIM signal.

Krueger, Alexander; Hovakimyan, Marina; Ramirez, Diego F.; Stachs, Oliver; Guthoff, Rudolf F.; Heisterkamp, Alexander

2009-07-01

96

It has been proposed to make practical use of chaos in communication, in enhancing mixing in chemical processes and in spreading the spectrum of switch-mode power suppies to avoid electromagnetic interference. It is however known that for most smooth chaotic systems, there is a dense set of periodic windows for any range of parameter values. Therefore in practical systems working in chaotic mode, slight inadvertent fluctuation of a parameter may take the system out of chaos. We say a chaotic attractor is robust if, for its parameter values there exists a neighborhood in the parameter space with no periodic attractor and the chaotic attractor is unique in that neighborhood. In this paper we show that robust chaos can occur in piecewise smooth systems and obtain the conditions of its occurrence. We illustrate this phenomenon with a practical example from electrical engineering.

Soumitro Banerjee; James A. Yorke; Celso Grebogi

1998-03-02

97

Chaos in World Politics: A Reflection

NASA Astrophysics Data System (ADS)

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.

Ferreira, Manuel Alberto Martins; Filipe, José António Candeias Bonito; Coelho, Manuel F. P.; Pedro, Isabel C.

98

NASA Astrophysics Data System (ADS)

Charged fine particles confined in an AC trap exhibit either periodic motion or irregular motion, depending on the frequency and amplitude of the AC electric field. This motion was analyzed using an idealized electric field model with a nonlinear term in the radial direction (r) and an angular (?-dependent) term. The potential U(r,?,z,t) generates a rotational diffusion of chaotic orbits, and a transition from ballistic motion to diffusive motion was observed in the mean square displacement (MSD) of ?. The distribution function f(?) for the lifetime of angular unidirectional motion is exponential. This exponential distribution is produced by the chaotic switching between clockwise and anticlockwise rotations of orbits on the xy-plane. The time-correlation function C(?) of v? also has an exponential decay form as a result of the lifetime distribution function f(?). The scaling function of the MSD of ?(?) is derived using the correlation time ?c of C(?).

Ishizaki, Ryuji; Hata, Hiroki; Shoji, Tatsuo

2011-04-01

99

NASA Astrophysics Data System (ADS)

The dependences of gain and nonlinear distortions in analogue fiber-optic links on bias of an external electrooptical modulator were investigated. The increase in the gain by up to 5 dB as compared with the conventional quadrature point operation was demonstrated by shift the bias voltage applied to the external electrooptical modulator to a low transmission. Dependences of nonlinear distortions on the bias voltage of an electrooptical modulator were investigated. A minor increase in nonlinear distortions (less than 0.5 %) was observed at the conditions of a maximum gain. Proposed theoretical model is in a good agreement with the experimental data.

Petrov, A.; Ilichev, I.; Agruzov, P.; Lebedev, V.; Velichko, E.; Shamray, A.

2014-10-01

100

We show the extension of the Gaussian Noise model, which describes non-linear propagation in uncompensated links of multilevel modulation formats, to systems using Raman amplification. We successfully validate the analytical results by comparison with numerical simulations of Nyquist-WDM PM-16QAM channels transmission over multi-span uncompensated links made of a single fiber type and using hybrid EDFA/Raman amplification with counter-propagating pumps. We analyze two typical high- and low-dispersion fiber types. We show that Raman amplification always induces a limited non-linear interference enhancement compared to the dominant ASE noise reduction. PMID:23481790

Curri, Vittorio; Carena, Andrea; Poggiolini, Pierluigi; Bosco, Gabriella; Forghieri, Fabrizio

2013-02-11

101

Tutorial: chaos theory--a primer for health care.

Chaos theory, also called nonlinear systems theory, provides new insights into processes previously thought to be unpredictable and random. It also provides a new set of tools that can be used to analyze common administrative and clinical data. This tutorial provides an introduction to chaos theory. Subsequent articles will address applications of those principles to the administrative activities of health care organizations, implications of those principles for clinical data, and application of chaos theory concepts to our understanding of organizational dynamics. PMID:10144786

Sharp, L F; Priesmeyer, H R

1995-01-01

102

NASA Astrophysics Data System (ADS)

Chaos Theory is an interesting and important branch of physics. Many physical systems, such as weather or fluid flow, exhibit chaotic behavior. Experiments in simple mechanical or electrical systems, as well as simple simulations can be used as methods of studying chaos. Using a mechanical method, we connected a speaker and to a frequency modulator to bounce a table tennis ball. We recorded the ball's motion at different frequencies using a video camera. Using Tracker software we observed it's position versus it's velocity in order to analyze its chaotic behavior. For a simple simulation, we used the visual-based programming in LabView to examine chaotic behavior produced by some non-linear differential equations. Results from both the mechanical system and the simulations will be discussed. For future work, we plan to continue to explore some chaotic simulations and perform a sequence of experiments with an electrical system. Exploring these nonlinear chaotic systems can help us to better understand and model many phenomena found in nature.

Maldonado, Armando; Bixler, David

2012-03-01

103

Instability, subharmonics, and chaos in power electronic systems

The concept of chaos is applied to a variety of nonlinear power electronic circuits. With the onset of instability, the phenomena of subharmonics, quasi-periodicity, and chaos are predicted and observed. The following examples are dealt with: diodes with charge storage (with application to resonant converters); a ferroresonant circuit; a controlled thyristor rectifier circuit; and a Buck converter controlled by pulse-width

JONATHAN H. B. DEANE; DAVID C. HAMILL

1990-01-01

104

Solitons and chaos in laser-plasma interaction

Transitions from soliton to chaos in laser irradiated inhomogeneous plasmas are studied for Resonance absorption and Raman backscattering. To model resonance absorption, both driven nonlinear Schroedinger equation and Zakharov equations with in homogeneity term added were solved to show that the final states of steady state of modified Airy function; periodic solutions-representing regular soliton emission; and chaos through period doubling,

C. S. Liu; W. Shyu; P. N. Guzdar; H. H. Chen; Y. C. Lee

1991-01-01

105

Applying Chaos Theory to Lesson Planning and Delivery

ERIC Educational Resources Information Center

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…

Cvetek, Slavko

2008-01-01

106

Maxwell on Chaos Brian R. Hunt and James A. Yorke*

. I Maxwell on Chaos Brian R. Hunt and James A. Yorke* James Clerk Maxwell (1831-1879) is perhaps Articles in this issue... Scientific Article Maxwell on Chaos Brian R. Hunt and James A. Yorke Feature contents on p. 2 #12;-'Nonlinear Science Today Hunt and Yorke continued from p. 1 Two spheres moving

Yorke, James

107

Monitoring chaos of cardiac rhythms

Chaos theory provides a new paradigm in monitoring complexity changes in heart rate variability. Even in cases where the spectral analysis only shows broad band characteristics estimations of dimensional complexity parameters can show quantitative changes in the degree of chaos present in the interbeat interval dynamics. We introduce the concept of dimensional complexity as dynamical monitoring parameter and discuss its properties in connection with control data and data taken during cardiac arrest. Whereas dimensional complexity provides a quantitative indicator of overall chaotic behavior, recurrence plots allow direct visualization of recurrences in arbitrary high dimensional pattern-space. In combination these two methods from non-linear dynamics exemplify a new approach in the problem of heart rate monitoring and identification of precursors of cardiac arrest. Finally we mention a new method of chaotic control, by which selective and highly effective perturbations of nonlinear dynamical systems could be used for improved pacing patterns. 11 refs., 6 figs.

Mayer-Kress, G.

1989-01-01

108

in games as a way to hide one's intentions (Maynard Smith, 1982).33 Since the human brain is a large that computers, which mimic some features of the49 brain, are not chaotic, and thus chaos is not essential present random noise might be11 beneficial for learning. In such a case, human subjects might exhibit an12

Sprott, Julien Clinton

109

:Literature, Culture and Chaos Theory demonstrated that these approaches workequallywell when applied to Renaissance Strange Weather:Culture, Science, and Technology in the Age of Limits, and more significantlyhe calling itself a coffee table work, is co-authored by Robin Chapman and Julien Clinton Sprott, colleagues

Sprott, Julien Clinton

110

Nonlinear problems of aeroelasticity

NASA Astrophysics Data System (ADS)

The presently treated nonlinear problems of aeroelasticity arise from both geometric and aerodynamic nonlinearities, and are characterized by the possibility of multiple solutions, chaos, and instabilities that often settle down to steady-state limit cycles. Structurally, nonlinearities can arise both geometrically and due to material nonlinearity that leads to nonlinear stiffness characteristics and hysteresis loops; from aerodynamics, nonlinearities are generated by high angles of attack and from bluff bodies, as well as from the transonic speed regime.

Dugundji, John

111

[Chaos and fractals and their applications in electrocardial signal research].

Chaos and fractals are ubiquitous phenomena of nature. A system with fractal structure usually behaves chaos. As a complicated nonlinear dynamics system, heart has fractals structure and behaves as chaos. The deeper inherent mechanism of heart can be opened out when the chaos and fractals theory is utilized in the research of the electrical activity of heart. Generally a time series of a system was used for describing the status of the strange attractor of the system. The indices include Poincare plot, fractals dimension, Lyapunov exponent, entropy, scaling exponent, Hurst index and so on. In this article, the basic concepts and the methods of chaos and fractals were introduced firstly. Then the applications of chaos and fractals theories in the study of electrocardial signal were expounded with example of how they are used for ventricular fibrillation. PMID:19634696

Jiao, Qing; Guo, Yongxin; Zhang, Zhengguo

2009-06-01

112

A recurrent theme of much recent research is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This research has two main goals, that is the mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, and that judge the usefulness of various new techniques of nonlinear dynamics to the study of populations.

Kot, M.

1990-07-01

113

Magnetic field induced dynamical chaos

In this article, we have studied the dynamics of a particle having charge in the presence of a magnetic field. The motion of the particle is confined in the x–y plane under a two dimensional nonlinear potential. We have shown that constant magnetic field induced dynamical chaos is possible even for a force which is derived from a simple potential. For a given strength of the magnetic field, initial position, and velocity of the particle, the dynamics may be regular, but it may become chaotic when the field is time dependent. Chaotic dynamics is very often if the field is time dependent. Origin of chaos has been explored using the Hamiltonian function of the dynamics in terms of action and angle variables. Applicability of the present study has been discussed with a few examples.

Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra, E-mail: bidhanchandra.bag@visva-bharati.ac.in [Department of Chemistry, Visva-Bharati, Santiniketan 731 235 (India)

2013-12-15

114

Sensitivity of sensors for characterizing chaos

Chaos describes a class of motions of a deterministic system whose time history is sensitive to initial conditions. Because of the sensitivity of initial conditions, the response of a dynamical system may result in instabilities. Hence, a study of nonlinear response of structures under the expected frequencies of excitation becomes important. Chaotic behavior, for example, may be found in the

Robert G. Vaughan

1991-01-01

115

Stochastic Representation of Chaos using Terminal Attractors

NASA Technical Reports Server (NTRS)

A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.

Zak, Michail

2005-01-01

116

Chaos in plasma simulation and experiment

We investigate the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas using data from both numerical simulations and experiment. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos. These tools include phase portraits and Poincard sections, correlation dimension, the spectrum of Lyapunov exponents and short term predictability. In addition, nonlinear noise reduction techniques are applied to the experimental data in an attempt to extract any underlying deterministic dynamics. Two model systems are used to simulate the plasma dynamics. These are -the DEBS code, which models global RFP dynamics, and the dissipative trapped electron mode (DTEM) model, which models drift wave turbulence. Data from both simulations show strong indications of low,dimensional chaos and simple determinism. Experimental data were obtained from the Madison Symmetric Torus RFP and consist of a wide array of both global and local diagnostic signals. None of the signals shows any indication of low dimensional chaos or other simple determinism. Moreover, most of the analysis tools indicate the experimental system is very high dimensional with properties similar to noise. Nonlinear noise reduction is unsuccessful at extracting an underlying deterministic system.

Watts, C. [Texas Univ., Austin, TX (United States). Fusion Research Center; Newman, D.E. [Oak Ridge National Lab., TN (United States); Sprott, J.C. [Wisconsin Univ., Madison, WI (United States). Plasma Physics Research

1993-09-01

117

NASA Astrophysics Data System (ADS)

We propose the following model equation, ut+1/2(u2-uus)x=f(x,us) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t?0. Here, us(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.

Kasimov, Aslan R.; Faria, Luiz M.; Rosales, Rodolfo R.

2013-03-01

118

Whether every effect can be precisely linked to a given cause or to a list of causes has been a matter of debate for centuries, particularly during the 17th century when astronomers became capable of predicting the trajectories of planets. Recent mathematical models applied to physics have included the idea that given phenomena cannot be predicted precisely although they can be predicted to some extent in line with the chaos theory Concepts such as deterministic models, sensitivity to initial conditions, strange attractors, and fractal dimensions are inherent to the development of this theory, A few situations involving normal or abnormal endogenous rhythms in biology have been analyzed following the principles of chaos theory This is particularly the case with cardiac arrhythmias, but less so with biological clocks and circadian rhythms. PMID:17969865

Oestreicher, Christian

2007-01-01

119

ERIC Educational Resources Information Center

Analysis of ordered binary and unordered binary data has received considerable attention in social and psychological research. This article introduces a Bayesian approach, which has several nice features in practical applications, for analyzing nonlinear structural equation models with dichotomous data. We demonstrate how to use the software…

Lee, Sik-Yum; Song, Xin-Yuan; Cai, Jing-Heng

2010-01-01

120

Physical white chaos generation

Physical chaos is a fascinating prospect for high-speed data security by serving as a masking carrier or a key source, but suffers from a colored spectrum that divulges system's intrinsic oscillations and degrades randomness. Here, we demonstrate that physical chaos with a white spectrum can be achieved by the optical heterodyning of two delayed-feedback lasers. A white chaotic spectrum with 1-dB fluctuation in a band of 11 GHz is experimentally obtained. The white chaos also has a perfect delta-like autocorrelation function and a high dimensionality of greater than 10, which makes chaos reconstruction extremely difficult and thus improves security.

Anbang Wang; Yuncai Wang; Bingjie Wang; Lei Li; Mingjiang Zhang; Wendong Zhang

2014-01-26

121

THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT

We study the chaotic orbital evolution of planetary systems, focusing on secular (i.e., orbit-averaged) interactions, which dominate on long timescales. We first focus on the evolution of a test particle that is forced by multiple planets. To linear order in eccentricity and inclination, its orbit precesses with constant frequencies. But nonlinearities modify the frequencies, and can shift them into and out of resonance with either the planets' eigenfrequencies (forming eccentricity or inclination secular resonances), or with linear combinations of those frequencies (forming mixed high-order secular resonances). The overlap of these nonlinear secular resonances drives secular chaos. We calculate the locations and widths of nonlinear secular resonances, display them together on a newly developed map (the 'map of the mean momenta'), and find good agreement between analytical and numerical results. This map also graphically demonstrates how chaos emerges from overlapping secular resonances. We then apply this newfound understanding to Mercury to elucidate the origin of its orbital chaos. We find that since Mercury's two free precession frequencies (in eccentricity and inclination) lie within {approx}25% of two other eigenfrequencies in the solar system (those of the Jupiter-dominated eccentricity mode and the Venus-dominated inclination mode), secular resonances involving these four modes overlap and cause Mercury's chaos. We confirm this with N-body integrations by showing that a slew of these resonant angles alternately librate and circulate. Our new analytical understanding allows us to calculate the criterion for Mercury to become chaotic: Jupiter and Venus must have eccentricity and inclination of a few percent. The timescale for Mercury's chaotic diffusion depends sensitively on the forcing. As it is, Mercury appears to be perched on the threshold for chaos, with an instability timescale comparable to the lifetime of the solar system.

Lithwick, Yoram [Department of Physics and Astronomy, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208 (United States); Wu Yanqin [Department of Astronomy and Astrophysics, University of Toronto, Toronto, ON M5S 3H4 (Canada)

2011-09-20

122

NASA Astrophysics Data System (ADS)

Theoretical physics seems to be in a kind of schizophrenic state. Many phenomena in the observable macroscopic world obey nonlinear evolution equations, whereas the microscopic world is governed by quantum mechanics, a fundamental theory that is supposedly linear. In order to combine these two worlds in a common formalism, at least one of them must sacrifice one of its dogmas. I claim that linearity in quantum mechanics is not as essential as it apparently seems since quantum mechanics can be reformulated in terms of nonlinear Riccati equations. In a first step, it will be shown where complex Riccati equations appear in time-dependent quantum mechanics and how they can be treated and compared with similar space-dependent Riccati equations in supersymmetric quantum mechanics. Furthermore, the time-independent Schrödinger equation can also be rewritten as a complex Riccati equation. Finally, it will be shown that (real and complex) Riccati equations also appear in many other fields of physics, like statistical thermodynamics and cosmology.

Schuch, Dieter

2014-04-01

123

Chaotic operation and chaos control of travelling wave ultrasonic motor.

The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. PMID:23490014

Shi, Jingzhuo; Zhao, Fujie; Shen, Xiaoxi; Wang, Xiaojie

2013-08-01

124

Chaos in the Kepler System C. Chicone , B. Mashhoony and D. G. Retzlo z

Chaos in the Kepler System C. Chicone , B. Mashhoony and D. G. Retzlo z The long-term dynamical dimensional Kepler system. Speci cally, we consider the nonlinear evolution of the relative orbit due Kepler problem 1], we have found evidence for transient chaos. Speci cally, we have considered in our

Chicone, Carmen

125

June 15, 2011 23:21 ws-ijbcREVISE International Journal of Bifurcation and Chaos

June 15, 2011 23:21 ws-ijbcREVISE International Journal of Bifurcation and Chaos c World Scientific in a simple coupled logistic map simulation used in previous communication research, permitting the investigation of properties of nonlinear systems such as bifurcation and onset to chaos, even in the streams

Richardson, Daniel C.

126

ERIC Educational Resources Information Center

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…

Murphy, David

2011-01-01

127

Solitons in the midst of chaos

NASA Astrophysics Data System (ADS)

A system of coupled nonlinear Schrödinger equations describes pulse propagation in weakly birefringent optical fibers. Soliton solutions of this system are found numerically through the shooting method. We employ Poincaré surface of section plots—a standard dynamical systems approach—to analyze the phase space behavior of these solutions and neighboring trajectories. Chaotic behavior around the solitons is apparent and suggests dynamical instability. A Lyapunov stability analysis confirms this result. Thus, solitons exist in the midst of chaos.

Seghete, Vlad; Menyuk, Curtis R.; Marks, Brian S.

2007-10-01

128

Phased-array cancellation of nonlinear FWM in coherent OFDM dispersive multi-span links.

We develop an analytic model of Coherent Optical Orthogonal Frequency Division Multiplexing (OFDM) propagation and detection over multi-span long-haul fiber links, comprehensively and rigorously analyzing the impairments due the combined effects of FWM, Dispersion and ASE noise. Consistent with prior work of Innoe and Schadt in the WDM context, our new closed-form expressions for the total FWM received power fluctuations in the wake of dispersive phase mismatch in OFDM transmission, indicate that the FWM contributions of the multitude of spans build-up on a phased-array basis. For particular ultra-long haul link designs, the effectiveness of dispersion in reducing FWM is far greater than previously assumed in OFDM system analysis. The key is having the dominant FWM intermodulation products due to the multiple spans, destructively interfere, mutually cancelling their FWM intermodulation products, analogous to operating at the null of a phased-array antenna system. By applying the new analysis tools, this mode of effectively mitigating the FWM impairment, is shown under specific dispersion and spectral management conditions, to substantially suppress the FWM power fluctuations. Accounting for the phased-array concept and applying the compact OFDM design formulas developed here, we analyzed system performance of a 40 Gbps coherent OFDM system, over standard G.652 fiber, with cyclic prefix based electronic dispersion compensation but no optical compensation along the link. The transmission range for 10-3 target BER is almost tripled from 2560 km to 6960 km, relative to a reference system performing optical dispersion compensation in every span (ideally accounting for FWM and ASE noise and the cyclic prefix overhead, but excluding additional impairments). PMID:18825217

Nazarathy, Moshe; Khurgin, Jacob; Weidenfeld, Rakefet; Meiman, Yehuda; Cho, Pak; Noe, Reinhold; Shpantzer, Isaac; Karagodsky, Vadim

2008-09-29

129

A new phenomenon, entrainment of chaos, which is understood as a seizure of an irregular behavior by limit cycles, is discussed. As a result, chaotic cycles appear if the chaos amplitude is small. Otherwise, the chaos is not necessarily cyclic, if the perturbations are strong and/or diameter of the limit cycle is small. Sensitivity as a main and a unique ingredient is considered and, in addition, period-doubling route to chaos is chosen for extension. The results may be of strong importance for engineering sciences, brainwaves and biomusicology phenomena as well as can be developed for hydrodynamics. Theoretical results are supported by simulations and discussions over Chua's oscillators, entrainment of chaos by toroidal attractors and controlling problems. Moreover, through an example, by means of the Lyapunov functions method, a chaotic attractor is provided.

Marat Akhmet; Mehmet Onur Fen

2012-09-09

130

Evolution of Channels Draining Mount St. Helens: Linking Non-Linear and Rapid, Threshold Responses

NASA Astrophysics Data System (ADS)

The catastrophic eruption of Mount St. Helens buried the valley of the North Fork Toutle River (NFT) to a depth of up to 140 m. Initial integration of a new drainage network took place episodically by the “filling and spilling” (from precipitation and seepage) of depressions formed during emplacement of the debris avalanche deposit. Channel incision to depths of 20-30 m occurred in the debris avalanche and extensive pyroclastic flow deposits, and headward migration of the channel network followed, with complete integration taking place within 2.5 years. Downstream reaches were converted from gravel-cobble streams with step-pool sequences to smoothed, infilled channels dominated by sand-sized materials. Subsequent channel evolution was dominated by channel widening with the ratio of changes in channel width to changes in channel depth ranging from about 60 to 100. Widening resulted in significant adjustment of hydraulic variables that control sediment-transport rates. For a given discharge over time, flow depths were reduced, relative roughness increased and flow velocity and boundary shear stress decreased non-linearly. These changes, in combination with coarsening of the channel bed with time resulted in systematically reduced rates of degradation (in upstream reaches), aggradation (in downstream reaches) and sediment-transport rates through much of the 1990s. Vertical adjustments were, therefore, easy to characterize with non-linear decay functions with bed-elevation attenuating with time. An empirical model of bed-level response was then created by plotting the total dimensionless change in elevation against river kilometer for both initial and secondary vertical adjustments. High magnitude events generated from the generated from upper part of the mountain, however, can cause rapid (threshold) morphologic changes. For example, a rain-on-snow event in November 2006 caused up to 9 m of incision along a 6.5 km reach of Loowit Creek and the upper NFT. The event triggered a debris flow which cutoff tributary channels to Glacier Creek and redirected Step and Loowit Creeks thereby forcing enhanced flow volumes through the main channel. Very coarse, armored bed materials were mobilized allowing for deep incision into the substrate. Incision continues today at slower rates but it is again the lateral shifting and widening of the channels that is dominant. Low and moderate flows undercut the toe of 30 m-high pyroclastic flow deposits causing significant erosion. As the channel continues to widen incision will attenuate non-linearly. Channels such as the multiple Step Creek channels will coalesce as narrow ridges erode by undercutting and mass failure much as reaches of lower Loowit Creek did in the late 1980’s. The resulting enlarged and over-widened sections will then again (as in downstream reaches) have lowered transporting power.

Simon, A.

2010-12-01

131

Abstract. In this study we test the hypothesis that nonlinear optical (NLO) multiphoton photoactivation of riboflavin using a focused femtosecond (FS) laser light can be used to induce cross-linking (CXL) and mechanically stiffen collagen as a potential clinical therapy for the treatment of keratoconus and corneal ectasia. Riboflavin-soaked, compressed collagen hydrogels are cross-linked using a FS laser tuned to 760 nm and set to either 100 mW (NLO CXL I) or 150 mW (NLO CXL II) of laser power. FS pulses are focused into the hydrogel using a 0.75 NA objective lens, and the hydrogel is three-dimensionally scanned. Measurement of hydrogel stiffness by indentation testing show that the calculated elastic modulus (E) values are significantly increased over twofold following NLO CXL I and II compared with baseline values (P<0.05). Additionally, no significant differences are detected between NLO CXL and single photon, UVA CXL (P>0.05). This data suggests that NLO CXL has a comparable effect to conventional UVA CXL in mechanically stiffening collagen and may provide a safe and effective approach to localize CXL at different regions and depths within the cornea. PMID:23515869

Chai, Dongyul; Juhasz, Tibor; Brown, Donald J.; Jester, James V.

2013-01-01

132

Decrease of cardiac chaos in congestive heart failure

NASA Astrophysics Data System (ADS)

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.

Poon, Chi-Sang; Merrill, Christopher K.

1997-10-01

133

A new route to chaos: sequences of topological torus bifurcations.

We consider a sequence of topological torus bifurcations (TTBs) in a nonlinear, quasiperiodic Mathieu equation. The sequence of TTBs and an ensuing transition to chaos are observed by computing the principal Lyapunov exponent over a range of the bifurcation parameter. We also consider the effect of the sequence on the power spectrum before and after the transition to chaos. We then describe the topology of the set of knotted tori that are present before the transition to chaos. Following the transition, solutions evolve on strange attractors that have the topology of fractal braids in Poincare sections. We examine the topology of fractal braids and the dynamics of solutions that evolve on them. We end with a brief discussion of the number of TTBs in the cascade that leads to chaos. PMID:16252982

Spears, Brian K; Szeri, Andrew J

2005-09-01

134

NASA Astrophysics Data System (ADS)

The local heating of the solar-wind gas during its expansion represents one of the most intriguing problems in space plasma physics and is at present the subject of a relevant scientific effort. The possible mechanisms that could account for local heat production in the interplanetary medium are most likely related to the turbulent character of the solar-wind plasma. Nowadays, many observational and numerical analyses are devoted to the identification of fluctuation channels along which energy is carried from large to short wavelengths during the development of the turbulent cascade; these fluctuation channels establish the link between macroscopic and microscopic scales. In this Letter, by means of a quantitative comparison between in situ measurements in the solar wind from the STEREO spacecraft and numerical results from kinetic simulations, we identify an electrostatic channel of fluctuations that develops along the turbulent cascade in a direction parallel to the ambient magnetic field. This channel appears to be efficient in transferring the energy from large Alfvénic to short electrostatic acoustic-like scales up to a range of wavelengths where it can finally be turned into heat, even when the electron to proton temperature ratio is of the order of unity.

Valentini, F.; Vecchio, A.; Donato, S.; Carbone, V.; Briand, C.; Bougeret, J.; Veltri, P.

2014-06-01

135

Chaos in atmospheric-pressure plasma jets

NASA Astrophysics Data System (ADS)

We report detailed characterization of a low-temperature atmospheric-pressure plasma jet that exhibits regimes of periodic, quasi-periodic and chaotic behaviors. Power spectra, phase portraits, stroboscopic section and bifurcation diagram of the discharge current combine to comprehensively demonstrate the existence of chaos, and this evidence is strengthened with a nonlinear dynamics analysis using two control parameters that maps out periodic, period-multiplication, and chaotic regimes over a wide range of the input voltage and gas flow rate. In addition, optical emission signatures of excited plasma species are used as the second and independent observable to demonstrate the presence of chaos and period-doubling in both the concentrations and composition of plasma species, suggesting a similar array of periodic, quasi-periodic and chaotic regimes in plasma chemistry. The presence of quasi-periodic and chaotic regimes in structurally unbounded low-temperature atmospheric plasmas not only is important as a fundamental scientific topic but also has interesting implications for their numerous applications. Chaos may be undesirable for industrial applications where cycle-to-cycle reproducibility is important, yet for treatment of cell-containing materials including living tissues it may offer a novel route to combat some of the major challenges in medicine such as drug resistance. Chaos in low-temperature atmospheric plasmas and its effective control are likely to open up new vistas for medical technologies.

Walsh, J. L.; Iza, F.; Janson, N. B.; Kong, M. G.

2012-06-01

136

NASA Astrophysics Data System (ADS)

When I finished graduate school I suppose I imagined myself as my dad. He worked hard, loved his job and family, made a good living. But I also saw myself as my mom - making a home, raising kids, cooking dinner, saving the world. I thought: I can handle being my mom and my dad. I can handle being a scientist and a mother. I can DO this.ÿ What I never imagined was the chaotic dynamic of the two career couple. The motions of bodies moving in response to the force of gravity cannot be predicted exactly if there are too many bodies. They dance in a jerky jumble, now faster, then slowly, bouncing, jostling, bumping and flying apart. Just so are the career trajectories of the two career couple. One rises up, the other, slower, pulls it down; overtaking, blocking preventing, now supporting, pulling along, now holding back - not moving, leap frogging, racing in opposite directions and snapping back together with a crack.ÿ The problem is non-linear. The outcome depends on feedback, whether positive or negative. The outcome cannot be predicted. Cannot be determined.ÿ Perhaps it cannot be done. Perhaps both husband and wife cannot be both mother and father. Too many mothers, too many fathers. Chaos.ÿ But I believe it can be done. Not like our mothers and fathers but a different way. And maybe our jerky paths will keep us sharp, make us work harder, and lead us through lives that at least cannot be described as dull.ÿ

Tauxe, L.

2002-12-01

137

ERIC Educational Resources Information Center

Described are the idea of chaos and the ability to control the chaotic behavior of a real-world physical system. Included is an explanation of the methodology and applications in biology and chemistry. (KR)

Peterson, Ivars

1991-01-01

138

Provided is a brief overview of the current status of the field of deterministic ''chaos'', stressing its interrelations and applications to other fields and suggesting a number of important open problems for future study.

Campbell, D.

1987-01-01

139

A new type of deterministic chaos for a system described by iterative two-dimensional maps is reported. The series being generated by the original map has an average upward trend while the first difference, which is the series of changes from one period to the next, exhibits chaotic behavior through period doubling bifurcation. Furthermore, step-wise time series appears as the values of the bifurcation parameter are large, and the first difference of the time series exhibits intermittent chaos.

Taisei Kaizoji

2010-07-21

140

We unveil chaotic behavior hidden in the energy spectrum of a Jahn-Teller ion vibrating in a cubic anharmonic potential as a typical model for rattling in cage-structure materials. When we evaluate the nearest-neighbor level-spacing distribution $P(s)$ of eigenenergies of the present oscillator system, we observe the transition of $P(s)$ from the Poisson to the Wigner distribution with the increase of cubic anharmonicity, showing the occurrence of chaos in the anharmonic Jahn-Teller vibration. The energy scale of the chaotic region is specified from the analysis of $P(s)$ and we discuss a possible way to observe chaotic behavior in the experiment of specific heat. It is an intriguing possibility that chaos in nonlinear physics could be detected by a standard experiment in condensed matter physics.

Takashi Hotta; Akira Shudo

2014-06-18

141

Chaos in hydrodynamic BL Herculis models

We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars - RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Pa...

Smolec, R

2014-01-01

142

Stochastic Representation of Chaos Using Terminal Attractors

NASA Technical Reports Server (NTRS)

A nonlinear version of the Liouville equation based on terminal attractors is part of a mathematical formalism for describing postinstability motions of dynamical systems characterized by exponential divergences of trajectories leading to chaos (including turbulence as a form of chaos). The formalism can be applied to both conservative systems (e.g., multibody systems in celestial mechanics) and dissipative systems (e.g., viscous fluids). The development of the present formalism was undertaken in an effort to remove positive Lyapunov exponents. The means chosen to accomplish this is coupling of the governing dynamical equations with the corresponding Liouville equation that describes the evolution of the flow of error probability. The underlying idea is to suppress the divergences of different trajectories that correspond to different initial conditions, without affecting a target trajectory, which is one that starts with prescribed initial conditions.

Zak, Michail

2006-01-01

143

Ecosystem Simulations and Chaos on the Graphing Calculator

ERIC Educational Resources Information Center

An eighth grade algebra class used graphing calculators to simulate ecosystems. One simulation introduced mathematical chaos. The activities exposed the students to nonlinear patterns and modeling. The rate-of-change investigations related the ideas of intercept and slope to the changing equilibrium. The chaotic model intrigued them and was useful…

Sinn, Robb

2007-01-01

144

ERIC Educational Resources Information Center

Recent findings from Western developed countries have linked home chaos to children's cognitive performance and behavioral problems. In the present paper we test whether the same pattern of associations can be replicated in a non-Western developing country. Our sample was 203 Pakistani primary school children. To assess home chaos the Confusion,…

Shamama-tus-Sabah, Syeda; Gilani, Nighat; Wachs, Theodore D.

2011-01-01

145

ERIC Educational Resources Information Center

The evolution of ideas about the concept of chaos is surveyed. Discussed are chaos in deterministic, dynamic systems; order in dissipative systems; and thermodynamics and irreversibility. Included are logistic and bifurcation maps to illustrate points made in the discussion. (CW)

Glasser, L.

1989-01-01

146

Quantum Chaos and Its Application

The present article is a note of my lecture in The Aizu University at Oct. 1994. The first part is designed to present an outline of the field called Quantum Chaos for primers. The problems in the quantization of classical system in the presence of chaos, the well-established results in this subject and the current status of Quantum Chaos are

Takahiro Mizusaki

1996-01-01

147

Speculations on Nonlinear Speculative Bubbles

This paper reviews a variety of issues related to speculative bubbles, especially those involving nonlinear dynamics. Models of irrational bubbles, rational bubbles, and bubbles arising from heterogeneous agents with varying degrees of knowledge or rationality are examined. The latter are shown to be prone to nonlinear dynamics with catastrophic discontinuities, chaos, and other forms of complex phenomena. Empirical evidence regarding

J. Barkley Rosser

1997-01-01

148

Nonlinear and Complex Dynamics in Real Systems

In this article we provide a review of the literature with respect to fluctuations in real systems and chaos. In doing so, we contrast the order and organization hypothesis of real systems to nonlinear chaotic dynamics and ...

Barnett, William A.; Serletis, Apostolos; Serletis, Demitre

2006-06-01

149

Networked control systems: a perspective from chaos

In this paper, a nonlinear system aiming at reducing the signal transmission rate in a networked control system is constructed by adding nonlinear constraints to a linear feedback control system. Its stability is investigated in detail. It turns out that this nonlinear system exhibits very interesting dynamical behaviors: in addition to local stability, its trajectories may converge to a non-origin equilibrium or be periodic or just be oscillatory. Furthermore it exhibits sensitive dependence on initial conditions --- a sign of chaos. Complicated bifurcation phenomena are exhibited by this system. After that, control of the chaotic system is discussed. All these are studied under scalar cases in detail. Some difficulties involved in the study of this type of systems are analyzed. Finally an example is employed to reveal the effectiveness of the scheme in the framework of networked control systems.

Guofeng Zhang; Tongwen Chen

2014-05-10

150

Intramolecular and nonlinear dynamics

Research in this program focuses on three interconnected areas. The first involves the study of intramolecular dynamics, particularly of highly excited systems. The second area involves the use of nonlinear dynamics as a tool for the study of molecular dynamics and complex kinetics. The third area is the study of the classical/quantum correspondence for highly excited systems, particularly systems exhibiting classical chaos.

Davis, M.J. [Argonne National Laboratory, IL (United States)

1993-12-01

151

Chaos in a Relativistic 3-Body Self-Gravitating System

NASA Astrophysics Data System (ADS)

We consider the 3-body problem in relativistic lineal [i.e., (1+1)-dimensional] gravity and obtain an exact expression for its Hamiltonian and equations of motion. While general-relativistic effects yield more tightly bound orbits of higher frequency compared to their nonrelativistic counterparts, as energy increases we find in the equal-mass case no evidence for either global chaos or a breakdown from regular to chaotic motion, despite the high degree of nonlinearity in the system. We find numerical evidence for mild chaos and a countably infinite class of nonchaotic orbits, yielding a fractal structure in the outer regions of the Poincaré plot.

Burnell, F.; Mann, R. B.; Ohta, T.

2003-04-01

152

Synchronization of coupled systems with spatiotemporal chaos

NASA Astrophysics Data System (ADS)

We argue that the synchronization transition of stochastically coupled cellular automata, discovered recently by Morelli et al. [Phys. Rev. E 58, R8 (1998)], is generically in the directed percolation universality class. In particular this holds numerically for the specific example studied by these authors, in contrast to their claim. For real-valued systems with spatiotemporal chaos such as coupled map lattices, we claim that the synchronization transition is generically in the universality class of the Kardar-Parisi-Zhang equation with a nonlinear growth limiting term.

Grassberger, Peter

1999-03-01

153

Chaos in symmetric phase oscillator networks.

Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization so far has been found to be chaotic only in systems with inhomogeneities. Here we show that even symmetric systems of identical oscillators may not only exhibit chaotic dynamics, but also chaotically fluctuating order parameters. Our findings imply that neither inhomogeneities nor amplitude variations are necessary to obtain chaos; i.e., nonlinear interactions of phases give rise to the necessary instabilities. PMID:22243002

Bick, Christian; Timme, Marc; Paulikat, Danilo; Rathlev, Dirk; Ashwin, Peter

2011-12-01

154

Chaos in a Fractional Order Chua System

NASA Technical Reports Server (NTRS)

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

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

1996-01-01

155

Regarding the role of link beams in the seismic behavior of coupled shear walls, in this study, at first a pre-designed concrete link beam of a coupled shear walls system, tested previusly under cyclic loading, has been analyzed by Finite Element Modeling (FEM). Then it has been substituted by a steel link beam, and the analyses have been repeated to

Mahmood Hosseini; Hossein Sadeghi; Seidali Habiby

2011-01-01

156

Formation and manipulation of optomechanical chaos via a bichromatic driving

NASA Astrophysics Data System (ADS)

We propose a scheme to efficiently manipulate optomechanical systems into and out of chaotic regimes. Here the optical system is coherently driven by a continuous-wave bichromatic laser field consisting of a pump field and a probe field, where the beat frequency of the bichromatic components plays an important role in controlling the appearance of chaotic motion and the corresponding chaotic dynamics. With state-of-the-art experimental parameters, we find that a broad chaos-absent window with sharp edges can be formed by properly adjusting the powers of the bichromatic input field. Moreover, the lifetime of the transient chaos and the chaotic degree of the optomechanical system can be well tuned simply by changing the initial phases of the bichromatic input field. This investigation may be useful for harnessing the optomechanical nonlinearity to manipulate rich chaotic dynamics and find applications in chaos-based communication.

Ma, Jinyong; You, Cai; Si, Liu-Gang; Xiong, Hao; Li, Jiahua; Yang, Xiaoxue; Wu, Ying

2014-10-01

157

The characteristics of chaos regions on Europa suggest they may be sites of melt-through from below. They are wide ranging in size, location, and age. The largest are hundreds of kilometers across. Most are similar to Conamara with a matrix reminiscent of frozen slush and often rafts of preexisting crust. Edges are of two types: ramps, perhaps the tapering of

Richard Greenberg; Gregory V. Hoppa; B. R. Tufts; Paul Geissler; Jeannemarie Riley; Steven Kadel

1999-01-01

158

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

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 Ro?ssler 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. PMID:22462991

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

2012-03-01

159

Effect of transmission fiber and amplifier noise on optical chaos synchronization

NASA Astrophysics Data System (ADS)

Optical chaos propagation has few constraints peculiar to itself which do not become as significant in conventional nonchaotic optical communication. We have investigated the effects of transmission fiber nonlinearities, dispersion and noise of erbium doped fiber amplifier (EDFA) on chaotic signal synchronization in lumped and distributed configuration. It is found that the effects of fiber dispersion can be easily compensated; however, the effects of fiber nonlinearity on chaos cannot be overdone and must be avoided. Three distinct configurations with different combinations of standard telecommunication fiber, dispersion compensation fiber and lumped and distributed EDF for amplification are analysed. The results are compared in terms of sync diagrams and noise figure. The chaos after propagation through distributed amplification performs better as compared to lumped amplification. Also, a new quantitative measure for the calculation of deviation in sync diagram of chaos is introduced.

Ali, Syed Zafar; Islam, Muhammad Khawar; Zafrullah, Muhammad

2012-09-01

160

Complex nonlinear dynamic systems are ubiquitous in the landscapes and phenomena studied by earth sciences in general and by geomorphology in particular. Concepts of chaos, fractals and self-organization, originating from research in nonlinear dynamics, have proven to be powerful approaches to understanding and modeling the evolution and characteristics of a wide variety of landscapes and bedforms. This paper presents a

Andreas C. W. Baas

2002-01-01

161

Noise tolerant spatiotemporal chaos computing

NASA Astrophysics Data System (ADS)

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.

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

2014-12-01

162

Weak-Chaos Ratchet Accelerator

Classical Hamiltonian systems with a mixed phase space and some asymmetry may exhibit chaotic ratchet effects. The most significant such effect is a directed momentum current or acceleration. In known model systems, this effect may arise only for sufficiently strong chaos. In this paper, a Hamiltonian ratchet accelerator is introduced, featuring a momentum current for arbitrarily weak chaos. The system is a realistic, generalized kicked rotor and is exactly solvable to some extent, leading to analytical expressions for the momentum current. While this current arises also for relatively strong chaos, the maximal current is shown to occur, at least in one case, precisely in a limit of arbitrarily weak chaos.

Itzhack Dana; Vladislav B. Roitberg

2012-05-28

163

Nonlinear aspects of shock response in isolated accelerometers

Numerous investigations have studied the potential for chaotic vibrations of nonlinear systems. It has been shown for many simple nonlinear systems, that when they are excited severely enough, or with the appropriate parametric combinations, that they will execute chaotic vibrations. The present investigation considers the potential for the occurrence of chaos in a practical nonlinear system -- the isolated accelerometer. A simple, first order model is proposed for the isolated accelerometer, and it is shown that chaos can occur in the isolated accelerometer. A preliminary investigation into the bearing that this chaos potential has on the measurement of shock response is summarized. 7 refs.

Paez, T.L. [Sandia National Labs., Albuquerque, NM (United States); Hunter, N. [Los Alamos National Lab., NM (United States)

1992-04-01

164

Stable chaos in fluctuation driven neural circuits

We study the dynamical stability of pulse coupled networks of leaky integrate-and-fire neurons against infinitesimal and finite perturbations. In particular, we compare current versus fluctuations driven networks, the former (latter) is realized by considering purely excitatory (inhibitory) sparse neural circuits. In the excitatory case the instabilities of the system can be completely captured by an usual linear stability (Lyapunov) analysis, on the other hand the inhibitory networks can display the coexistence of linear and nonlinear instabilities. The nonlinear effects are associated to finite amplitude instabilities, which have been characterized in terms of suitable indicators. For inhibitory coupling one observes a transition from chaotic to non chaotic dynamics by decreasing the pulse width. For sufficiently fast synapses the system, despite showing an erratic evolution, is linearly stable, thus representing a prototypical example of Stable Chaos.

David Angulo-Garcia; Alessandro Torcini

2014-03-03

165

A chaos model of meandering rivers

A meandering river is a nonlinear dynamic system, and fractal geometry describes well the meander bends of such rivers. Based on a qualitative, sedimentological model of the process of meandering, a chaos model is proposed, describing meandering as the outcome of two processes: the feedback interaction between river curvature and a high-velocity thalweg channel within the river; and the interaction between meander bends causing abandonment and straightening of the river course. The system, when initiated from a nearly straight river course, moves toward a dynamic equilibrium in which the meander bends are fractal. This development is a case of self-organized criticality. The equilibrium represents a state of optimal energy dissipation in a situation where two counteracting processes are balancing each other. Sedimentology may be seen as the science that describes how nonlinear dynamic processes interact to create a depositional system. As indicated by the example of meandering rivers, the use of chaos and fractal models may give sedimentology a new turn toward understanding sedimentary processes and the 3-D architecture of sediment bodies.

Stoelum, H.H.

1991-03-01

166

NASA Astrophysics Data System (ADS)

The cyano and nitro groups were chosen as acceptor groups, and the substituent amino or ether groups as donor groups to the matrix. Polyurethane (PU) was modified by glycerol to increase the content of chromophore and to improve the stability of the nonlinearity. Tg and Tm were raised and solubility, film-forming ability and other physical properties were improved. The average functional groups of the reactant can be adjusted to ? 2 with polygroups and monogroups mixture. These poled polymers show high second-order optical nonlinearity and would have potential application in frequency-doubling or electro-optical controlling devices.

Ye, Mingxin; Xu, Lei; Ji, Liyong; Liu, Liying; Wang, Wencheng

167

NASA Technical Reports Server (NTRS)

(Released 11 June 2002) The Science This fractured surface belongs to a portion of a region called Gorgonum Chaos located in the southern hemisphere of Mars. Gorgonum Chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars and lolling tongues who lived in caves. As it turns out this is indeed a fitting name for this region of Mars because it contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of chaos. Upon closer examination one finds that these gullies and alluvial deposits, initially discovered by Mars Global Surveyor, are visible on the trough walls (best seen near the bottom of the image). These gullies appear to emanate from a specific layer in the walls. The gullies have been proposed to have formed by the subsurface release of water. The Story This fractured, almost spooky-looking surface belongs to a region called Gorgonum Chaos in the southern hemisphere of Mars. Chaos is a term used for regions of Mars with distinctive areas of broken terrain like the one seen above. This area of Martian chaos is named after the Gorgons in ancient Greek mythology. The Gorgons were monstrous sisters with snakes for hair, tusks like boars, and lolling tongues, who lived in caves. The Gorgons, including famous sister Medusa, could turn a person to stone, and their writhing, snakelike locks cause revulsion to this day. Given the afflicted nature of this contorted terrain, with all of its twisted, branching channels and hard, stony-looking hills in the top half of the image, this is indeed a fitting name for this region of Mars. The name also has great appeal, because the area contains a high density of gullies that 'snake' their way down the walls of the troughs located in this region of Martian chaos. Gullies are trenches cut into the land as accelerated streams of water (or another liquid) erode the surface. To see these, click on the above image to get a high-resolution view, and then focus on the trenches at the bottom. Running down the walls of the trough are the thin, dark lines of the gullies. Beneath the grooved, gully channels are faint, softer-looking fans of material. These are called alluvial deposits. Alluvial simply means all of the sand, gravel, and dirt that is carried and deposited by a liquid. On Earth, that liquid is typically water. As the liquid carves the gully, the eroded material from the channels get carried along and deposited below in fan-like shapes. These gully features were initially discovered by Odyssey's sister orbiter, Mars Global Surveyor, and caused quite a bit of emotional chaos in the scientific community when they were announced. Why? If you look closely, you can see that the gullies seem to form from a specific layer in the wall. That is, they all seem to begin at roughly the same point on the wall. That suggests that maybe, just maybe, there's a subsurface source of water at that layer that sometimes leaks out and runs down the walls to form both the gullies and the skirt-like fans of deposits beneath them. Other scientists, however, loudly assert that another liquid besides water could have carved the gullies. The debate sometimes gets so intense, you'd think that the opposing sides would want to turn each other's ideas to stone! But not for long. While the debate rages on, the neat thing is that everyone's really united. The goal is to find out, and the way to find out is to keep proposing different hypotheses and testing them out. That's the excitement of science, where everyone's solid research counts, and divergent views are appreciated for keeping science sound.

2002-01-01

168

The annihilation operator for harmonic oscillator is a weighted shift operator and can be realized on a family of over complete coherent states. Shift operators arise in dynamical maps of systems exhibiting deterministic chaos. Generalized coherent states, called harmonious states, realize these maps in a simple manner. By analytic continuation the spectral family can be altered, thus furnishing an alternative perspective on resonant scattering. Singular distributions are necessary to reproduce the rich structure of chaotic and scattering systems.

Sudarshan, E.C.G.

1993-12-31

169

We investigate the chaotic behavior of a circular test string in the Lifshitz spacetimes considering the critical exponent $z$ as an external control parameter. It is demonstrated that two primary tools to observe chaos in this system are Poincar\\'{e} section and Lyapunov exponent. Finally, the numerical result shows that if $z=1$, the string dynamics is regular, while in a case slightly larger than $z=1$, the dynamics can be irregular and chaotic.

Xiaojian Bai; Junde Chen; Bum-Hoon Lee; Taeyoon Moon

2014-06-23

170

This paper explores the ancient Greek quasi-mystical concepts of Chronos and then Kairos, particularly in relation to group analysis and individual analytic psychotherapy. It concludes with some thoughts on the nature of time and space and introduces Chaos, a third Greek concept, with a consideration of the chaotic patterns of movement in space-time which are, it seems, self-organizing and have

Jeff Roberts

2003-01-01

171

Some Ionic and Bioelectric Properties of the Ameba Chaos chaos

Ionic relationships in the giant ameba Chaos chaos were studied by analyzing bulk preparations of ground cytoplasm for K, Na, and (31. Ion levels under normal conditions were compared with the levels in cells exposed to varying concentrations of different ions, for varying times and at different temperatures. By standard intracellular electrode techniques, the bioelectric potential, electrical resistance, and rectifying

DAVID L. BRUCE; JOHN M. MARSHALL

1965-01-01

172

NASA Astrophysics Data System (ADS)

This paper proposes a modified four-leg distribution static compensator (DSTATCOM) topology for compensation of unbalanced and nonlinear loads in three-phase four-wire distribution system. DSTATCOM, connected in parallel to the load, supplies reactive and harmonic powers demanded by unbalanced nonlinear loads. In this proposed topology, the voltage source inverter (VSI) of DSTATCOM is connected to point of common coupling (point of interconnection of source, load, DSTATCOM) through interface inductor and series capacitance, unlike the conventional topology which consists of interface inductor alone. Load compensation with a lower value of input DC link voltage of VSI is possible in this modified topology compared to conventional topology. A comparative study on modified and conventional topologies in terms of voltage rating of inverter power switches, switching losses in VSI and power rating of input DC capacitor of VSI is presented. The detailed design aspects of DC link capacitor and interface series capacitor are also presented. The reference filter currents are generated using instantaneous symmetrical component theory and are tracked using hysteresis current control technique. A detailed simulation study is carried out, to compare the compensation performances of conventional, modified topologies using PSCAD simulator and experimental studies are done to validate the simulation results.

Geddada, Nagesh; Karanki, Srinivas B.; Mishra, Mahesh K.

2014-06-01

173

Chaos Theory and Post Modernism

ERIC Educational Resources Information Center

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…

Snell, Joel

2009-01-01

174

The fundamentals of controlling chaos.

The concepts of chaos and its control are reviewed. Both are discussed from an experimental as well as a theoretical viewpoint. A detailed exposition of the mathematics of chaos control is presented, with an eye toward implementation in computer-controlled experiments. PMID:7811644

Spano, M L; Ditto, W L

1994-01-01

175

Quantum chaos in quantum dots coupled to bosons

Chaos transition, as an important topic, has become an active research subject in non-linear science. By considering a Dicke Hamiltonian coupled to a bath of harmonic oscillator, we have been able to introduce a logistic map with quantum corrections. Some basic dynamical properties, such as Lyapunov exponents and bifurcation diagram of the model are studied. we show that in this model, the transition from integrable motion to periodic, chaotic and hyperchaotic as the control parameter $r$ is increased.

S. Ahadpour; N. Hematpour

2012-07-24

176

NASA Astrophysics Data System (ADS)

A recently developed metaheuristic optimization algorithm, firefly algorithm (FA), mimics the social behavior of fireflies based on the flashing and attraction characteristics of fireflies. In the present study, we will introduce chaos into FA so as to increase its global search mobility for robust global optimization. Detailed studies are carried out on benchmark problems with different chaotic maps. Here, 12 different chaotic maps are utilized to tune the attractive movement of the fireflies in the algorithm. The results show that some chaotic FAs can clearly outperform the standard FA.

Gandomi, A. H.; Yang, X.-S.; Talatahari, S.; Alavi, A. H.

2013-01-01

177

The asymptotic distance between trajectories $d_{\\infty}$, is studied in detail to characterize the occurrence of chaos. We show that this quantity is quite distinct and complementary to the Lyapunov exponents, and it allows for a quantitave estimate for the folding mechanism which keeps the motion bounded in phase space. We study the behaviour of $d_{\\infty}$ in simple unidimensional maps. Near a critical point $d_{\\infty}$ has a power law dependence on the control parameter. Furthermore, at variance with the Lyapunov exponents, it shows jumps when there are sudden changes on the available phase-space.

Virgil Baran; Aldo Bonasera

1998-04-13

178

9 Nonlinear Time Series Analysis in a Nutshell

Ion Nonlinear time series analysis is a practical spinoff from complex dynamical systems theory and chaos theory125 9 Nonlinear Time Series Analysis in a Nutshell Ralph Gregor Andrzejak 9.1 Introduct. It allows one to characterize dynamical systems in which nonlinearities give rise to a complex temporal

Andrzejak, Ralph Gregor

179

Feigenbaum graphs at the onset of chaos

We analyze the properties of the self-similar network obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We first show that this network is uniquely determined by the encoded sequence of positions in the dynamics within the Feigenbaum attractor and it is universal in that it is independent of the shape and nonlinearity of the maps in this class. We then find that the network degrees fluctuate at all scales with an amplitude that increases as the size of the network grows. This suggests the definition of a graph-theoretical Lyapunov exponent that measures the expansion rate of trajectories in network space. On good agreement with the map's counterpart, while at the onset of chaos this exponent vanishes, the subexponential expansion and contraction of network degrees can be fully described via a Tsallis-type scalar deformation of the expansion rate, that yields a discrete spectrum of non-null generalized exponents. We further explore the possibility of defining an entropy growth rate that describes the amount of information created along the trajectories in network space. Making use of the trajectory distributions in the map's accumulation point and the scaling properties of the associated network, we show that such entropic growth rate coincides with the spectrum of graph-theoretical exponents, what appears as a set of Pesin-like identities in the network.

Bartolo Luque; Lucas Lacasa; Alberto Robledo

2012-05-09

180

Chaos in hydrodynamic BL Herculis models

We present non-linear, convective, BL Her-type hydrodynamic models that show complex variability characteristic for deterministic chaos. The bifurcation diagram reveals a rich structure, with many phenomena detected for the first time in hydrodynamic models of pulsating stars. The phenomena include not only period doubling cascades en route to chaos (detected in earlier studies) but also periodic windows within chaotic band, type-I and type-III intermittent behaviour, interior crisis bifurcation and others. Such phenomena are known in many textbook chaotic systems, from the simplest discrete logistic map, to more complex systems like Lorenz equations. We discuss the physical relevance of our models. Although except of period doubling such phenomena were not detected in any BL Her star, chaotic variability was claimed in several higher luminosity siblings of BL Her stars - RV Tau variables, and also in longer-period, luminous irregular pulsators. Our models may help to understand these poorly studied stars. Particularly interesting are periodic windows which are intrinsic property of chaotic systems and are not necessarily caused by resonances between pulsation modes, as sometimes claimed in the literature.

R. Smolec; P. Moskalik

2014-03-19

181

The application of the Hartley modulating functions (HMF) method is investigated to estimate the physical parameters of a single link robotic manipulator with flexible joint. The approach uses a weighted least-squares algorithm in the frequency domain. Knowing the structure of a continuous-time system, the identification method will only focus on the estimation of the physically-based system parameters using input and

S. Daniel-Berhe; Heinz Unbehauen

1997-01-01

182

Implementation of an offline chaos-based EEG encryption software

In the paper, we use Microsoft visual studio development kit and C# programming to implement a chaos-based electroencephalogram (EEG) encryption software. A chaos logic map, and initial value of the chaos logic map are used to generate level I chaos-based EEG encryption bit streams. A chaos logic map, initial value, a bifurcation parameter of the chaos logic map, and two

Chin-Feng Lin; Shun-Han Shih; Jin-De Zhu; Sang-Hung Lee

2012-01-01

183

The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (?y/?x) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks. PMID:25296836

Kondo, Yuuki; Urayama, Kenji; Kidowaki, Masatoshi; Mayumi, Koichi; Takigawa, Toshikazu; Ito, Kohzo

2014-10-01

184

NASA Astrophysics Data System (ADS)

The strain energy density function (F) of the polyrotaxane-based slide-ring (SR) gels with movable cross-links along the network strands is characterized by unequal biaxial stretching which can achieve various types of deformation. The SR gels as prepared without any post-preparation complication exhibit considerably smaller values of the ratio of the stresses (?y/?x) in the stretched (x) and constrained (y) directions in planar extension than classical chemical gels with heterogeneous and nearly homogeneous network structures do. This feature of the SR gels leads to the peculiar characteristic that the strain energy density function (F) has no explicit cross term of strains in different directions, which is in contrast to F with explicit strain cross terms for most chemical gels and elastomers. The biaxial stress-strain data of the SR gels are successfully described by F of the Gent model with only two parameters (small-strain shear modulus and a parameter representing ultimate elongation), which introduces the finite extensibility effect into the neo-Hookean model with no explicit cross term of strain. The biaxial data of the deswollen SR gels examined in previous study, which underwent a considerable reduction in volume from the preparation state, are also well described by the Gent model, which is in contrast to the case of the classical chemical gels that the stress-strain relations before and after large deswelling are not described by a common type of F due to a significant degree of collapse of the network strands in the deswollen state. These intriguing features of nonlinear elasticity of the SR gels originate from a novel function of the slidable cross-links that can maximize the arrangement entropy of cross-linked and non-cross-linked cyclic molecules in the deformed networks.

Kondo, Yuuki; Urayama, Kenji; Kidowaki, Masatoshi; Mayumi, Koichi; Takigawa, Toshikazu; Ito, Kohzo

2014-10-01

185

Random bit generation using polarization chaos from free-running laser diode

NASA Astrophysics Data System (ADS)

During the last five years, optical chaos-based random bit generators (RBGs) attracted a lot of attention and demonstrated impressive performances with bit rates up to hundreds of Gbps. However all the suggested schemes use external injection schemes (optical injection or feedback) to turn the lasers into chaos, hence strongly increasing setup complexity. On the other hand, we reported that a laser diode can generate a chaotic output without the need for external perturbation or forcing, hence unveiling a highly simplified way to generate an optical chaos at high frequency. However the low dimension and limited number of positive Lyapunov exponent casted doubts about its direct use for chaos-based applications. Here we make a proof-of-concept demonstration for a Random Bit Generator based on polarization chaos. We therefore suggest a highly simplified RBG scheme using only a free-running laser and small-bandwidth acquisition electronics and demonstrate convincing performances with bit rates up to 100 Gbps without unusual or complex post-processing methods. We link these performances to the double-scroll structure of the chaotic attractor rather than the bandwidth of the dynamics, hence bringing new light on the importance of chaos topology for chaos-based applications. In addition our scheme exhibit a strong potential as it enables a low-cost and/or integrated in parallel on-chip scheme.

Virte, Martin; Mercier, Emeric; Thienpont, Hugo; Panajotov, Krassimir; Sciamanna, Marc

2014-05-01

186

Chao Family Comprehensive Cancer Center

The University of California, Irvine (UCI) Cancer Center was established in 1989 as a university-based cancer center. In 1994, it became an NCI-designated cancer center, and it achieved comprehensive cancer center status in 1997. Soon after, it was renamed in honor of the Chao family as the Chao Family Comprehensive Cancer Center (CFCCC), operating fully integrated research, prevention, diagnostic, treatment, and rehabilitation programs.

187

Category:Quantum chaos Quantum Chaos emerged as a new field of physics from the

Category:Quantum chaos Quantum Chaos emerged as a new field of physics from the efforts in number theory, fractal and complex spectra, atomic and molecular physics, clusters and nuclei, quantum billiards and quantum chaos Categories: Chaos Physics Quantum Mechanics Dynamical Systems Category:Quantum

Shepelyansky, Dima

188

On nonlinear control design for autonomous chaotic systems of integer and fractional orders

In this paper, we address the problem of chaos control for autonomous nonlinear chaotic systems. We use the recursive “backstepping” method of nonlinear control design to derive the nonlinear controllers. The controller effect is to stabilize the output chaotic trajectory by driving it to the nearest equilibrium point in the basin of attraction. We study two nonlinear chaotic systems: an

Wajdi M. Ahmad; Ahmad M. Harb

2003-01-01

189

Spiral defect chaos in an advection-reaction-diffusion system.

This paper comprises numerical and theoretical studies of spatiotemporal patterns in advection-reaction-diffusion systems in which the chemical species interact with the hydrodynamic fluid. Due to the interplay between the two, we obtained the spiral defect chaos in the activator-inhibitor-type model. We formulated the generalized Swift-Hohenberg-type model for this system. Then the evolution of fractal boundaries due to the effect of the strong nonlinearity at the interface of the two chemical species is studied numerically. The purpose of the present paper is to point out that spiral defect chaos, observed in model equations of the extended Swift-Hohenberg equation for low Prandtl number convection, may actually be obtained also in certain advection-reaction-diffusion systems. PMID:25019864

Affan, H; Friedrich, R

2014-06-01

190

Intermittency and chaos in intracavity doubled lasers. II

NASA Astrophysics Data System (ADS)

We describe the nonlinear dynamics of intracavity doubled multimode lasers. Baer [J. Opt. Soc. Am. B 3, 1175 (1986)] observed irregular amplitude fluctuations in a multimode yttrium aluminum garnet laser with an intracavity potassium titanyl phosphate frequency-doubling crystal; we identify type-III intermittency as the route to chaos. Subsequently, Oka and Kubota [Opt. Lett. 13, 805 (1988)] demonstrated the stabilization of such a laser by the introduction of a quarter wave plate into the cavity. A generalized model of rate equations for this case is introduced. It is shown that a second route to chaos through a Hopf bifurcation, synchronization, and period-doubling sequence occurs on rotation of the quarter wave plate within the cavity. In addition, we predict that the laser output may be stable for particular lengths of the doubling crystal.

James, Glenn E.; Harrell, Evans M., II; Roy, Rajarshi

1990-03-01

191

Deterministic Chaos and Noise in Three In Vitro Hippocampal Models of Epilepsy

Deterministic Chaos and Noise in Three In Vitro Hippocampal Models of Epilepsy MARC W. SLUTZKY,1. UPOs of multiple periods were highly prevalent in experiments from all three epilepsy models: 73, Epilepsy, Nonlinear, Un- stable periodic orbit, Lyapunov exponent, Determinism, Potas- sium, GABA

Cvitanovc', Predrag

192

Developing Integrated Arts Curriculum in Hong Kong: Chaos Theory at Work?

ERIC Educational Resources Information Center

This article reports the development of integrated arts curriculum in two Hong Kong secondary schools over a 9-year period. Initial findings display a range of individual responses to educational change that are both non-predictable and non-linear. Chaos theory is used to explain these varied responses in terms of bifurcations. The findings of…

Wong, Marina

2013-01-01

193

October 19, 2010 13:7 papernonsmoothijbc International Journal of Bifurcation and Chaos

Â´ostoles, Madrid, Spain MIGUEL A.F. SANJUÂ´AN Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de FÂ´isica Universidad Rey Juan Carlos, TulipÂ´an s/n, 28933 MÂ´ostoles, Madrid, Spain Department of Mathematics, School diagrams and the basins of attraction elucidate the existence of new attractors into the system

Rey Juan Carlos, Universidad

194

QUADRATURE CHAOS SHIFT KEYING Zbigniew Galias and Gian Mario Maggio y

to the BPSK (binary phase shift keying) modulation scheme [1]. In BPSK one transmits a sin(#1;) function at the receiver. One of the modifications of BPSK is the QPSK (quadraÂ ture phase shift keying) scheme, whichQUADRATURE CHAOS SHIFT KEYING Zbigniew Galias #3; and Gian Mario Maggio y Institute for Nonlinear

Galias, Zbigniew

195

Strong and Weak Chaos in Networks of Semiconductor Lasers with Time-delayed Couplings

Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed self-feedback or for small networks. We examine the dependence on the pump current and consider the question whether strong and weak chaos can be identified from the shape of the intensity trace, the auto-correlations and the external cavity modes. The concept of the sub-Lyapunov exponent $\\lambda_0$ is generalized to the case of two time-scale separated delays in the system. We give the first experimental evidence of strong and weak chaos in a network of lasers which supports the sequence 'weak to strong to weak chaos' upon monotonically increasing the coupling strength. Finally, we discuss strong and weak chaos for networks with several distinct sub-Lyapunov exponents and comment on the dependence of the sub-Lyapunov exponent on the number of a laser's inputs in a network.

Sven Heiligenthal; Thomas Jüngling; Otti D'Huys; Diana A. Arroyo-Almanza; Miguel C. Soriano; Ingo Fischer; Ido Kanter; Wolfgang Kinzel

2012-10-05

196

Strong and weak chaos in networks of semiconductor lasers with time-delayed couplings.

Nonlinear networks with time-delayed couplings may show strong and weak chaos, depending on the scaling of their Lyapunov exponent with the delay time. We study strong and weak chaos for semiconductor lasers, either with time-delayed self-feedback or for small networks. We examine the dependence on the pump current and consider the question of whether strong and weak chaos can be identified from the shape of the intensity trace, the autocorrelations, and the external cavity modes. The concept of the sub-Lyapunov exponent ?(0) is generalized to the case of two time-scale-separated delays in the system. We give experimental evidence of strong and weak chaos in a network of lasers, which supports the sequence of weak to strong to weak chaos upon monotonically increasing the coupling strength. Finally, we discuss strong and weak chaos for networks with several distinct sub-Lyapunov exponents and comment on the dependence of the sub-Lyapunov exponent on the number of a laser's inputs in a network. PMID:23944533

Heiligenthal, Sven; Jüngling, Thomas; D'Huys, Otti; Arroyo-Almanza, Diana A; Soriano, Miguel C; Fischer, Ingo; Kanter, Ido; Kinzel, Wolfgang

2013-07-01

197

Cognitive aspects of chaos in random networks.

A special case of deterministic chaos that is independent of the architecture of the connections has been observed in a computer model of a purely excitatory neuronal network. Chaos onsets when the level of connectivity is critically low. The results indicate a typical period-doubling route to chaos as the connectivity decreases. A cognitive interpretation of such type of chaos, based on information theory and phase-transitions, is proposed. PMID:22196110

Aiello, Gaetano L

2012-01-01

198

Magnetospheric Dynamics and Chaos Theory

The results of this study were announced and published in Greek in the Fifth Panhellenic Conference Proceedings of the Hellenic Physical Society. It is the sequel of a previous study (Pavlos, 1988), in which it was introduced the hypothesis of magnetospheric chaos for the interpretation of magnetic substorms. In this study it is described the possibility of tracing magnetospheric chaos through Grassberger and Procassia method for the estimation of correlation dimension. In addition, it is proposed, the estimation of chaoticity through the computation of Lyapunov exponents. This study and its previous one constitute the first studies ever concerning the hypothesis of magnetospheric chaos for the interpretation and understanding the magnetospheric substorms. A series of publications of G.P.Pavlos followed the initial two studies in scientific journals and conference proceedings (www.gpavlos.gr). The publication of this study in English version has a historical importance and interest regarding the history of evolution of the concept of magnetospheric chaos. For an extended discussion concerning magnetospheric chaos, see, Pavlos 2012 ArXiv.

G. P. Pavlos

2012-03-26

199

Nonlinear analysis and prediction of pulsatile hormone secretion

NASA Astrophysics Data System (ADS)

Pulsatile hormone secretion is observed in almost every hormonal system. The frequency of episodic hormone release ranges from approximately 10 to 100 pulses in 24 hours. This temporal mode of secretion is an important feature of intercellular information transfer in addition to a dose-response dependent regulation. It has been demonstrated in a number of experiments that changes in the temporal pattern of pulsatile hormone secretion specifically regulate cellular and organ function and structure. Recent evidence links osteoporosis, a disease characterized by loss of bone mass and structure, to changes in the dynamics of pulsatile parathyroid hormone (PTH) secretion. In our study we applied nonlinear and linear time series prediction to characterize the secretory dynamics of PTH in both healthy human subjects and patients with osteoporosis. Osteoporotic patients appear to lack periods of high predictability found in normal humans. In contrast to patients with osteoporosis patients with hyperparathyroidism, a condition which despite sometimes reduced bone mass has a preserved bone architecture, show periods of high predictability of PTH secretion. Using stochastic surrogate data sets which match certain statistical properties of the original time series significant nonlinear determinism could be found for the PTH time series of a group of healthy subjects. Using classical nonlinear analytical techniques we could demonstrate that the irregular pattern of pulsatile PTH secretion in healthy men exhibits characteristics of deterministic chaos. Pulsatile secretion of PTH in healthy subjects seems to be a first example of nonlinear determinism in an apparently irregular hormonal rhythm in human physiology.

Prank, Klaus; Kloppstech, Mirko; Nowlan, Steven J.; Harms, Heio M.; Brabant, Georg; Hesch, Rolf-Dieter; Sejnowski, Terrence J.

1996-06-01

200

NASA Astrophysics Data System (ADS)

In this study the existence of chaotic oscillations in signals from vortex induced vibrations is investigated using some experimental data of flexible risers. VIV is traditionally known as a periodic phenomenon for which the oscillations are mainly at a fundamental frequency of oscillations. As observed recently, in many VIV signals, there is a second peak at three times the fundamental frequency, which represents the existence of a third harmonic oscillation. This view is based on analyzing a statistically stationary region of experimental VIV signals. The original non-filtered signals, however, do not show a statistically stationary behavior in the entire period of oscillations. Practically, the major part of the signal illustrates non-stationary behavior. Here, we do not limit our analysis to the statistically stationary regions; instead, we use the entire experimental signal. The time histories, PSD and phase plane plots, and Poincaré maps of analyzed signals show cases where the signal is (i) mainly periodic/quasiperiodic or (ii) periodic/quasiperiodic with bursts of chaos or (iii) entirely chaotic.

Modarres-Sadeghi, Yahya; Triantafyllou, Michael

2008-11-01

201

NSDL National Science Digital Library

For the third time in the last 14 months, Russian President Boris Yeltsin deposed his Prime Minister and Cabinet, intensifying the political chaos in a country beleaguered by economic insolvency, administrative corruption, and governmental mismanagement. The dismissals handed down on Wednesday, which included the popular PM Yevgeny M. Primakov, occurred the day before impeachment proceedings were to begin against Yeltsin in the lower house of the Russian parliament, the communist-led State Duma. Russia's first democratically elected President faces five impeachment charges, including initiating the collapse of the USSR, ordering an attack on parliament in 1993, destroying the armed forces, punishing the Russian people through harsh economic policies, and waging an illegal war against the secessionist Chechnya in 1994 through 1996. Political analysts forecast that only the last charge has a chance of passing the necessary two-thirds vote, slated for Saturday, in the 450-seat State Duma. Even if charged, it is unlikely that Yeltsin will be removed from office because the charge must also be approved by the Constitutional Court, the Supreme Court, and the Council of Federation, the parliament's upper house. However, the political imbroglio will paralyze the Russian government for months to come, and has already disrupted Russian diplomatic efforts to mediate a resolution to the crisis in Yugoslavia. The sites listed provide insight into this current Russian political crisis.

Osmond, Andrew.

202

Deterministic chaos in government debt dynamics with mechanistic primary balance rules

This paper shows that with mechanistic primary budget rules and with some simple assumptions on interest rates the well-known debt dynamics equation transforms into the infamous logistic map. The logistic map has very peculiar and rich nonlinear behaviour and it can exhibit deterministic chaos with certain parameter regimes. Deterministic chaos means the existence of the butterfly effect which in turn is qualitatively very important, as it shows that even deterministic budget rules produce unpredictable behaviour of the debt-to-GDP ratio, as chaotic systems are extremely sensitive to initial conditions.

Jussi Ilmari Lindgren

2011-09-05

203

Deterministic chaos in government debt dynamics with mechanistic primary balance rules

This paper shows that with mechanistic primary budget rules and with some simple assumptions on interest rates the well-known debt dynamics equation transforms into the infamous logistic map. The logistic map has very peculiar and rich nonlinear behaviour and it can exhibit deterministic chaos with certain parameter regimes. Deterministic chaos means the existence of the butterfly effect which in turn is qualitatively very important, as it shows that even deterministic budget rules produce unpredictable behaviour of the debt-to-GDP ratio, as chaotic systems are extremely sensitive to initial conditions.

Lindgren, Jussi Ilmari

2011-01-01

204

Low-order chaos in sympathetic nerve activity causes 1/f fluctuation of heartbeat intervals

NASA Astrophysics Data System (ADS)

The mechanism of 1/f scaling of heartbeat intervals remains unknown. We recorded heartbeat intervals, sympathetic nerve activity, and blood pressure in conscious rats with normal or high blood pressure. Using nonlinear analyses, we demonstrate that the dynamics of this system of 3 variables is low-order chaos, and that sympathetic nerve activity leads to heartbeat interval and blood pressure changes. It is suggested that 1/f scaling of heartbeat intervals results from the low-order chaos of these variables and that impaired regulation of blood pressure by sympathetic nerve activity is likely to cause experimentally observable steeper scaling of heartbeat intervals in hypertensive (high blood pressure) rats.

Osaka, Motohisa; Kumagai, Hiroo; Sakata, Katsufumi; Onami, Toshiko; Chon, Ki H.; Watanabe, Mari A.; Saruta, Takao

2004-04-01

205

NASA Astrophysics Data System (ADS)

The collision problem of a chaos-based hash function with both modification detection and localization capability is investigated [Xiao D, Shih FY, Liao XF. A chaos-based hash function with both modification detection and localization capabilities. Commun Nonlinear Sci Numer Simulat 2010;15(9):2254-61]. The simulation gives the same detection and localization hash values for distinct messages. The expense of the birthday attack on the hash function is far less than expected. The certain symmetries of message distribution may result in the same detection hash value for distinct messages.

Wang, Shihong; Li, Da; Zhou, Hu

2012-02-01

206

Quantum and nonlinear optics research

NASA Astrophysics Data System (ADS)

Since the research on this AFOSR grant started on March 1, 1990, a number of new results were obtained by this principal investigator and his group in the field of nonlinear optics and quantum electronics. The research progressed basically in these directions: Pilot theoretical research on X-ray nonlinear optics, including resonant saturation related effects in plasmas (nonlinear absorption and nonlinear refractive index), and proposals for X-ray third harmonics generation, X-ray laser with noncoherent pumping, and X-ray four-wave mixing; Experimental discovery and experimental and theoretical research on dark spatial solitons; Theoretical investigation of previously discovered by this PI and his group dispersion related multimode amplification, instabilities, oscillations and chaos in nonlinear counterpropagating waves; Theoretical research on the fundamental problem of gradient-field-induced second-order nonlinear optical processing vacuum due to the photon-photon scattering of intense laser radiation in a dc magnetic field.

Kaplan, Alexander E.

1994-06-01

207

Bistability and chaos at low levels of quanta

NASA Astrophysics Data System (ADS)

We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose, we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to the dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in the oscillatory mode are investigated in the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincaré section. Considering bistability at a low limit of quanta, we analyze the minimal level of excitation numbers at which the bistable regime of the system is displayed. We also discuss the formation of an oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of a few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by a train of Gaussian pulses. We establish the border of quantum-classical correspondence for chaotic regimes in the case of strong nonlinearities.

Gevorgyan, T. V.; Shahinyan, A. R.; Chew, Lock Yue; Kryuchkyan, G. Yu.

2013-08-01

208

Predicting chaos in memristive oscillator via harmonic balance method

NASA Astrophysics Data System (ADS)

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.

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

2012-12-01

209

Hamiltonian chaos in a coupled BEC-optomechanical-cavity system

We present a theoretical study of a hybrid optomechanical system consisting of a Bose-Einstein condensate (BEC) trapped inside a single-mode optical cavity with a moving end mirror. The intracavity light field has a dual role: it excites a momentum side mode of the condensate, and acts as a nonlinear spring that couples the vibrating mirror to that collective density excitation. We present the dynamics in a regime where the intracavity optical field, the mirror, and the side-mode excitation all display bistable behavior. In this regime we find that the dynamics of the system exhibits Hamiltonian chaos for appropriate initial conditions.

Zhang, K. [State Key Laboratory of Precision Spectroscopy, Department of Physics, East China Normal University, Shanghai 200062 (China); Chen, W.; Bhattacharya, M.; Meystre, P. [B2 Institute, Department of Physics and College of Optical Sciences, University of Arizona, Tucson, Arizona 85721 (United States)

2010-01-15

210

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

A new computational technique based on the symbolic description utilizing kneading invariants is proposed and verified for explorations of dynamical and parametric chaos in a few exemplary systems with the Lorenz attractor. The technique allows for uncovering the stunning complexity and universality of bi-parametric structures and detect their organizing centers - codimension-two T-points and separating saddles in the kneading-based scans of the iconic Lorenz equation from hydrodynamics, a normal model from mathematics, and a laser model from nonlinear optics.

Roberto Barrio; Andrey Shilnikov; Leonid Shilnikov

2012-04-15

211

Exploration of Order in Chaos with Replica Exchange Monte Carlo

A method for exploring unstable structures generated by nonlinear dynamical systems is introduced. It is based on the sampling of initial conditions and parameters by Replica Exchange Monte Carlo (REM), and efficient both for the search of rare initial conditions and for the combined search of rare initial conditions and parameters. Examples discussed here include the sampling of unstable periodic orbits in chaos and search for the stable manifold of unstable fixed points, as well as construction of the global bifurcation diagram of a map.

Tatsuo Yanagita; Yukito Iba

2008-11-18

212

Urban chaos and replacement dynamics in nature and society

NASA Astrophysics Data System (ADS)

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.

Chen, Yanguang

2014-11-01

213

Chaos control in passive walking dynamics of a compass-gait model

NASA Astrophysics Data System (ADS)

The compass-gait walker is a two-degree-of-freedom biped that can walk passively and steadily down an incline without any actuation. The mathematical model of the walking dynamics is represented by an impulsive hybrid nonlinear model. It is capable of displaying cyclic motions and chaos. In this paper, we propose a new approach to controlling chaos cropped up from the passive dynamic walking of the compass-gait model. The proposed technique is to linearize the nonlinear model around a desired passive hybrid limit cycle. Then, we show that the nonlinear model is transformed to an impulsive hybrid linear model with a controlled jump. Basing on the linearized model, we derive an analytical expression of a constrained controlled Poincaré map. We present a method for the numerical simulation of this constrained map where bifurcation diagrams are plotted. Relying on these diagrams, we show that the linear model is fairly close to the nonlinear one. Using the linearized controlled Poincaré map, we design a state feedback controller in order to stabilize the fixed point of the Poincaré map. We show that this controller is very efficient for the control of chaos for the original nonlinear model.

Gritli, Hassène; Khraief, Nahla; Belghith, Safya

2013-08-01

214

Nonlinear modeling and bifurcations in the boost converter

The occurrence of nonlinear phenomena like subharmonics and chaos in power electronic circuits has been reported recently. In this paper, the authors investigate these phenomena in the current-mode-controlled boost power converter. A nonlinear model in the form of a mapping from one point of observation to the next has been derived. The map has a closed form even when the

Soumitro Banerjee; Krishnendu Chakrabarty

1998-01-01

215

Gordon Research Conference: Classical Mechanics and Nonlinear Dynmaics

NSDL National Science Digital Library

This conference will bring together teachers of classical mechanics and nonlinear dynamics, forefront researchers in these areas, and physics education researchers. The goal is to identify ways to effectively teach relevant lecture, laboratory, and computational courses in classical mechanics and nonlinear dynamics (including fractals and classical chaos), primarily at the undergraduate level.

2003-11-26

216

Chaotic systems, irregular functions, and nonlinear time series

With the advent of the studies of fractals, chaos, and non-linear dynamical processes by Mandelbrot, Falconer, Ruelle, and others, many of these results suggested to the researchers concerned with the mathematical modeling of non-linear physical behavior that there thus existed analytical bridges between the macroscopic and the microscopic world in the many scientific disciplines of particular concern. Of particular interest

Robert C. McCarty

1993-01-01

217

Chaos Rules! Robert L. Devaney

Chaos Rules! Robert L. Devaney #3; September 16, 2003 #3; Please address all correspondence to Robert L. Devaney, Department of Mathematics, Boston University, Boston MA 02215, or email bob@bu.edu. 1 of this #12;gure are all bounded by the well known Koch snow ake fractal! Figure 2: The Sierpinski hexagon

Devaney, Robert L.

218

Schematic of a simple nonlinear time-delay system with feedback gain and time delay . Time-delayed feedback of such a result is the broadband chaos we observe in a particular nonlinear time-delayed feedback system-dimensional chaotic solutions. There- fore, systems with sufficiently long time-delayed feedback can often

Illing, Lucas

219

Nonlinear dynamics in cardiac conduction

NASA Technical Reports Server (NTRS)

Electrical conduction in the heart shows many phenomena familiar from nonlinear dynamics. Among these phenomena are multiple basins of attraction, phase locking, and perhaps period-doubling bifurcations and chaos. We describe a simple cellular-automation model of electrical conduction which simulates normal conduction patterns in the heart as well as a wide range of disturbances of heart rhythm. In addition, we review the application of percolation theory to the analysis of the development of complex, self-sustaining conduction patterns.

Kaplan, D. T.; Smith, J. M.; Saxberg, B. E.; Cohen, R. J.

1988-01-01

220

The dangers of rounding errors for simulations and analysis of nonlinear circuits and systems --

--nonlinear system, chaos, interval analysis, Chua's circuit, HÂ´enon map. I. INTRODUCTION Numerical simulations play1 The dangers of rounding errors for simulations and analysis of nonlinear circuits and systems by nu- merical simulations of nonlinear systems may be unreliable. It is however possible to carry out

Galias, Zbigniew

221

Science of Chaos or Chaos in Science? \\Lambda Physique Th'eorique, UCL,

, no doubt. But illuminating, nevertheless. Alvin Toffler (preface to [96]). Popularization of science seemsScience of Chaos or Chaos in Science? \\Lambda J.Bricmont Physique Th'eorique, UCL, BÂ1348 LouvainÂlaÂNeuve, Belgium Abstract I try to clarify several confusions in the popular literature concerning chaos

Sokal, Alan

222

Does chaos assist localization or delocalization?

NASA Astrophysics Data System (ADS)

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.

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

2014-12-01

223

Europa: Tidal heating of upwelling thermal plumes and the origin of lenticulae and chaos melting

Tidal heating models are linked to thermal convection models for ice having strongly temperature dependent viscosity. In the range of ice viscosity inferred from laboratory experiments, tidal forces will heat up rising diapirs on Europa. Partial melt produced in the rising diapirs is predicted to create disruption of near-surface materials and formation of lenticulae and chaos, even if the average

Christophe Sotin; James W. Head; Gabriel Tobie

2002-01-01

224

Haotic, Fractal, and Nonlinear Signal Processing. Proceedings

These proceedings include papers presented at the Third Technical Conference on Nonlinear Dynamics and Full{minus}Spectrum Processing held in Mystic, Connecticut. The Conference focus was on the latest advances in chaotic, fractal and nonlinear signal processing methods. Topics of discussion covered in the Conference include: mathematical frontiers; predictability and control of chaos, detection and classification with applications in acoustics; advanced applied signal processing methods(linear and nonlinear); stochastic resonance; machinery diagnostics; turbulence; geophysics; medicine; and recent novel approaches to modeling nonlinear systems. There were 58 papers in the conference and all have been abstracted for the Energy Science and Technology database. (AIP)

Katz, R.A. [Naval Undersea Warfare Center, Newport, RI (United States)

1996-10-01

225

Subharmonics, Chaos, and Beyond

NASA Technical Reports Server (NTRS)

While studying finite amplitude ultrasonic wave resonance in a one dimensional liquid-filled cavity, which is formed by a narrow band transducer and a plane reflector, subharmonics of the driver's frequency were observed in addition to the expected harmonic structure. Subsequently it was realized that the system was one of the many examples where parametric resonance takes place and in which the observed subharmonics are parametrically generated. Parametric resonance occurs in any physical system which has a periodically modulated natural frequency. The generation mechanism also requires a sufficiently high threshold value of the driving amplitude so that the system becomes increasingly nonlinear in response. The nonlinear features were recently investigated and are the objective of this presentation. An ultrasonic interferometer with optical precision was built. The transducers were compressional undamped quartz and Lithium Niobate crystals ranging from 1-10 Mhz, and driven by a high power amplifier. Both an optical diffraction system and a receive transducer attached to an aligned reflector with lapped flat and parallel surfaces were used to observe the generated frequency components in the cavity.

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

2011-01-01

226

Parameter Uncertainties on the Predictability of Periodicity and Chaos

Nonlinear dynamical systems, ranging from insect populations to lasers and chemical reactions, might exhibit sensitivity to small perturbations in their control parameters, resulting in uncertainties on the predictability of tunning parameters that lead these systems to either a chaotic or a periodic behavior. By quantifying such uncertainties in four different classes of nonlinear systems, we show that this sensitivity is to be expected because the boundary between the sets of parameters leading to chaos and to periodicity is fractal. Moreover, the dimension of this fractal boundary was shown to be roughly the same for these classes of systems. Using an heuristic model for the way periodic windows appear in parameter spaces, we provide an explanation for the universal character of this fractal boundary.

E. S. Medeiros; I. L. Caldas; M. S. Baptista

2014-02-27

227

Chaos and Statistical Mechanics in the Hamiltonian Mean Field Model

We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of $N$ fully-coupled rotators which shows a second order phase transition. The canonical thermodynamical solution is briefly recalled and its predictions are tested numerically at finite $N$. The Vlasov stationary solution is shown to give the same consistency equation of the canonical solution and its predictions for rotator angle and momenta distribution functions agree very well with numerical simulations. A link is established between the behavior of the maximal Lyapunov exponent and that of thermodynamical fluctuations, expressed by kinetic energy fluctuations or specific heat. The extensivity of chaos in the $N \\to \\infty$ limit is tested through the scaling properties of Lyapunov spectra and of the Kolmogorov-Sinai entropy. Chaotic dynamics provides the mixing property in phase space necessary for obtaining equilibration; however, the relaxation time to equilibrium grows with $N$, at least near the critical point. Our results constitute an interesting bridge between Hamiltonian chaos in many degrees of freedom systems and equilibrium thermodynamics.

Vito Latora; Andrea Rapisarda; Stefano Ruffo

1998-03-13

228

Ray chaos and ray clustering in an ocean waveguide

NASA Astrophysics Data System (ADS)

We consider ray propagation in a waveguide with a designed sound-speed profile perturbed by a range-dependent perturbation caused by internal waves in deep ocean environments. The Hamiltonian formalism in terms of the action and angle variables is applied to study nonlinear ray dynamics with two sound-channel models and three perturbation models: a single-mode perturbation, a randomlike sound-speed fluctuations, and a mixed perturbation. In the integrable limit without any perturbation, we derive analytical expressions for ray arrival times and timefronts at a given range, the main measurable characteristics in field experiments in the ocean. In the presence of a single-mode perturbation, ray chaos is shown to arise as a result of overlapping nonlinear ray-medium resonances. Poincaré maps, plots of variations of the action per ray cycle length, and plots with rays escaping the channel reveal inhomogeneous structure of the underlying phase space with remarkable zones of stability where stable coherent ray clusters may be formed. We demonstrate the possibility of determining the wavelength of the perturbation mode from the arrival time distribution under conditions of ray chaos. It is surprising that coherent ray clusters, consisting of fans of rays which propagate over long ranges with close dynamical characteristics, can survive under a randomlike multiplicative perturbation modelling sound-speed fluctuations caused by a wide spectrum of internal waves.

Makarov, D. V.; Uleysky, M. Yu.; Prants, S. V.

2004-03-01

229

of a large class of continuous-time chaotic systems in the chaos research literature. Simulation results studied in communications research [Cuomo et al., 1993; Dedieu et al., 1993; Chua et al., 1996; Dedieu of Chua's circuits, can be transformed into a class of nonlinear systems in the so-called nonautonomous

Ge, Shuzhi Sam

230

In this short report the first attempt of a new approach to the still mysterious phenomenon of the life, and its peak, the human being, is presented from the view point of the natural sciences, i.e. of the physics in the broad sense of the word. This idea has come to my mind about 10 years ago when doing a completely different problem I suddenly have noticed to my surprise (see [1], p.20) a wonderful relation between a very complicated human (physical) conception {\\it creation} and the relatively simple mathematical theorem due to Alekseev - Brudno (see for instance [2]) in an almost unknown for physicists field of the so-called {\\it symbolic dynamics} and {\\it algorithmic chaos}, which one I have immediately christen {\\it the creating chaos}.

Boris Chirikov

2005-03-09

231

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

NASA Astrophysics Data System (ADS)

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.

Mackey, Peter Francis

1995-01-01

232

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 modulation 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.

Ogawa, T.

1988-06-01

233

Introduction to chaos and diffusion

This contribution is relative to the opening lectures of the ISSAOS 2001 summer school and it has the aim to provide the reader with some concepts and techniques concerning chaotic dynamics and transport processes in fluids. Our intention is twofold: to give a self-consistent introduction to chaos and diffusion, and to offer a guide for the reading of the rest of this volume.

G. Boffetta; G. Lacorata; A. Vulpiani

2004-11-10

234

Chaos in Geophysical Fluids I. General Introduction

NASA Astrophysics Data System (ADS)

Irregular buoyancy-driven flows occur in the atmospheres and fluid interiors of the Earth and other planets, and of the Sun and other stars, where they influence and often control the transfer of heat. Their presence is manifest in or implied by a wide variety of observed phenomena, including external magnetic fields generated by self-exciting magnetohydrodynamic (MHD) dynamo action. Based on the laws of classical mechanics, thermodynamics and, in the case of electrically conducting fluids, electrodynamics, the governing mathematical equations are well known, but they are generally intractable owing to their essential nonlinearity. Computers play a key role in modern theoretical research in geophysical and astrophysical fluid dynamics, where ideas based on chaos theory are being applied in the analysis of models and the assessment of predictability. The aim of this paper is to provide a largely qualitative survey for non-specialists. The survey comprises two parts, namely a general introduction (Part I) followed by a discussion of two representative areas of research, both concerned with phenomena attributable to symmetry-breaking bifurcations caused by gyroscopic (Coriolis) forces (Part II), namely (a) large-scale waves and eddies in the atmospheres of the Earth, Jupiter and other planets (where, exceptionally, laboratory experiments have been influential), and (b) MHD dynamos. Various combinations of Faraday disc dynamos have been studied numerically as low-dimensional nonlinear electromechanical analogues of MHD dynamos, particularly in efforts to elucidate the complex time series of geomagnetic polarity reversals over geological time. The ability of the intensively studied Rikitake coupled disc dynamo system to behave chaotically appears to be a consequence of the neglect of mechanical friction, the inclusion of which renders the system structurally unstable.

Hide, Raymond

1994-09-01

235

NASA Astrophysics Data System (ADS)

This paper presents the novel approach to evaluate the effects of different motor activation tasks of the human electroencephalogram (EEG). The applications of chaos and fractal properties that are the most important tools in nonlinear analysis are been presented for four tasks of EEG during the real and imaginary motor movement. Three subjects, aged 23-30 years, participated in the experiment. Correlation dimension (D2), Lyapunov spectrum (?i), and Lyapunov dimension (DL) are been estimated to characterize the movement related EEG signals. Experimental results show that these nonlinear measures are good discriminators of EEG signals. There are significant differences in all conditions of subjective task. The fractal dimension appeared to be higher in movement conditions compared to the baseline condition. It is concluded that chaos and fractal analysis could be powerful methods in investigating brain activities during motor movements.

Soe, Ni Ni; Nakagawa, Masahiro

2008-04-01

236

Chaos in Derrida and Student Texts.

ERIC Educational Resources Information Center

Students must learn to maintain authority over their texts as they attempt to deal with the chaos they encounter when they approach a writing task. The authority with which Jacques Derrida deals with chaos in his essay, "...That Dangerous Supplement," suggests some strategies. In his essay, Derrida seems to be able to move the reader back and…

Corbett, Janice M.

237

Can Feedback Traders Rock the Markets? A Logistic Tale of Persistence and Chaos

Can Feedback Traders Rock the Markets? A Logistic Tale of Persistence and Chaos Demosthenes N. Tambakis? Pembroke College, Cambridge and CERF March 24, 2006 Abstract This paper introduces a nonlinear feedback trading model at high frequency. All... ”, American Math- ematical Monthly 82: 985-92. [24] Longstaff, F. 2004. “The flight-to-liquidity premium in U.S. Treasury bond prices”, Journal of Business 77: 511-26. [25] Nelson, D. 1991. “Conditional heteroscedasticity in stock returns: a new approach...

Tambakis, Demosthenes N

238

Controlling chaos in a fluid flow past a movable cylinder Juan C. Vallejo a

Controlling chaos in a fluid flow past a movable cylinder Juan C. Vallejo a , Inees P. Mari Carlos, Tulipaan s/n, 28933 Moostoles, Madrid, Spain b Nonlinear Dynamics, Institute of Physics for a passive advected dye particle in the xÂy plane have the form: uÃ°x; y; tÃ? Â¼ dxÃ°tÃ? dt Â¼ owÃ°x; y; tÃ? oy vÃ°x

Rey Juan Carlos, Universidad

239

Chaos control and duration time of a class of uncertain chaotic systems

NASA Astrophysics Data System (ADS)

This Letter presents a robust control scheme for a class of uncertain chaotic systems in the canonical form, with unknown nonlinearities. To cope with the uncertainties, we combine Lyapunov methodology with observer design. The proposed strategy comprises an exponential linearizing feedback and an uncertainty estimator. The developed control scheme allows chaos suppression. The advantage of this method over the existing results is that the control time is explicitly computed. Simulations studies are conducted to verify the effectiveness of the scheme.

Bowong, Samuel; Moukam Kakmeni, F. M.

2003-09-01

240

Anomalous scenario of the dynamic chaos onset in multimode laser diodes

Anomalous transition to the regime of dynamic chaos in a multimode quantum-well heterolaser (? = 635 nm) is possible as a\\u000a result of an injection-current-induced change in the gain. A stable multimode regime (featuring more than ten longitudinal\\u000a modes) is established near the lasing threshold under conditions of weak nonlinear coupling. As the injection current increases,\\u000a the competition of modes

G. G. Akchurin; A. G. Akchurin

2005-01-01

241

Chaos control for the Boost converter under current-mode control

Chaotic phenomena of the Boost converter under current-mode control are studied further. According to the reference current Iref which works as a bifurcation parameter, the bifurcation map, the 3-period window diagram and the strange attractors of the intermittent chaos are obtained by applying the discrete map. By employing a nonlinear feedback controller which is a piecewise-quadratic function in the form

Lihong He; Meimei Jia; Zhongwen Dong; Jianhua Wu

2010-01-01

242

Temperature chaos and quenched heterogeneities.

We present a treatable generalization of the Sherrington-Kirkpatrick (SK) model which introduces correlations in the elements of the coupling matrix through multiplicative disorder on the single variables and investigate the consequences on the phase diagram. We define a generalized qEA parameter and test the structural stability of the SK results in this correlated case evaluating the de Almeida-Thouless line of the model. As a main result we demonstrate the increase of temperature chaos effects due to heterogeneities. PMID:24730812

Barucca, Paolo; Parisi, Giorgio; Rizzo, Tommaso

2014-03-01

243

Decoherence, determinism and chaos revisited

We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes` contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools.

Noyes, H.P.

1994-11-15

244

Quantum chaos on discrete graphs

Adapting a method developed for the study of quantum chaos on {\\it quantum (metric)} graphs \\cite {KS}, spectral $\\zeta$ functions and trace formulae for {\\it discrete} Laplacians on graphs are derived. This is achieved by expressing the spectral secular equation in terms of the periodic orbits of the graph, and obtaining functions which belongs to the class of $\\zeta$ functions proposed originally by Ihara \\cite {Ihara}, and expanded by subsequent authors \\cite {Stark,Sunada}. Finally, a model of "classical dynamics" on the discrete graph is proposed. It is analogous to the corresponding classical dynamics derived for quantum graphs \\cite {KS}.

Uzy Smilansky

2007-04-26

245

The Quantum Emergence of Chaos

The dynamical status of isolated quantum systems, partly due to the linearity of the Schrodinger equation is unclear: Conventional measures fail to detect chaos in such systems. However, when quantum systems are subjected to observation -- as all experimental systems must be -- their dynamics is no longer linear and, in the appropriate limit(s), the evolution of expectation values, conditioned on the observations, closely approaches the behavior of classical trajectories. Here we show, by analyzing a specific example, that microscopic continuously observed quantum systems, even far from any classical limit, can have a positive Lyapunov exponent, and thus be truly chaotic.

Salman Habib; Kurt Jacobs; Kosuke Shizume

2004-12-21

246

Persistent Chaos in High Dimensions

An extensive statistical survey of universal approximators shows that as the dimension of a typical dissipative dynamical system is increased, the number of positive Lyapunov exponents increases monotonically and the number of parameter windows with periodic behavior decreases. A subset of parameter space remains in which topological change induced by small parameter variation is very common. It turns out, however, that if the system's dimension is sufficiently high, this inevitable, and expected, topological change is never catastrophic, in the sense chaotic behavior is preserved. One concludes that deterministic chaos is persistent in high dimensions.

D. J. Albers; J. C. Sprott; J. P. Crutchfield

2005-04-19

247

Nonlinear lattice waves in heterogeneous media

We review recent progress in the dynamics of nonlinear lattice waves in heterogeneous media, which enforce complete wave localization in the linear wave equation limit, especially Anderson localization for random potentials, and Aubry-Andre localization for quasiperiodic potentials. Additional nonlinear terms in the wave equations can either preserve the phase-coherent localization of waves, or destroy it through nonintegrability and deterministic chaos. Spreading wave packets are observed to show universal features in their dynamics which are related to properties of nonlinear diffusion equations.

T. V. Laptyeva; M. V. Ivanchenko; S. Flach

2014-07-05

248

We report on very recent achievements in optical chaos communications. Electro-optic phase modulation principles have been used to design a new chaos generator based on nonlinear delay dynamics. A multiple delay (both short and long) architecture allowed for an enhanced chaotic complexity, as well as a more accurate synchronization capability, over the full bandwidth of a typical 10 Gb\\/s binary

Laurent Larger; Roman Lavrov; Maxime Jacquot

2010-01-01

249

A three-variable model of deterministic chaos in the Belousov-Zhabotinsky reaction

NASA Astrophysics Data System (ADS)

CHAOS is exhibited by a wide variety of systems governed by nonlinear dynamic laws1-3. Its most striking feature is an apparent randomness which seems to contradict its deterministic origin. The best-studied chaotic chemical system is the Belousov-Zhabotinsky (BZ) reaction4-6 in a continuous-flow stirred-tank reactor (CSTR). Here we present a simple mechanism for the BZ reaction which allows us to develop a description in terms of a set of differential equations containing only three variables, the minimum number required to generate chaos in a continuous (non-iterative) dynamical system2. In common with experiments, our model shows aperiodicity and transitions between periodicity and chaos near bifurcations between oscillatory and steady-state behaviour, which occur at both low and high CSTR flow rates. While remaining closely related to a real chaotic chemical system, our model is sufficiently simple to allow detailed mathematical analysis. It also reproduces many other features of the BZ reaction better than does the simple Oregonator7 (which cannot produce chaos).

Györgyi, László; Field, Richard J.

1992-02-01

250

Four dimensional chaos and intermittency in a mesoscopic model of the electroencephalogram

NASA Astrophysics Data System (ADS)

The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy.

Dafilis, Mathew P.; Frascoli, Federico; Cadusch, Peter J.; Liley, David T. J.

2013-06-01

251

Chaos detection in the space debris population.

NASA Astrophysics Data System (ADS)

Semi-analytical propagations, on the basis of long term analysis of artificial satellite trajectories, are a very efficient tool to define storage orbits, and to characterize the main properties within a given region. In particular the altitude of the perigee or the lifetime can be estimated. Dedicated s/w such as STELA (Semi-analytical Tool for End of Life Analysis), developed in the frame of the French Space Operations Act, offer these kinds of capabilities. With a very large integration step size, it is then possible to get time series of the equinoctial elements over long period of time (typically, from 20 to 200yr), after only a few seconds of CPU. In case of resonant trajectories, due to the third body potential or to the Earth gravity field, getting an accurate lifetime estimation is not that obvious: it is likely to be much more time consuming since a Monte Carlo analysis may be required. The last version of the STELA s/w offers as well the capability to derive some quantities linked to the chaoticity of a trajectory, or a family of trajectories, linked to the resonances. In particular the FLI (Fast Lyapunov Indicator) and the maximum exponent of Lyapunov are now implemented into the s/w. We show in this presentation some examples that are obtained from the propagation of the transition matrix, simultaneously with the equations of motion. We derive some general properties about the detection of chaos in the space debris population by propagating the whole TLE catalogue.

Deleflie, Florent; Hautesserres, Denis; Daquin, Jérôme; Morand, Vincent; Pretot, Nastassia; Fouchard, Marc

252

Extended Chaos Theory and Multiparticle Production

First, using the method of the soliton-solution, the fermion probability density equation, which corresponds to the Dirac equation, is derived. Next, we extend the chaos theory, in which the period bifurcation is equivalent to the particle production. Then this extended chaos theory can be used for description of the multiparticle production and the extensive air showers at high energy. Let the parameter takes a suitable value, the quantitative results will be obtained, and an approximate formula will be derived. Many properties of the multiparticle production and of the chaos theory are universal.

Yi-Fang Chang

2008-08-02

253

Curvature and Chaos in General Relativity

We clarify some points about the systems considered by Sota, Suzuki and Maeda in Class. Quantum Grav. 13, 1241 (1996). Contrary to the authors' claim for a non-homoclinic kind of chaos, we show the chaotic cases they considered are homoclinic in origin. The power of local criteria to predict chaos is once more questioned. We find that their local, curvature--based criterion is neither necessary nor sufficient for the occurrence of chaos. In fact, we argue that a merit of their search for local criteria applied to General Relativity is just to stress the weakness of locality itself, free of any pathologies related to the motion in effective Riemannian geometries.

Werner M. Vieira; Patricio S. Letelier

1996-08-30

254

Bifurcations and Chaos in Simple Dynamical Systems

Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many studies have been made in chaotic dynamics during the past three decades and many simple chaotic systems have been discovered. in this work-bifurcations and chaos in simple dynamical systems - the behavior of some simple dynamical systems is studied by constructing mathematical models. investigations are made on the periodic orbits for continuous maps and idea of sensitive dependence on initial conditions,which is the hallmark of chaos, is obtained.

Mrs. T. Theivasanthi

2009-07-16

255

Nonlinear analysis and prediction of pulsatile hormone secretion

Pulsatile hormone secretion is observed in almost every hormonal system. The frequency of episodic hormone release ranges from approximately 10 to 100 pulses in 24 hours. This temporal mode of secretion is an important feature of intercellular information transfer in addition to a dose-response dependent regulation. It has been demonstrated in a number of experiments that changes in the temporal pattern of pulsatile hormone secretion specifically regulate cellular and organ function and structure. Recent evidence links osteoporosis, a disease characterized by loss of bone mass and structure, to changes in the dynamics of pulsatile parathyroid hormone (PTH) secretion. In our study we applied nonlinear and linear time series prediction to characterize the secretory dynamics of PTH in both healthy human subjects and patients with osteoporosis. Osteoporotic patients appear to lack periods of high predictability found in normal humans. In contrast to patients with osteoporosis patients with hyperparathyroidism, a condition which despite sometimes reduced bone mass has a preserved bone architecture, show periods of high predictability of PTH secretion. Using stochastic surrogate data sets which match certain statistical properties of the original time series significant nonlinear determinism could be found for the PTH time series of a group of healthy subjects. Using classical nonlinear analytical techniques we could demonstrate that the irregular pattern of pulsatile PTH secretion in healthy men exhibits characteristics of deterministic chaos. Pulsatile secretion of PTH in healthy subjects seems to be a first example of nonlinear determinism in an apparently irregular hormonal rhythm in human physiology. {copyright} {ital 1996 American Institute of Physics.}

Prank, K. [Abteilung Klinische Endokrinologie, Medizinische Hochschule Hannover, D-30623 Hannover (Germany)]|[Howard Hughes Medical Institute and Computational Neurobiology Laboratory, The Salk Institute, San Diego, California 92186-5800 (United States); Kloppstech, M. [Abteilung Klinische Endokrinologie, Medizinische Hochschule Hannover, D-30623 Hannover (Germany); Nowlan, S.J. [Howard Hughes Medical Institute and Computational Neurobiology Laboratory, The Salk Institute, San Diego, California 92186-5800 (United States); Harms, H.M.; Brabant, G.; Hesch, R. [Abteilung Klinische Endokrinologie, Medizinische Hochschule Hannover, D-30623 Hannover (Germany); Sejnowski, T.J. [Howard Hughes Medical Institute and Computational Neurobiology Laboratory, The Salk Institute, San Diego, California 92186-5800 (United States)

1996-06-01

256

Wave chaos in the nonequilibrium dynamics of the Gross-Pitaevskii equation

The Gross-Pitaevskii equation (GPE) plays an important role in the description of Bose-Einstein condensates (BECs) at the mean-field level. The GPE belongs to the class of nonlinear Schroedinger equations which are known to feature dynamical instability and collapse for attractive nonlinear interactions. We show that the GPE with repulsive nonlinear interactions typical for BECs features chaotic wave dynamics. We find positive Lyapunov exponents for BECs expanding in periodic and aperiodic smooth external potentials, as well as disorder potentials. Our analysis demonstrates that wave chaos characterized by the exponential divergence of nearby initial wave functions is to be distinguished from the notion of nonintegrability of nonlinear wave equations. We discuss the implications of these observations for the limits of applicability of the GPE, the problem of Anderson localization, and the properties of the underlying many-body dynamics.

Brezinova, Iva; Ludwig, Katharina; Burgdoerfer, Joachim [Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10/136, A-1040 Vienna (Austria); Collins, Lee A. [Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Schneider, Barry I. [Physics Division, National Science Foundation, Arlington, Virginia 22230 (United States); Electron and Atomic Physics Division, National Institute of Standards and Technology, Gaithersburg, Maryland 20899 (United States)

2011-04-15

257

VOLUME50, NUMBER9 P H Y S I C A L R E V I E W L E T T E R S 28 FEBRUARY1983 Comment on "Chaos chaotic from nonchaotic se- quences. Charles F. F. Karney Plasma Physics Laboratory, Princeton University Society Link: http://charles.karney.info/biblio/karney83b.html #12;

Karney, Charles

258

Embracing Chaos and Complexity: A Quantum Change for Public Health

Public health research and practice have been guided by a cognitive, rational paradigm where inputs produce linear, predictable changes in outputs. However, the conceptual and statistical assumptions underlying this paradigm may be flawed. In particular, this perspective does not adequately account for nonlinear and quantum influences on human behavior. We propose that health behavior change is better understood through the lens of chaos theory and complex adaptive systems. Key relevant principles include that behavior change (1) is often a quantum event; (2) can resemble a chaotic process that is sensitive to initial conditions, highly variable, and difficult to predict; and (3) occurs within a complex adaptive system with multiple components, where results are often greater than the sum of their parts. PMID:18556599

Resnicow, Kenneth; Page, Scott E.

2008-01-01

259

Detection of "noisy" chaos in a time series

NASA Technical Reports Server (NTRS)

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.

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

1997-01-01

260

Order and chaos : articulating support, housing transformation

This thesis presents an exploration on the theme of order and chaos, as a formal and social phenomenon, particularly as it relates to housing. The work stems from an attraction to the messy vitality we find in certain ...

Boehm, William Hollister

1990-01-01

261

Chaos synchronization of general complex dynamical networks

Abstract Recently, it has been demonstrated that many large-scale complex dynamical networks display a collective synchronization motion. Here, we introduce a time-varying complex dynamical net- work model and further investigate its synchronization phenomenon. Based on this new complex network model, two network chaos synchronization theorems are proved. We show that the chaos synchronization ofa time-varying complex network is determined by

Jinhu Luu; Xinghuo Yu; G. Chen

2004-01-01

262

Wave chaos in rapidly rotating stars

Effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens new perspectives for rapidly rotating star seismology and also provides a new and potentially observable manifestation of wave chaos in a large scale natural system.

F. Lignieres; B. Georgeot

2008-03-12

263

Can beauty help us adapt, evolve, and cope with environmental crisis? This article challenges the longstanding Kantian view that beauty is “disinterested,” while linking Kant’s view of the sublime with chaos theory and the fractal forms of nature. We humans participate in beauty as open systems in ongoing process, coevolving with all of existence. Beauty offers us conscious awareness and

Ruth Richards

2001-01-01

264

NASA Astrophysics Data System (ADS)

Electromagnetic sources of chaotic radiation offer a new technology for designing versatile, high-power, wide-bandwidth communication and radar systems. Vacuum electronic devices such as a traveling wave tube (TWT) amplifier may provide attractive sources for these applications. TWTs are known for their wide bandwidths and capability to generate high powers. Using chaos in these applications involves direct utilization of nonlinear behavior, allowing the amplifier to operate at or near a saturated state thereby at maximum electronic efficiency. Potential advantages of chaos in communications include greater number of users in a given bandwidth, low probability of interception and low probability of detection. In this paper we report investigations of a driven TWT amplifier with delayed feedback as a potential source of wide-band, high-power, chaotic radiation. This configuration is different from conventional oscillator schemes for generation of chaotic radiation as found in the literature. We present observations and characterization of chaos when the TWT amplifier with a gain bandwith of 3 - 8 GHz and a gain of 45 dB, is made to operate in a highly nonlinear regime at overdriven feedback. The experimental variables include the driver signal power and frequency and the feedback signal amplitude and delay time. Experimental results on time series as a function of feedback amplitude, phase plots, FFT spectra of waveforms and Poincare maps, will be presented.

Bhattacharjee, Sudeep; Marchewka, Chad; Booske, John; Ryskin, Nikita M.

2003-10-01

265

Chaos and microbial systems. Progress report, July 1989--July 1990

A recurrent theme of much recent research is that seemingly random fluctuations often occur as the result of simple deterministic mechanisms. Hence, much of the recent work in nonlinear dynamics has centered on new techniques for identifying order in seemingly chaotic systems. To determine the robustness of these techniques, chaos must, to some extent, be brought into the laboratory. Preliminary investigations of the forced double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation in inflowing substrate concentration, suggest that simple microbial systems may provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. This research has two main goals, that is the mathematical analysis and computer simulation of the periodically forced double-Monod equations and of related models; and experimental (chemostat) population studies that evaluate the accuracy and generality of the models, and that judge the usefulness of various new techniques of nonlinear dynamics to the study of populations.

Kot, M.

1990-07-01

266

Supporting Workflow in a Course Management System Chavdar Botev Hubert Chao Theodore Chao Yim Cheng

Supporting Workflow in a Course Management System Chavdar Botev Hubert Chao Theodore Chao Yim Cheng is a secure and scalable web-based course management sys- tem developed by the Cornell University Computer of the workflow associated with running a large course, such as course creation, importing students, management

Kozen, Dexter

267

Temporal chaos in Boussinesq magnetoconvection

NASA Astrophysics Data System (ADS)

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

Bekki, Naoaki; Moriguchi, Hirofumi

2007-01-01

268

NASA Technical Reports Server (NTRS)

[figure removed for brevity, see original site] Click on image for animation of 3-dimensional model with 5x vertical exaggeration

This image of chaotic terrain in the Aureum Chaos region of Mars was taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) at 0858UTC (3:58 a.m. EST) on January 24, 2008, near 3.66 degrees south latitude, 26.5 degrees west longitude. The image was taken in 544 colors covering 0.36-3.92 micrometers, and shows features as small as 18 meters (60 feet) across. The image is about 10 kilometers (6.2 miles) wide at its narrowest point.

Aureum Chaos is a 368 kilometer (229 mile) wide area of chaotic terrain in the eastern part of Valles Marineris. The chaotic terrain is thought to have formed by collapse of the surrounding Margaritifer Terra highland region. Aureum Chaos contains heavily eroded, randomly oriented mesas, plateaus, and knobs many revealing distinct layered deposits along their slopes. These deposits may be formed from remnants of the collapsed highlands, sand carried by Martian winds, dust or volcanic ash that settled out of the atmosphere, or sediments laid down on the floor of an ancient lake.

The top panel in the montage above shows the location of the CRISM image on a mosaic taken by the Mars Odyssey spacecraft's Thermal Emission Imaging System (THEMIS). The CRISM data cover a narrow plateau near the edge of the chaotic terrain, that stretches across from the southwest to the northeast.

The lower left image, an infrared false color image, reveals the plateau and several eroded knobs of varying sizes. The plateau's layer-cake structure is similar to that of other layered outcrops in Valles Marineris.

The lower right image reveals the strengths of mineral spectral features overlain on a black-and-white version of the infrared image. Areas shaded in red hold more of the mineral pyroxene, a primary component of basaltic rocks that are prevalent in the highlands. Spots of green indicate monohydrated sulfate minerals (sulfates with one water molecule incorporated into each molecule of the mineral), while blue indicates polyhydrated sulfate minerals (sulfates with multiple waters per mineral molecule).

Although the plateau's dark cap rock is somewhat mineralogically non-descript, the bright, white swath of underlying material cascading down the plateau's flanks appears to hold polyhydrated sulfates. Dark eolian or wind deposited sediments in the south-central part of the plateau are also rich in polyhydrated sulfates.

Surrounding the plateau are small greenish spots of monoyhydrated sulfates. These are erosional remnants of an even lower part of the layered deposits that is compositionally distinct from the main part of the plateau.

The deepest layer visible is preexisting 'basement' rock that forms the floor of Aureum Chaos around the plateau. It is comprised of basaltic rock exposed by collapse of the crust and the debris derived from that collapse.

The animation (see above) of a 3-dimensional topographic model illustrates the relationship of these materials. It was made using the lower right CRISM image, draped over MOLA topography with 5X vertical exaggeration.

CRISM is one of six science instruments on NASA's Mars Reconnaissance Orbiter. Led by The Johns Hopkins University Applied Physics Laboratory, Laurel, Md., the CRISM team includes expertise from universities, government agencies and small businesses in the United States and abroad. NASA's Jet Propulsion Laboratory, a division of the California Institute of Technology in Pasadena, manages the Mars Reconnaissance Orbiter and the Mars Science Laboratory for NASA's Science Mission Directorate, Washington. Lockheed Martin Space Systems, Denver, built the orbiter.

2008-01-01

269

Temporal chaos in Boussinesq magnetoconvection

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

Bekki, Naoaki; Moriguchi, Hirofumi [College of Engineering, Nihon University, Koriyama, Fukushima 963-8642 (Japan); Fundamental Science, Gifu National College of Technology, Motosu, Gifu 501-0495 (Japan)

2007-01-15

270

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by a spring to an external static point and, due to the dragging effect of the belt, the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can be achieved only by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic, dynamics and phase transition-like behavior. Noise-induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks (around five). PMID:23679502

Sándor, Bulcsú; Járai-Szabó, Ferenc; Tél, Tamás; Néda, Zoltán

2013-04-01

271

Experimental observation of chaos-chaos intermittency types in spherical Couette flow

NASA Astrophysics Data System (ADS)

Flows between concentric, counter rotating spherical boundaries are under investigation in a gap with a size equal to the inner sphere radius. The outer sphere rotational rate is fixed, while the inner sphere rotational rate was modulated. The amplitudes and frequencies of modulation are small relative to the averaged rotational rates of both spheres. With modulation amplitude increase, a transition from initial periodical flow to chaos occurs. To determine the state of the flow, time series of azimuthal velocity were used. Measurements were carried out by laser Doppler anemometer. Flow states with chaos-chaos and cycle-chaos-chaos intermittency were detected. The quantitative characteristics are considered, which allow separate different patterns of the flow state with distinct properties.

Zhilenko, D.; Krivonosova, O.

2014-01-01

272

Probability density of the empirical wavelet coefficients of a noisy chaos

NASA Astrophysics Data System (ADS)

We are interested in the random empirical wavelet coefficients of a noisy signal when this signal is a unidimensional or multidimensional chaos. More precisely we provide an expression of the conditional probability density of such coefficients, given a discrete observation grid. The noise is assumed to be described by a symmetric alpha-stable random variable. If the noise is a dynamic noise, then we present the exact expression of the probability density of each wavelet coefficient of the noisy signal. If we face a measurement noise, then the noise has a non-linear influence and we propose two approximations. The first one relies on a Taylor expansion whereas the second one, relying on an Edgeworth expansion, improves the first general Taylor approximation if the cumulants of the noise are defined. We give some illustrations of these theoretical results for the logistic map, the tent map and a multidimensional chaos, the Hénon map, disrupted by a Gaussian or a Cauchy noise.

Garcin, Matthieu; Guégan, Dominique

2014-05-01

273

Controlling Chaos Via Knowledge of Initial Condition for a Curved Structure

NASA Technical Reports Server (NTRS)

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.

Maestrello, L.

2000-01-01

274

on the response time of the nonlinear system and the time delay T of the feedback loop. When T ) , in most casesMultistability and Chaos in a Semiconductor Microwave Device with TimeÂDelay Feedback Yuo, 2002) We propose a tunable microwave device consisting of a Gunn diode with timeÂdelay feedback, which

275

Volume 138, number 1.2 PHYSICS LETTERS A 12 June 1989 HORSESHOE CHAOS IN A PERIODICALLY PERTURBED, and the optical beam Los Alamos, NM 87545, USA. intensity. 29 #12;Volume 138, number 1,2 PHYSICS LETTERS A 2 June, polarized, laser pulse propagating as a travelling wave in an anisotropic, cubically nonlinear, lossless

Holm, Darryl D.

276

Â Published: 14 April 2004 Part of Special Issue "International Workshops on Nonlinear Waves and Chaos) are commonly observed in the plasma sheet boundary layer (PSBL) of the Earth's magnetosphere (Scarf et al layer are not con- tinuous noise but consists of electrostatic impulsive solitary waves. The data from

Boyer, Edmond

277

Parameter identification using experimental nonlinear dynamics and chaos

linear system defined in (4. 3) CHAPTER I INTRODUCTION Many mechanical and structural systems that are key to everyday life undergo vibrations driven by either internal or external sources. Examples include skyscrapers under wind loading... linear system defined in (4. 3) CHAPTER I INTRODUCTION Many mechanical and structural systems that are key to everyday life undergo vibrations driven by either internal or external sources. Examples include skyscrapers under wind loading...

Chancellor, Roy Scott

2012-06-07

278

Bifurcation, Limit Cycle and Chaos of Nonlinear Dynamical Systems

.1.5. Numerical simulation results 18 2.2. Internet congestion model 24 2.2.1. Hopf bifurcation 26 2.2.2. Hopf.2.3. Example 3: The Oregonator model 104 4.2.4. Example 4: The smooth Chua system 105 4.3. Application of CM

Yu, Pei

279

Nonlinear Thermoacoustic Instability Dynamics in a Rijke Tube

We present a data-driven nonlinear and chaos theory–based analysis of thermoacoustic instabilities in a simple Rijke tube. Thermoacoustic instability modes in this simple Rijke tube display very rich nonlinear behavior because of the interaction of acoustic modes and unsteady heat-release processes during combustion. This approach of analyzing thermoacoustic instabilities, their evolution, and interactions differs from traditional linear time-series–based approaches, such

Andrew C. Noble; Galen B. King; Normand M. Laurendeau; James R. Gord; Sukesh Roy

2012-01-01

280

The effect of Lagrangian chaos on locking bifurcations in shear flows.

The effect of an externally imposed perturbation on an unstable or weakly stable shear flow is investigated, with a focus on the role of Lagrangian chaos in the bifurcations that occur. The external perturbation is at rest in the laboratory frame and can form a chain of resonances or cat's eyes where the initial velocity v(x0)(y) vanishes. If in addition the shear profile is unstable or weakly stable to a Kelvin-Helmholtz instability, for a certain amplitude of the external perturbation there can be an unlocking bifurcation to a nonlinear wave resonant around a different value of y, with nonzero phase velocity. The interaction of the propagating nonlinear wave with the external perturbation leads to Lagrangian chaos. We discuss results based on numerical simulations for different amplitudes of the external perturbation. The response to the external perturbation is strong, apparently because of non-normality of the linear operator, and the unlocking bifurcation is hysteretic. The results indicate that the observed Lagrangian chaos is responsible for a second bifurcation occurring at larger external perturbation, locking the wave to the wall. This bifurcation is nonhysteretic. The mechanism by which the chaos leads to locking in this second bifurcation is by means of chaotic advective transport of momentum from one chain of resonances to the other (Reynolds stress) and momentum transport to the vicinity of the wall via chaotic scattering. These results suggest that locking of waves in rotating tank experiments in the presence of two unstable modes is due to a similar process. (c) 2002 American Institute of Physics. PMID:12779581

Finn, John M.

2002-06-01

281

Genome chaos: survival strategy during crisis.

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. PMID:24299711

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

2014-02-15

282

Chaos theory in hydrology: important issues and interpretations

The application of the concept of chaos theory in hydrology has been gaining considerable interest in recent times. However, studies reporting the existence of chaos in hydrological processes are often criticized due to the fundamental assumptions with which the chaos identification methods have been developed, i.e. infinite and noise-free time series, and the inherent limitations of the hydrological time series,

B. Sivakumar

2000-01-01

283

Identification of Bayesian posteriors for coefficients of chaos expansions

: stochastic inversion, identification, Bayesian, maximum likelihood, polynomial chaos, validation, uncertainty the Bayesian paradigm can be applied to formulate and solve the inverse problem. The estimated polynomial chaosIdentification of Bayesian posteriors for coefficients of chaos expansions M. Arnst* a , R. Ghanem

Boyer, Edmond

284

Book Reviews Chaos and Coarse Graining in Statistical Mechanics.

Book Reviews Chaos and Coarse Graining in Statistical Mechanics. Patrizia Castiglione, Massimo.1198/jasa.2010.br1006 873 #12;874 Book Reviews Chaos and Coarse Graining in Statistical Mechanics. Patrizia of complex systems lying between. Chaos and Coarse Graining in Statistical Mechanics, by Patrizia Cas

Boehning, Dankmar

285

Water quality situation in the Chao Phraya Delta

The Pollution Control Department (PCD) has been monitoring the water quality of the Chao Phraya Delta (Chao Phraya, Tha Chin, and Meklong Rivers) for decades. The results indicated that river quality in the lower parts of the Chao Phraya and Tha Chin Rivers have been degraded and the levels of parameters concerned have been lower than the Surface Water Quality

Wijarn Simachaya; Pimon Watanamahart; Vuttichai Kaewkrajang

286

Integral observer approach for chaos synchronization with transmission disturbances

The paper addresses the issue of chaos synchronization with disturbances in the transmission channel. Using an integral observer approach, a new scheme for chaos synchronization is developed for a class of chaotic systems. Based on the Lyapunov stability theory, a sufficient condition is derived for chaos synchronization in this setting. By using the Schur theorem and some matrix operation techniques,

Guo-ping Jiang; Wei Xing Zheng; Wallace Kit-sang Tang; Guanrong Chen

2005-01-01

287

Nonlinear contraction tools for constrained optimization

This thesis derives new results linking nonlinear contraction analysis, a recent stability theory for nonlinear systems, and constrained optimization theory. Although dynamic systems and optimization are both areas that ...

Soto, Jonathan

2010-01-01

288

The capabilities of chaos and complexity.

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

Abel, David L

2009-01-01

289

Nonlinear Dynamics of a Diffusing Interface

NASA Technical Reports Server (NTRS)

Excitation of two miscible-viscous liquids inside a bounded enclosure in a microgravity environment has shown the evolution of quasi-stationary waves of various modes for a range of parameters. We examine computationally the nonlinear dynamics of the system as the interface breakup and bifurcates to resonance structures typified by the Rayleigh-Taylor instability mechanism. Results show that when the mean steady field is much smaller than the amplitude of the sinusoidal excitation, the system behaves linearly, and growth of quasi-stationary waves occurs through the Kelvin-Helmholtz instability mechanism. However, as the amplitude of excitation increases, nonlinearity occurs through subharmonic bifurcation prior to broadband chaos.

Duval, Walter M. B.

2001-01-01

290

Chaos Based Secure IP Communications over Satellite DVB

NASA Astrophysics Data System (ADS)

The Digital Video Broadcasting—Satellite (DVB-S) standard was originally conceived for TV and radio broadcasting. Later, it became possible to send IP packets using encapsulation methods such as Multi Protocol Encapsulation, MPE, or Unidirectional Lightweight Encapsulation, ULE. This paper proposes a chaos based security system for IP communications over DVB-S with ULE encapsulation. The proposed security system satisfies all the security requirements while respecting the characteristics of satellite links, such as the importance of efficient bandwidth utilization and high latency time. It uses chaotic functions to generate the keys and to encrypt the data. The key management is realized using a multi-layer architecture. A theoretical analysis of the system and a simulation of FTP and HTTP traffic are presented and discussed to show the cost of the security enhancement and to provide the necessary tools for security parameters setup.

Caragata, Daniel; El Assad, Safwan; Tutanescu, Ion; Sofron, Emil

2010-06-01

291

Lagrangian chaos and coupled chemical oscillators

NASA Astrophysics Data System (ADS)

Experimental studies are presented of the dynamics of coupled Belousov-Zhabotinsky oscillators in linear and annular chains of alternating vortices. Coupling between the vortices -- each of which acts like an individual batch reactor -- is dominated by Lagrangian chaos (chaotic mixing), achieved either by oscillating the vortex chain periodically in the lateral direction or by introducing a convective (thermal) flow in the perpendicular direction. Earlier studies have shown that Lagrangian chaos in these systems results either in enhanced ``normal'' diffusion or in superdiffusion characterized by Lévy flights -- long jumps in the trajectories that effectively couple distant parts of the system. Experimentally, synchronization of the chemical oscillations is observed in the presence of Lagrangian chaos. Traveling wave states are commonly observed. Global ``flashing'' states are also observed as long transients, as well as more complicated states in which chemical patterns circulate within lobe structures that typically characterize chaotic mixing.

Spohn, Courtney; Miller, Nathan; Solomon, Tom

2001-11-01

292

Topological approximation of the nonlinear Anderson model

NASA Astrophysics Data System (ADS)

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrödinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance overlap in phase space, ranging from a fully developed chaos involving Lévy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that the quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on the infinite Cayley tree (Bethe lattice). It is found in the vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t ?+?. The second moment of the associated probability distribution grows with time as a power law ? t?, with the exponent ? =1/3 exactly. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to the details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of "stripes" propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

293

Feigenbaum graphs: a complex network perspective of chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos.

Bartolo Luque; Lucas Lacasa; Fernando J. Ballesteros; Alberto Robledo

2011-09-06

294

Nonlinear models Nonlinear Regression

the framework implemented in the SPM function spm-nlsi-GN.m. It implements Bayesian estimation of nonlinear density References VL Posteriors The Variational Laplace (VL) algorithm, implemented in spm-nlsi

Penny, Will

295

Resurvey of order and chaos in spinning compact binaries

This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself.

Wu Xin [Department of Physics, Nanchang University, Nanchang 330031 (China); Xie Yi [Department of Astronomy, Nanjing University, Nanjing 210093 (China)

2008-05-15

296

Resurvey of order and chaos in spinning compact binaries

This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself.

Wu, Xin; 10.1103/PhysRevD.77.103012

2010-01-01

297

Resurvey of order and chaos in spinning compact binaries

This paper is mainly devoted to applying the invariant, fast, Lyapunov indicator to clarify some doubt regarding the apparently conflicting results of chaos in spinning compact binaries at the second-order post-Newtonian approximation of general relativity from previous literatures. It is shown with a number of examples that no single physical parameter or initial condition can be described as responsible for causing chaos, but a complicated combination of all parameters and initial conditions is responsible. In other words, a universal rule for the dependence of chaos on each parameter or initial condition cannot be found in general. Chaos does not depend only on the mass ratio, and the maximal spins do not necessarily bring the strongest effect of chaos. Additionally, chaos does not always become drastic when the initial spin vectors are nearly perpendicular to the orbital plane, and the alignment of spins cannot trigger chaos by itself.

Xin Wu; Yi Xie

2010-04-29

298

The uncertainty principle and quantum chaos

NASA Technical Reports Server (NTRS)

The conception of quantum chaos is described in some detail. The most striking feature of this novel phenomenon is that all the properties of classical dynamical chaos persist here but, typically, on the finite and different time scales only. The ultimate origin of such a universal quantum stability is in the fundamental uncertainty principle which makes discrete the phase space and, hence, the spectrum of bounded quantum motion. Reformulation of the ergodic theory, as a part of the general theory of dynamical systems, is briefly discussed.

Chirikov, Boris V.

1993-01-01

299

Chaos and complexity in astrophysics

Methods and techniques of the theory of nonlinear dynamical systems and patterns can be useful in astrophysical applications. Some works on the subjects of dynamical astronomy, stellar pulsation and variability, as well as spatial complexity in extended systems, in which such approaches have already been utilized, are reviewed. Prospects for future directions in applications of this kind are outlined.

Oded Regev

2007-05-16

300

Bifurcation structures and transient chaos in a four-dimensional Chua model

A four-dimensional four-parameter Chua model with cubic nonlinearity is studied applying numerical continuation and numerical solutions methods. Regarding numerical solution methods, its dynamics is characterized on Lyapunov and isoperiodic diagrams and regarding numerical continuation method, the bifurcation curves are obtained. Combining both methods the bifurcation structures of the model were obtained with the possibility to describe the {\\it shrimp}-shaped domains and their endoskeletons. We study the effect of a parameter that controls the dimension of the system leading the model to present transient chaos with its corresponding basin of attraction being riddled.

Anderson Hoff; Denilson T. da Silva; Cesar Manchein; Holokx A. Albuquerque

2013-12-06

301

Low-order chaos in sympathetic nerve activity and scaling of heartbeat intervals

NASA Astrophysics Data System (ADS)

The mechanism of 1/f scaling of heartbeat intervals remains unknown. We recorded heartbeat intervals, sympathetic nerve activity, and blood pressure in conscious rats with normal or high blood pressure. Using nonlinear analyses, we demonstrate that the dynamics of this system of three variables is low-order chaos, and that sympathetic nerve activity leads to heartbeat interval and blood pressure changes. It is suggested that impaired regulation of blood pressure by sympathetic nerve activity is likely to cause experimentally observable steeper scaling of heartbeat intervals in hypertensive (high blood pressure) rats.

Osaka, Motohisa; Kumagai, Hiroo; Sakata, Katsufumi; Onami, Toshiko; Chon, Ki H.; Watanabe, Mari A.; Saruta, Takao

2003-04-01

302

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

A comprehensive framework is proposed for the description and analysis of nonlinear problems in flight dynamics. Emphasis is placed on the aerodynamic component as the major source of nonlinearities in the flight dynamic system. Four aerodynamic flows are examined to illustrate the richness and regularity of the flow structures and the nature of the flow structures and the nature of the resulting nonlinear aerodynamic forces and moments. A framework to facilitate the study of the aerodynamic system is proposed having parallel observational and mathematical components. The observational component, structure is described in the language of topology. Changes in flow structure are described via bifurcation theory. Chaos or turbulence is related to the analogous chaotic behavior of nonlinear dynamical systems characterized by the existence of strange attractors having fractal dimensionality. Scales of the flow are considered in the light of ideas from group theory. Several one and two degree of freedom dynamical systems with various mathematical models of the nonlinear aerodynamic forces and moments are examined to illustrate the resulting types of dynamical behavior. The mathematical ideas that proved useful in the description of fluid flows are shown to be similarly useful in the description of flight dynamic behavior.

Chapman, G. T.; Tobak, M.

1984-01-01

303

Somalia after state collapse: Chaos or improvement?

Many people believe that Somalia's economy has been in chaos since the collapse of its national government in 1991. We take a comparative institutional approach to examine Somalia's performance relative to other African countries both when Somalia had a government and during its extended period of anarchy. We find that although Somalia is poor, its relative economic performance has improved

Benjamin Powell; Ryan Ford; Alex Nowrasteh

2008-01-01

304

Strange Attractors: Creating Patterns in Chaos

an appendix with an equivalent version in C. You may find the exercises in this book an enjoyable way to hone and Wreaths 7.6 Swings and Springs 7.7 Roll Your Own Chapter 8: Epilogue 8.1 How Common is Chaos? 8

Sprott, Julien Clinton

305

Chaos: a real phenomenon in power electronics

An introductory tutorial on chaotic behavior in DC-DC convertors is presented. Chaos is characterized by an emipirical spectrum which has a continuous component, and may even have no discrete components. Chaotic behavior frequently occurs when a power converter operates in a protective mode such as in a short-circuit or overload condition. Chaotic behavior in power converters is described in terms

Jonathan R. Wood; Bedford MA

1989-01-01

306

Quantum Chaos: A Brief First Visit

These notes contain a slightly expanded version of six lectures I delivered at the Cuernavaca Summer School on Analysis and Mathematical Physics (June 2000). They provide an elementary and self-contained introduction to some aspects of quantum chaos that is adapted it is hoped to the audience of the school, which consisted of advanced undergraduate and beginning graduate students in mathematics

Stephan De Bièvre

307

A Framework for Chaos Theory Career Counselling

ERIC Educational Resources Information Center

Theory in career development counselling provides a map that counsellors can use to understand and structure the career counselling process. It also provides a means to communicate this understanding and structuring to their clients as part of the counselling intervention. The chaos theory of careers draws attention to the complexity,…

Pryor, Robert G. L.

2010-01-01

308

Chaos: Connecting Science and the Humanities

NSDL National Science Digital Library

In this article, we learn about a team-taught course entitled Chaos in Science and Literature. The goals of the course were to place science in a nontechnological context, emphasizing its intellectual and cultural aspects, and to provide a forum for the exchange of ideas between "scientists" and "humanists," with the authors serving as role models.

Paddy, David; Lagan, Seamus

2005-01-01

309

Chaos, Fractals and Bifurcations Lecturer: Chris King king@math.auckland.ac.nz, Ph 88818

and Bifurcations to physics, chemistry, biology, medicine, geography, and economics. Chaos Chaos, fractals and bifurcation, and their application to wide areas including commerce, medicine-dimensional strange attractors. Quantum chaos and complexity theory are emerging frontier areas discussed

King, Chris

310

This thesis examines two challenging problems in chaos analysis: distinguishing deterministic chaos and stochastic (noise-induced) chaos, and applying chaotic heart rate variability (HRV) analysis to the prognosis of ...

Arzeno, Natalia M. (Natalia María Arzeno Soltero)

2007-01-01

311

Previous research documented a robust link between difficulties in self-regulation and development of externalizing problems (i.e., aggression and delinquency). In this study, we examined the longitudinal additive and interactive genetic and environmental covariation underlying this well-established link using a twin design. The sample included 131 pairs of monozygotic twins and 173 pairs of same-sex dizygotic twins who participated in three waves of annual assessment. Mothers and fathers provided reports of externalizing problems. Teacher report and observer rating were used to assess twin's attention regulation. The etiology underlying the link between externalizing problems and attention regulation shifted from a common genetic mechanism to a common environmental mechanism in the transition across middle childhood. Household chaos moderated the genetic variance of and covariance between externalizing problems and attention regulation. The genetic influence on individual differences in both externalizing problems and attention regulation was stronger in more chaotic households. However, higher levels of household chaos attenuated the genetic link between externalizing problems and attention regulation. PMID:22781853

Wang, Zhe; Deater-Deckard, Kirby; Petrill, Stephen A; Thompson, Lee A

2012-08-01

312

Entrainment by Spatiotemporal Chaos in Glow Discharge-Semiconductor Systems

Entrainment of limit cycles by chaos [1] is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach [2], 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 [3].

Marat Akhmet; Ismail Rafatov; Mehmet Onur Fen

2014-06-15

313

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

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

Schmeer, Kammi K.; Taylor, Miles

2013-01-01

314

Asymptotic problems in stochastic partial differential equations: A Wiener chaos approach

NASA Astrophysics Data System (ADS)

It has been known for a while that certain non-linear as well as bilinear stochastic partial differential equations driven by a singular noise must be interpreted in the re-normalized, or Wick, form. In this dissertation we study two such equations. In the first part of the dissertation, we study the stochastic Burgers equation with Wick non-linearity. We show that, in the stochastic Burgers equation, Wick non- linearity forces the solution to be a generalized process no matter how regular the random perturbation is. On the other hand, certain multiplicative random perturbations of the deterministic Burgers equation can only be interpreted in the Wick form and, for such equations, existence and uniqueness of a solution in appropriate generalized spaces is shown. This dissertation is based on the analysis of the coefficients of the chaos expansion of the solution at different stochastic scales. In the second part of the dissertation, we investigate a homogenization problem for stochastic bilinear elliptic equations. It is known that for such equations, solutions exist in generalized spaces. In this dissertation, homogenization results are proved in appropriate generalized spaces. The main tools of the investigation are analysis of the coefficients of the chaos expansion and the well known concept of two-scale convergence.

Kaligotla, Sivaditya

315

Bifurcation and chaos in the spontaneously firing spike train of cultured neuronal network

NASA Astrophysics Data System (ADS)

Both neuroscience and nonlinear science have focused attention on the dynamics of the neural network. However, litter is known concerning the electrical activity of the cultured neuronal network because of the high complexity and moment change. Instead of traditional methods, we use chaotic time series analysis and temporal coding to analyze the spontaneous firing spike train recorded from hippocampal neuronal network cultured on multi-electrode array. When analyzing interspike interval series of different firing patterns, we found when single spike and burst alternate, the largest Lyapunov exponent of interspike interval (ISI) series is positive. It suggests that chaos should exist. Furthermore, a nonlinear phenomenon of bifurcation is found in the ISI vs. number histogram. It determined that this complex firing pattern of neuron and the irregular ISI series were resulted from deterministic factors and chaos should exist in cultured term.These results suggest that chaotic time series analysis and temporal coding provide us effective methods to investigate the role played by deterministic and stochastic component in neuron information coding, but further research should be carried out because of the high complexity and remarkable noise of the electric activity.

Chen, Wenjuan; Li, Xiangning; Zhu, Geng; Zhou, Wei; Zeng, Shaoqun; Luo, Qingming

2008-02-01

316

Neutral line chaos and phase space structure

NASA Technical Reports Server (NTRS)

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.

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

1991-01-01

317

Are earthquakes an example of deterministic chaos?

NASA Technical Reports Server (NTRS)

A simple mass-spring model is used to systematically examine the dynamical behavior introduced by fault zone heterogeneities. The model consists of two sliding blocks coupled to each other and to a constant velocity driver by elastic springs. The state of this system can be characterized by the positions of the two blocks relative to the driver. A simple static/dynamic friction law is used. When the system is symmetric, cyclic behavior is observed. For an asymmetric system, where the frictional forces for the two blocks are not equal, the solutions exhibit deterministic chaos. Chaotic windows occur repeatedly between regions of limit cycles on bifurcation diagrams. The model behavior is similar to that of the one-dimensional logistic map. The results provide substantial evidence that earthquakes are an example of deterministic chaos.

Huang, Jie; Turcotte, Donald L.

1990-01-01

318

Digital cyphering system using chaos time series

NASA Astrophysics Data System (ADS)

A voltage-mode CMOS looped circuit generates complex chaos time series, and it is digitized by an AD converter. The digitized time series of internal state shows an irreversible multiple complexity in the past, due to bifurcation. The multiple complexity of internal states in chaos time series is utilized as a scramble code in a digital ciphering system. A binary coded information is bit-serially converted into a corresponding scramble code. An average conversion rate of the ciphering system using 8-bit data base is 102 k bit/sec. On the other hand, the internal states in the future time series are quite deterministic, even if it has multiple internal states in the past. The scramble code can be decoded by the deterministic phenomenon.

Takakubo, Hajime; Shono, Katsufusa

1995-12-01

319

Noise suppressions in synchronized chaos lidars.

The noise suppressions in the chaos lidar (CLIDAR) and the synchronized chaos lidar (S-CLIDAR) systems with the optoelectronic feedback (OEF) and optical feedback (OF) schemes are studied numerically. Compared with the CLIDAR system, the S-CLIDAR system with the OEF scheme has better correlation coefficients in the large noise regime for SNR < 15 dB. For the S-CLIDAR system with the OF scheme, better detections are also achieved in wide ranges depending on the levels of the phase noise presented in the channel. To have the best synchronization and detection quality, the optimized conditions for the coupling and feedback strengths in the S-CLIDAR system are also discussed. PMID:21164964

Wu, Wen-Ting; Liao, Yi-Huan; Lin, Fan-Yi

2010-12-01

320

Chaos: Understanding and Controlling Laser Instability

NASA Technical Reports Server (NTRS)

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.

Blass, William E.

1997-01-01

321

A Matched Filter For Communicating With Chaos

NASA Astrophysics Data System (ADS)

In conventional communication systems, a matched filter provides optimal receiver performance in the presence of noise. As such, matched filters are highly desirable, yet they are practical only when a relatively small number of known basis functions are used to represent information. For communications using chaotic waveforms, the unpredictable and nonrepeating nature of chaos suggests the basis functions are uncertain and ever changing, which would preclude the use of a simple matched filter. Consequently, it is widely accepted that the performance of chaos communications lags that of conventional, no chaotic systems. In this paper, we show this assumption is not necessarily true. We describe a simple, low-dimensional chaotic oscillator that admits an exact analytic solution containing a single fixed basis function. The solution is written as the linear convolution of a symbol sequence and the basis function, similar to how conventional communications waveforms are usually represented. Despite the linear nature of the solution, waveform returns sampled at regular switching times are conjugate to a shift map, proving the oscillator is chaotic. A matched filter for the basis function is defined and used to extract symbolic information from the chaotic wave-form. Its performance in additive white Gaussian noise is comparable to that of binary phase-shift keying (BPSK). The oscillator and its matched filter have potential application in Hayes-type chaos communications where a message signal is encoded in the symbolic dynamics via small perturbation control. The discovery of a practical matched filter for chaos finally provides a coherent receiver to complement this elegant encoding scheme.

Corron, Ned J.; Blakely, Jonathan N.

2011-04-01

322

Oscillations, Synchrony and DeterministicChaos

The coherence and robustness of biological systems is an astonishing phenomenon that depends on oscillations, synchronous\\u000a behaviour and, in some instances, deterministic chaos. Understanding of dynamic interactions on an extended range of timescales\\u000a involves homeodynamic rather than homeostatic concepts. Thereby, oscillations produce highly complex processes of intracellular\\u000a as well as intercellular synchrony and have led to the evolutionary emergence of

D. Lloyd

323

Advances in Ecological Research, Volume 37, 2005, 101-141 Nonlinear stochastic population dynamics

fluctuations observed in animal abundances led to an intense search for chaos in extant population data is a common feature of nonlinear models, could, in principle, be tested under controlled laboratory conditions beginning of our collaboration, fundamental questions greeted us at every turn as we looked at historical

Cushing, Jim. M.

324

Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

The cubic nonlinear Schroedinger equation, in the presence of driving and Landau damping, is studied numerically. As the pump intensity is increased, the system exhibits a transition from intermittency to a two-torus to chaos. The laminar phase of the intermittency is also a two-torus motion which corresponds in physical space to two identical solitons of amplitude determined by a power-balance equation.

Moon, H. T.; Goldman, M. V.

1984-01-01

325

Chaos, Self-Similarity, Musical Phrase and Form

The idea of chaos is aesthetically strangely satisfying. Chaos represents the antithesis of artistic production, but it also marks the edge of an abyss along which art often wanders, letting the fumes from below cast a lightly corrosive coat over the order the artist has worked so hard to create. Art can overcome, and may even to a certain degree

Gerald Bennett

326

Master Teachers: Making a Difference on the Edge of Chaos

ERIC Educational Resources Information Center

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…

Chapin, Dexter

2008-01-01

327

Using a quantum computer to investigate quantum chaos

We show that the quantum baker's map, a prototypical map invented for theoretical studies of quantum chaos, has a very simple realization in terms of quantum gates. Chaos in the quantum baker's map could be investigated experimentally on a quantum computer based on only 3 qubits.

Ruediger Schack

1997-05-10

328

Chaos in Black Holes Surrounded by Electromagnetic Fields

Chaos in Black Holes Surrounded by Electromagnetic Fields Manuele Santoprete #3; and Giampaolo a Schwarzschild black hole, perturbed by uniform elec- tric and magnetic #12;elds. The appearance of chaos is analyzed resorting to the Poincar#19;e-Melnikov method. Keywords: Chaotic dynamics; Black holes; Ernst

329

Communication using Synchronization of Chaos in Semiconductor Lasers with optoelectronic

Communication using Synchronization of Chaos in Semiconductor Lasers with optoelectronic feedback S scheme based on the synchronization of two chaotic semiconductor lasers is experimentally tested. The Chaos in the single-mode semiconductor lasers is generated by means of an optoelectronic feedback

Illing, Lucas

330

Chaos: A Topic for Interdisciplinary Education in Physics

ERIC Educational Resources Information Center

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…

Bae, Saebyok

2009-01-01

331

Mathematical models describing the chaotic behaviours in the recently reportedTwin-T, Wien-bridge and family of minimum component electronic chaos generators are derived.Nonideal effects of the active element in these circuits are integrated into analysis where necessarywhile a two segment piece-wise-linear approximation of the passive nonlinear voltage controlledresistor characteristics is adopted. The chaotic behaviour is shown to extend to the case where

A. S. Elwakil; A. M. Soliman

1999-01-01

332

Amplitude death in coupled robust-chaos oscillators

We investigate the synchronization behavior of a system of globally coupled, continuous-time oscillators possessing robust chaos. The local dynamics corresponds to the Shimizu-Morioka model where the occurrence of robust chaos in a region of its parameter space has been recently discovered. We show that the global coupling can drive the oscillators to synchronization into a fixed point created by the coupling, resulting in amplitude death in the system. The existence of robust chaos allows to introduce heterogeneity in the local parameters, while guaranteeing the functioning of all the oscillators in a chaotic mode. In this case, the system reaches a state of oscillation death, with coexisting clusters of oscillators in different steady states. The phenomena of amplitude death or oscillation death in coupled robust-chaos flows could be employed as mechanisms for stabilization and control in systems that require reliable operation under chaos.

M. J. Palazzi; M. G. Cosenza

2014-03-13

333

Supporting Workflow in a Course Management System Chavdar Botev Hubert Chao Theodore Chao Raymond, a secure and scalable web-based course management sys- tem developed by the Cornell University Computer Science De- partment, helps manage the workflow associated with running a course. Our goal in designing

Myers, Andrew C.

334

Chaos and chaos control in a strongly driven thermionic plasma diode

In a periodically driven thermionic diode period doubling cascades, period adding and low-dimensional chaos are found. Some dynamical properties of the driven discharge are comparable to strongly driven diode resonant circuits. The chaotic oscillations of the discharge current are controlled using occasional proportional feedback and an improved difference feedback method. Feedback constants are predetermined by the local analysis of the

T. Mausbach; T. Klinger; A. Piel

1999-01-01

335

Chaos in the Classroom: Exposing Gifted Elementary School Children to Chaos and Fractals.

ERIC Educational Resources Information Center

A unit of study for gifted fourth and fifth graders is described on the subject of mathematical periodicity and chaos and the underlying physical processes which produce these phenomena. Hands-on activities, data analysis tools and computer aids are used for instruction in simple periodic motion (pendulum), complex superposition of motions…

Adams, Helen M.; Russ, John C.

1992-01-01

336

Chaotifying Continuous-Time Nonlinear Autonomous Systems

Based on the principle of chaotification for continuous-time autonomous systems, which relies on two basic properties of chaos, i.e., globally bounded with necessary positive-zero-negative Lyapunov exponents, this paper derives a feasible and unified chaotification method of designing a general chaotic continuous-time autonomous nonlinear system. For a system consisting of a linear and a nonlinear subsystem, chaotification is achieved using separation of state variables, which decomposes the system into two open-loop subsystems interacting through mutual feedback resulting in an overall closed-loop nonlinear feedback system. Under the condition that the nonlinear feedback control output is uniformly bounded where the nonlinear function is of bounded-input/bounded-output, it is proved that the resulting system is chaotic in the sense of being globally bounded with a required placement of Lyapunov exponents. Several numerical examples are given to verify the effectiveness of the theoretical design. Since linear systems are special cases of nonlinear systems, the new method is also applicable to linear systems in general.

Simin Yu; Guanrong Chen

2012-03-27

337

The Curious Shorelines of Gorgonum Chaos

NASA Technical Reports Server (NTRS)

Level, bench-like platforms in the interior of the Gorgonum Chaos basin appear to be shorelines associated with an ancient lake. These shorelines, however, seem to lack the typical features of shorelines associated with wave and current transport and erosion, such as crescentic embayments, spits, barrier islands, and wave-cut cliffs. Rather, the lakefacing platform edges are commonly rounded and cumulate in planform, often evenly encircling presumed islands. We interpret these shorelines to have been formed by outward growth in a quiescent environment, possibly in ice-covered bodies of water and possibly, in part, as chemical precipitates.

Howard, A. D.; Moore, J. M.

2003-01-01

338

Classical and Quantum Chaos in Atom Optics

The interaction of an atom with an electromagnetic field is discussed in the presence of a time periodic external modulating force. It is explained that a control on atom by electromagnetic fields helps to design the quantum analog of classical optical systems. In these atom optical systems chaos may appear at the onset of external fields. The classical and quantum chaotic dynamics is discussed, in particular in an atom optics Fermi accelerator. It is found that the quantum dynamics exhibits dynamical localization and quantum recurrences.

Farhan Saif

2006-04-10

339

NASA Astrophysics Data System (ADS)

We uncover the dynamics at the chaos threshold ?? of the logistic map and find that it consists of trajectories made of intertwined power laws that reproduce the entire period-doubling cascade that occurs for ?nonlinear maps.

Baldovin, F.; Robledo, A.

2002-10-01

340

NASA Astrophysics Data System (ADS)

A nonlinear waveguide of the type considered by Stegeman, Seaton, Chilwell, and Smith (1984), but with a prism coupler, is used to study the prism excitation. The nonlinear medium is a substrate which exhibits the Kerr effect. It is shown that such a device experiences optical bistability and that there is a close link between optical bistability and resonant excitation of nonlinear guided modes propagating along this nonlinear waveguide.

Reinisch, R.; Arlot, P.; Vitrant, G.; Pic, E.

1985-12-01

341

A topological approximation of the nonlinear Anderson model

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear Schrodinger models with arbitrary power nonlinearity is analyzed. We conceive the various regimes of behavior, depending on the topology of resonance-overlap in phase space, ranging from a fully developed chaos involving Levy flights to pseudochaotic dynamics at the onset of delocalization. It is demonstrated that quadratic nonlinearity plays a dynamically very distinguished role in that it is the only type of power nonlinearity permitting an abrupt localization-delocalization transition with unlimited spreading already at the delocalization border. We describe this localization-delocalization transition as a percolation transition on a Cayley tree. It is found in vicinity of the criticality that the spreading of the wave field is subdiffusive in the limit t\\rightarrow+\\infty. The second moment grows with time as a powerlaw t^\\alpha, with \\alpha = 1/3. Also we find for superquadratic nonlinearity that the analog pseudochaotic regime at the edge of chaos is self-controlling in that it has feedback on the topology of the structure on which the transport processes concentrate. Then the system automatically (without tuning of parameters) develops its percolation point. We classify this type of behavior in terms of self-organized criticality dynamics in Hilbert space. For subquadratic nonlinearities, the behavior is shown to be sensitive to details of definition of the nonlinear term. A transport model is proposed based on modified nonlinearity, using the idea of stripes propagating the wave process to large distances. Theoretical investigations, presented here, are the basis for consistency analysis of the different localization-delocalization patterns in systems with many coupled degrees of freedom in association with the asymptotic properties of the transport.

Alexander V. Milovanov; Alexander Iomin

2014-06-03

342

NASA Technical Reports Server (NTRS)

A technique for designing automatic flight controllers for aircraft which utilizes the transformation theory of nonlinear systems to linear systems is presently being developed at NASA Ames Research Center. A method is considered in which a given nonlinear is transformed to a controllable linear system in Brunovsky canonical form. A linear approximation is introduced to the nonlinear system called the modified tangent model. This model is easily computed. Constructing the transformation for this model enables the designer to find an approximate transformation for the nonlinear system.

Ford, H.; Hunt, L. R.; Su, R.

1983-01-01

343

Quantum Chaos in Physical Systems: from Super Conductors to Quarks

This article is the written version of a talk delivered at the Bexbach Colloquium of Science 2000 and starts with an introduction into quantum chaos and its relationship to classical chaos. The Bohigas-Giannoni-Schmit conjecture is formulated and evaluated within random-matrix theory. Several examples of physical systems exhibiting quantum chaos ranging from nuclear to solid state physics are presented. The presentation concludes with recent research work on quantum chromodynamics and the quark-gluon plasma. In the case of a chemical potential the eigenvalue spectrum becomes complex and one has to deal with non-Hermitian random-matrix theory.

Elmar Bittner; Harald Markum; Rainer Pullirsch

2001-10-31

344

Chaos, Fractal and Quantum Poincare Recurrences in Diamagnetic Kepler Problem

The statistics of quantum Poincare recurrences in Hilbert space for diamagnetic hydrogen atom in strong magnetic field has been investigated. It has been shown that quantities characterizing classical chaos are in a good agreement with the ones that are used to describe quantum chaos. The equality of classical and quantum Poincare recurrences has been shown. It has been proved that one of the signs of the emergence of quantum chaos is the irreversible transition from a pure quantum mechanical state to the mixed one.

A. Ugulava; L. Chotorlishvili; T. Kereselidze; V. Skrinnikov

2006-08-01

345

Chaos and microbial systems. Final project report, July 1989--July 1992

The field of nonlinear dynamics has generated a variety of new techniques for identifying order in seemingly chaotic systems. These techniques have led to new insights for several ecological and epidemiological systems, most notably childhood disease epidemics. To better test the efficacy and relevance of these new techniques to population biology research with two components namely a mathematical analysis of some simple microbial models with chaotic dynamics; and experimental (chemostat) population studies to evaluate the accuracy of these models. I have completed a thorough analysis of the forced double-Monod model and of the phase-locking route to chaos that it exhibits. I have also analyzed a simpler pulsed system with mass action kinetics and a period-doubling route to chaos. This research also motivated detailed analyses of discrete-time predator-prey and dispersal models, and a fast new method for computing fractal dimension. My colleagues and I have assembled a complete laboratory system to determine the appropriateness of the forced double-Monod model. We have tested assays for concentration and density and have performed a variety of diagnostic tests on this system. We have measured growth parameters for bacteria and for protozoa in chemostat.

Kot, M.

1992-10-01

346

NSDL National Science Digital Library

This compiled site contains titles and links to over 40 sites, journal articles, course and tutorial materials, simulations, batteries, and other resources. Definitions of chemistry, theoretical chemistry, organic, physical and nuclear chemistry are integrated with the links to outside materials. A number of useful keywords are included to help users navigate the materials.

Charnine, Michael

2011-04-01

347

NSDL National Science Digital Library

The econometriclinks.com website is a collection of Econometric Links offered by the Econometrics Journal. The links covered include time series analysis, microeconometrics, labormetrics, cliometrics, finance metrics, risk metrics, credit metrics, crash metrics, pension metrics, analyst metrics, Web metrics, econophysics, environmetrics, spatial econometrics, markometrics, marketing research, customer service metrics, inventory metrics, demand metrics, psychometrics, medicometrics, and other schools of applied statistics related to (inter)human behaviour. (Econometrics theory is not included). The website is intended to support anyone teaching econometrics. The links are organized so that newly added links are listed at the top of the page followed by a section listing Econometricians. The remaining sections provide links to Econometrics papers, such as preprints, articles and dissertations; econometric software; code and data; (metadata) data sources (which are listed alphabetically); news lists; conferences and summer courses, and journals. The entire table of contents can be searched using a Web browser. Visitors are encouraged to email their additions, especially conferences.

348

simulations demonstrate the effectiveness of the equalizer as applied to a chaotic communication system. IChannel Equalization for Chaos-based Communication Systems Jiu-chao Feng, Chi K. Tse and Francis C -- The performance of chaos-based communication sys- tems is greatly affected by non-ideal channel characteristics

Tse, Chi K. "Michael"

349

Generalized synchronization of chaos in autonomous systems

We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an autonomous system can be synchronized to each other but not to a coupling function defined from them. The form of the coupling function is not crucial; it may not depend on all the state variables nor it needs to be active for all times for achieving generalized synchronization. The procedure is based on the analogy between a response map subject to an external drive acting with a probability p and an autonomous system of coupled maps where a global interaction between the maps takes place with this same probability. It is shown that, under some circumstances, the conditions for stability of generalized synchronized states are equivalent in both types of systems. Our results reveal the existence of similar minimal conditions for the emergence of generalized synchronization of chaos in driven and in autonomous spatiotemporal systems.

O. Alvarez-Llamoza; M. G. Cosenza

2008-06-10

350

Chaos and scaling in daily river flow

Adequate knowledge of the nature of river flow process is crucial for proper planning and management of our water resources and environment. This study attempts to detect the salient characteristics of flow dynamics of the Karoon River in Iran. Daily discharge series observed over a period of six years (1999-2004) is analyzed to examine the chaotic and scaling characteristics of the flow dynamics. The presence of chaos is investigated through the correlation dimension and Lyapunov exponent methods, while the Hurst exponent and R\\'enyi dimension analyses are performed to explore the scaling characteristics. The low correlation dimension ($2.60 \\pm 0.07$) and the positive largest Lyapunov exponent ($0.014 \\pm 0.001$) suggest the presence of low-dimensional chaos; they also imply that the flow dynamics are dominantly governed by three variables and can be reliably predicted up to 48 days (i.e. prediction horizon). Results from the Hurst exponent and R\\'enyi dimension analyses reveal the multifractal character of the flow dynamics, with persistent and anti-persistent behaviors observed at different time scales.

M. De Domenico; M. Ali Ghorbani

2010-01-30

351

RAPID DYNAMICAL CHAOS IN AN EXOPLANETARY SYSTEM

We report on the long-term dynamical evolution of the two-planet Kepler-36 system, which consists of a super-Earth and a sub-Neptune in a tightly packed orbital configuration. The orbits of the planets, which we studied through numerical integrations of initial conditions that are consistent with observations of the system, are chaotic with a Lyapunov time of only {approx}10 years. The chaos is a consequence of a particular set of orbital resonances, with the inner planet orbiting 34 times for every 29 orbits of the outer planet. The rapidity of the chaos is due to the interaction of the 29:34 resonance with the nearby first-order 6:7 resonance, in contrast to the usual case in which secular terms in the Hamiltonian play a dominant role. Only one contiguous region of phase space, accounting for {approx}4.5% of the sample of initial conditions studied, corresponds to planetary orbits that do not show large-scale orbital instabilities on the timescale of our integrations ({approx}200 million years). Restricting the orbits to this long-lived region allows a refinement of estimates of the masses and radii of the planets. We find that the long-lived region consists of the initial conditions that satisfy the Hill stability criterion by the largest margin. Any successful theory for the formation of this system will need to account for why its current state is so close to unstable regions of phase space.

Deck, Katherine M.; Winn, Joshua N. [Department of Physics and Kavli Institute for Astrophysics and Space Research, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139 (United States); Holman, Matthew J.; Carter, Joshua A.; Ragozzine, Darin [Harvard-Smithsonian Center for Astrophysics, 60 Garden Street, Cambridge, MA 02138 (United States); Agol, Eric [Department of Astronomy, Box 351580, University of Washington, Seattle, WA 98195 (United States); Lissauer, Jack J. [NASA Ames Research Center, Moffet Field, CA 94035 (United States)

2012-08-10

352

A nonlinear small-world network model has been presented to investigate the effect of nonlinear interaction and time delay on the dynamic properties of small-world networks. Both numerical simulations and analytical analysis for networks with time delay and nonlinear interaction show chaotic features in the system response when nonlinear interaction is strong enough or the length scale is large enough. In addition, the small-world system may behave very differently on different scales. Time-delay parameter also has a very strong effect on properties such as the critical length and response time of small-world networks.

Yang, Xin-She

2010-01-01

353

PREFACE: XI Latin American Workshop on Nonlinear Phenomena

NASA Astrophysics Data System (ADS)

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

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

2010-09-01

354

Chaos Synchronization and Chaos Anticontrol of a Rotationally Supported Simple Pendulum

NASA Astrophysics Data System (ADS)

Chaos synchronization and anticontrol of a rotationally supported simple pendulum was studied in this paper. Different kinds of coupling terms are used to synchronize the two identical chaotic systems with different initial conditions. An observed-based scheme is also used to achieve synchronization. The results are demonstrated by phase portrait, Lyapunov exponent, Poincaré maps and synchronization time. Next, in order to analyze the transient behavior of the synchronized systems, Euclidean distance is used to plot a figure with coupling strength versus the distance. The chaotic signals are used to mask the message function in the secure communication system. Finally, anticontrol of chaos is achieved by adding constant term, periodic term, impulse term, time-delay term and adaptive control.

Ge, Zheng-Ming; Yu, Chia-Yang; Chen, Yen-Sheng

355

Experimental observation of a chaos-to-chaos transition in laser droplet generation

We examine the dynamics of laser droplet generation in dependence on the detachment pulse power. In the absence of the detachment pulse, undulating pendant droplets are formed at the end of a properly fed metal wire due to the impact of the primary laser pulse that induces melting. Eventually, these droplets detach, i.e. overcome the surface tension, because of their increasing mass. We show that this spontaneous dripping is deterministically chaotic by means of a positive largest Lyapunov exponent and a negative divergence. In the presence of the detachment pulse, however, the generation of droplets is fastened depending on the pulse power. At high powers, the spontaneity of dripping is completely overshadowed by the impact of the detachment pulse. Still, amplitude chaos can be detected, which similarly as the spontaneous dripping, is characterized by a positive largest Lyapunov exponent and a negative divergence, thus indicating that the observed dynamics is deterministically chaotic with an attractor as solution in the phase space. In the intermediate regime, i.e. for low and medium detachment pulse powers, the two chaotic states compete for supremacy, yielding an intermittent period-doubling to amplitude chaos transition, which we characterize by means of recurrence plots and their properties. Altogether, the transition from spontaneous to triggered laser droplet generation is characterized by a chaos-to-chaos transition with an intermediate dynamically nonstationary phase in-between. Since metal droplets can be used in various industrial applications, we hope that the accurate determination of the dynamical properties underlying their formation will facilitate their use and guide future attempts at mathematical modeling.

Blaz Krese; Matjaz Perc; Edvard Govekar

2010-08-03

356

Chaos due to parametric excitation: phase space symmetry and photon correlations

We discuss dissipative chaos showing symmetries in the phase space and nonclassical statistics for a parametrically driven nonlinear Kerr resonator (PDNR). In this system an oscillatory mode is created in the process of degenerate down-conversion of photons under interaction with a train of external Gaussian pulses. For chaotic regime we demonstrate, that the Poincar\\'e section showing a strange attractor, as well as the resonator mode contour plots of the Wigner functions display two-fold symmetry in the phase space. We show that quantum-to-classical correspondence is strongly violated for some chaotic regimes of the PDNR. Considering the second-order correlation function we show that the high-level of photons correlation leading to squeezing in the regular regime strongly decreases if the system transits to the chaotic regime. Thus, observation of the photon-number correlation allows to extract information about the chaotic regime.

T. V. Gevorgyan; G. H. Hovsepyan; A. R. Shahinyan; G. Yu. Kryuchkyan

2014-07-29

357

Takagi-Sugeno fuzzy modeling and chaos control of partial differential systems

NASA Astrophysics Data System (ADS)

In this paper a unified approach is presented for controlling chaos in nonlinear partial differential systems by a fuzzy control design. First almost all known chaotic partial differential equation systems are represented by Takagi-Sugeno fuzzy model. For investigating design procedure, Kuramoto-Sivashinsky (K-S) equation is selected. Then, all linear subsystems of K-S equation are transformed to ordinary differential equation (ODE) systems by truncated Fourier series of sine-cosine functions. By solving Riccati equation for each ODE systems, parallel stabilizing feedback controllers are determined. Finally, a distributed fuzzy feedback for K-S equation is designed. Numerical simulations are given to show that the distributed fuzzy controller is very easy to design, efficient, and capable to extend.

Vasegh, Nastaran; Khellat, Farhad

2013-12-01

358

Numerical and experimental exploration of phase control of chaos

NASA Astrophysics Data System (ADS)

A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this technique. A thorough numerical exploration has been made focused in the important role played by the phase, from which new interesting patterns in parameter space have appeared. On the other hand, our novel experimental implementation of phase control in an electronic circuit confirms both the well-known features of this method and the new ones detected numerically. All this may help in future implementations of phase control of chaos, which is globally confirmed here to be robust and easy to implement experimentally.

Zambrano, Samuel; Allaria, Enrico; Brugioni, Stefano; Leyva, Immaculada; Meucci, Riccardo; Sanjuán, Miguel A. F.; Arecchi, Fortunato T.

2006-03-01

359

Chaos, Fractals, and Tom Stoppard's Arcadia Robert L. Devaney

Chaos, Fractals, and Tom Stoppard's Arcadia Robert L. Devaney Department of Mathematics Boston University Boston, MA 02215 1 #12; Tom Stoppard's wonderful play, Arcadia, o#11;ers teachers of both math

Devaney, Robert L.

360

Boris Chirikov -Sputnik of Chaos D.L.Shepelyansky

Boris Chirikov - Sputnik of Chaos D.L.Shepelyansky CNRS, Toulouse, France (Dated: December 12, 2008) In Russian, the word Sputnik means companion. But after the very first artificial satellite Sputnik, launched

Shepelyansky, Dima

361

Boris Chirikov (6-6-1998) A pioneer of chaos

selected proceedings of the Sputnik Conference of STATPHYS 20 `Classical Chaos and its Quantum in Toulouse, France on 16-18 July 1998. Sputnik is the name of the very first artificial satellite, launched

Shepelyansky, Dima

362

Parameter Mismatches, Chaos Synchronization and Fast Dynamic Logic Gates

By using chaos synchronization between non-identical multiple time delay semiconductor lasers with optoelectronic feedbacks, we demonstrate numerically how fast dynamic logic gates can be constructed. The results may be helpful to obtain a computational hardware with reconfigurable properties.

E. M. Shahverdiev

2009-06-30

363

Chaos-assisted, broadband trapping of light in optical resonators

Chaos is a phenomenon that occurs in many aspects of contemporary science. In classical dynamics, chaos is defined as a hypersensitivity to initial conditions. The presence of chaos is often unwanted, as it introduces unpredictability, which makes it difficult to predict or explain experimental results. Conversely, we demonstrate here how chaos can be used to enhance the ability of an optical resonator to store energy. We combine analytic theory with ab-initio simulations and experiments in photonic crystal resonators to show that a chaotic resonator can store six times more energy than its classical counterpart of the same volume. We explain the observed increase with the equipartition of energy among all degrees of freedom of the chaotic resonator, i.e. the cavity modes, which is evident from the convergence of their lifetime towards a single value. A compelling illustration of the theory is provided by demonstrating enhanced absorption in deformed polystyrene microspheres.

Liu, C; Molinari, D; Khan, Y; Ooi, B S; Krauss, T F; Fratalocchi, A

2012-01-01

364

Discrete chaos in fractional sine and standard maps

NASA Astrophysics Data System (ADS)

Fractional standard and sine maps are proposed by using the discrete fractional calculus. The chaos behaviors are then numerically discussed when the difference order is a fractional one. The bifurcation diagrams and the phase portraits are presented, respectively.

Wu, Guo-Cheng; Baleanu, Dumitru; Zeng, Sheng-Da

2014-01-01

365

Dynamical and Wave Chaos in the Bose-Einstein Condensate

NASA Astrophysics Data System (ADS)

Within the past five years Albert Einstein's concept of a dilute atomic Bose Condensate has been realized in many experimental laboratories. Temperatures in the nano-Kelvin regime have been achieved using magnetic and optical trapping of laser and evaporatively cooled atoms. At such temperatures the relative de Broglie wavelengths of the gaseous trapped atoms can become long compared to their mean spacing, and through a process of bosonic amplification a “quantum phase transition” takes place involving 103 to 1011 atoms, most of which end up in identical single particle quantum states, whose length scales are determined by the external trap. Rb, Na, Li and atomic H have been trapped at variable densities of the order of 1013/cm3, and in traps of varying geometries. Of these all but Li have an effective repulsive atomic pair interaction, but utilization of molecular Feshbach resonances allows the interactions of other species to be tuned over wide ranges of strengths, including control of the sign of the effective atomic pair interactions. Fully quantum and macroscopic systems at such low densities are a theorist's dream: simple Hartree type mean field theory provides a startlingly accurate description of density profiles, low energy excitation frequencies, and such a description, commonly called the Non-linear Schrödinger Equation (NLSE) or the Gross-Pitaevskii (GP) Equation, will be explored here. The NLSE appropriate for attractive atomic interactions is known to lead to chaotically unstable dynamics, and eventual implosion of the condensate should the local number density exceed a critical value. In this work we illustrate this type of chaotic collapse for attractive condensates, and then explore the types of chaotic dynamics of solitons and vortices, which are the signatures of dynamical non-linearity in the repulsive case. Finally the implications of the symmetry-breaking associated with phase rigidity are explored in model simulations of repulsive condensates: condensates with repulsive atomic interactions break into phase domains when subject to weak shocks and, perhaps surprisingly, break into chaotic “laser-speckle” type patterns as the shock level increases. The fully quantum mechanical NLSE thus displays a full range of chaotic types of motion: from particle-like chaotic collisions of solitons and vortices to fully developed time dependent wave chaos.

Reinhardt, William P.; McKinney, Sarah B.

366

Dynamical and Wave Chaos in the Bose-Einstein Condensate

NASA Astrophysics Data System (ADS)

Within the past five years Albert Einstein's concept of a dilute atomic Bose Condensate has been realized in many experimental laboratories. Temperatures in the nano-Kelvin regime have been achieved using magnetic and optical trapping of laser and evaporatively cooled atoms. At such temperatures the relative de Broglie wavelengths of the gaseous trapped atoms can become long compared to their mean spacing, and through a process of bosonic amplification a "quantum phase transition" takes place involving 103 to 1011 atoms, most of which end up in identical single particle quantum states, whose length scales are determined by the external trap. Rb, Na, Li and atomic H have been trapped at variable densities of the order of 1013/cm3, and in traps of varying geometries. Of these all but Li have an effective repulsive atomic pair interaction, but utilization of molecular Feshbach resonances allows the interactions of other species to be tuned over wide ranges of strengths, including control of the sign of the effective atomic pair interactions. Fully quantum and macroscopic systems at such low densities are a theorist's dream: simple Hartree type mean field theory provides a startlingly accurate description of density profiles, low energy excitation frequencies, and such a description, commonly called the Non-linear Schrödinger Equation (NLSE) or the Gross-Pitaevskii (GP) Equation, will be explored here. The NLSE appropriate for attractive atomic interactions is known to lead to chaotically unstable dynamics, and eventual implosion of the condensate should the local number density exceed a critical value. In this work we illustrate this type of chaotic collapse for attractive condensates, and then explore the types of chaotic dynamics of solitons and vortices, which are the signatures of dynamical non-linearity in the repulsive case. Finally the implications of the symmetry-breaking associated with phase rigidity are explored in model simulations of repulsive condensates: condensates with repulsive atomic interactions break into phase domains when subject to weak shocks and, perhaps surprisingly, break into chaotic "laser-speckle" type patterns as the shock level increases. The fully quantum mechanical NLSE thus displays a full range of chaotic types of motion: from particle-like chaotic collisions of solitons and vortices to fully developed time dependent wave chaos.

Reinhardt, William P.; McKinney, Sarah B.

2001-10-01

367

High precision framework for chaos many-body engine

NASA Astrophysics Data System (ADS)

In this paper we present a C# 4.0 high precision framework for simulation of relativistic many-body systems. In order to benefit from the, previously developed, chaos analysis instruments, all new modules were integrated with Chaos Many-Body Engine (Grossu et al. 2010, 2013). As a direct application, we used 46 digits precision for analyzing the "Butterfly Effect" of the gravitational force in a specific relativistic nuclear collision toy-model.

Grossu, I. V.; Besliu, C.; Felea, D.; Jipa, Al.

2014-04-01

368

Suppression of quantum chaos in a quantum computer hardware

We present numerical and analytical studies of a quantum computer proposed by the Yamamoto group in Phys. Rev. Lett. 89, 017901 (2002). The stable and quantum chaos regimes in the quantum computer hardware are identified as a function of magnetic field gradient and dipole-dipole couplings between qubits on a square lattice. It is shown that a strong magnetic field gradient leads to suppression of quantum chaos.

J. Lages; D. L. Shepelyansky

2005-10-14

369

Non-Markovian Quantum Dynamics and Classical Chaos

We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular we remark the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude -- a fundamental quantity used to measure sensitivity to perturbations, and identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.

Garcia-Mata, I; Wisniacki, D A

2012-01-01

370

Philosophical perspectives on quantum chaos: Models and interpretations

NASA Astrophysics Data System (ADS)

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.

Bokulich, Alisa Nicole

2001-09-01

371

Quantum chaos in the nuclear collective model: II. Peres lattices

This is a continuation of our preceding paper devoted to signatures of quantum chaos in the geometric collective model of atomic nuclei. We apply the method by Peres to study ordered and disordered patterns in quantum spectra drawn as lattices in the plane of energy vs. average of a chosen observable. A good qualitative agreement with standard measures of chaos is manifested. The method provides an efficient tool for studying structural changes of eigenstates across quantum spectra of general systems.

Pavel Stransky; Petr Hruska; Pavel Cejnar

2009-02-23

372

From classical chaos to decoherence in Robertson-Walker cosmology

We analyse the relationship between classical chaos and particle creation in Robertson-Walker cosmological models with gravity coupled to a scalar field. Within our class of models chaos and particle production are seen to arise in the same cases. Particle production is viewed as the seed of decoherence, which both enables the quantum to classical transition, and ensures that the correspondence between the quantum and classically chaotic models will be valid

Fernando C. Lombardo; Mario Castagnino; Luca Bombelli

1998-06-25

373

EEG and chaos: Description of underlying dynamics and its relation to dissociative states

NASA Technical Reports Server (NTRS)

The goal of this work is the identification of states especially as related to the process of error production and lapses of awareness as might be experienced during aviation. Given the need for further articulation of the characteristics of 'error prone state' or 'hazardous state of awareness,' this NASA grant focused on basic ground work for the study of the psychophysiology of these states. In specific, the purpose of this grant was to establish the necessary methodology for addressing three broad questions. The first is how the error prone state should be conceptualized, and whether it is similar to a dissociative state, a hypnotic state, or absent mindedness. Over 1200 subjects completed a variety of psychometric measures reflecting internal states and proneness to mental lapses and absent mindedness; the study suggests that there exists a consistency of patterns displayed by individuals who self-report dissociative experiences such that those individuals who score high on measures of dissociation also score high on measures of absent mindedness, errors, and absorption, but not on scales of hypnotizability. The second broad question is whether some individuals are more prone to enter these states than others. A study of 14 young adults who scored either high or low on the dissociation experiences scale performed a series of six tasks. This study suggests that high and low dissociative individuals arrive at the experiment in similar electrocortical states and perform cognitive tasks (e.g., mental math) in a similar manner; it is in the processing of internal emotional states that differences begin to emerge. The third question to be answered is whether recent research in nonlinear dynamics, i.e., chaos, offer an addition and/or alternative to traditional signal processing methods, i.e., fast Fourier transforms, and whether chaos procedures can be modified to offer additional information useful in identifying brain states. A preliminary review suggests that current nonlinear dynamical techniques such as dimensional analysis can be successfully applied to electrocortical activity. Using the data set developed in the study of the young adults, chaos analyses using the Farmer algorithm were performed; it is concluded that dimensionality measures reflect information not contained in traditional EEG Fourier analysis.

Ray, William J.

1994-01-01

374

NASA Astrophysics Data System (ADS)

In recent research, propagation of plane electromagnetic (EM) waves through a turbulent medium with modified von Karman phase characteristics was modeled and numerically simulated using transverse planar apertures representing narrow phase turbulence along the propagation path. The case for extended turbulence was also studied by repeating the planar phase screens multiple times over the propagation path and incorporating diffractive effects via a split-step algorithm. The goal of the research reported here is to examine two random phenomena: (a) atmospheric turbulence due to von Karman-type phase fluctuations, and (b) chaos generated in an acousto-optic (A-O) Bragg cell under hybrid feedback. The latter problem has been thoroughly examined for its nonlinear dynamics and applications in secure communications. However, the statistical characteristics (such as the power spectral density (PSD)) of the chaos have not been estimated in recent work. To that end, treating the chaos phenomena as a random process, the time waveforms of the chaos intensity and their spectra are numerically evaluated over a (large) number of time iterations. These spectra are then averaged to derive the equivalent PSD of the A-O chaos. For the turbulence problem, an optical beam passing through an input pinhole is propagated through a random phase screen (placed at different locations) to a desired distance (typically near-field) under different levels of turbulence strength. The resulting spatial intensity profile is then averaged and the process repeated over a (large) number of pre-specified time intervals. From this data, once again, the turbulence PSD is calculated via the Fourier spectra of the average intensity snapshots. The results for the two systems are compared.

Chatterjee, Monish R.; Mohamed, Fathi H. A.

2014-10-01

375

A study of chaos in a rotor system supported by ball bearings

. Numerous researchers have published a myriad of papers on the application of chaos theory to mechanical, electrical and biological systems. However, control theories of chaos have been in existence for only a decade and have not been applied to rotor...

Ortiz, Steven Rey

2013-02-22

376

Chaos in the Showalter-Noyes-Bar-Eli model of the Belousov-Zhabotinskii reaction

NASA Astrophysics Data System (ADS)

The observation of robust, large-scale chaos in the Showalter-Noyes-Bar-Eli model of the Belousov-Zhabotinskii reaction is reported. The chaos observed is comparable to that found in CSTR experiments at low flow rates.

Lindberg, David; Turner, Jack S.; Barkley, Dwight

1990-03-01

377

Federal Register 2010, 2011, 2012, 2013

...Determinations: ``Chaos and Classicism: Art in France, Italy, and Germany, 1918-1936'' SUMMARY: Notice is hereby given...in the exhibition ``Chaos and Classicism: Art in France, Italy, and Germany, 1918-1936,'' imported from abroad for...

2010-08-30

378

Chaos control for the family of Rossler systems using feedback controllers

of chaos control begun. The main goal of chaos control was to eliminate chaotic motion and to stabilize one it does not sat- isfy global Lipschitz condition. So far it is not known if, like the Lorenz system

Yu, Pei

379

Human ventilation at rest exhibits mathematical chaos-like complexity that can be described as long-term unpredictability mediated (in whole or in part) by some low-dimensional nonlinear deterministic process. Although various physiological and pathological situations can affect respiratory complexity, the underlying mechanisms remain incompletely elucidated. If such chaos-like complexity is an intrinsic property of central respiratory generators, it should appear or increase when these structures mature or are stimulated. To test this hypothesis, we employed the isolated tadpole brainstem model [Rana (Pelophylax) esculenta] and recorded the neural respiratory output (buccal and lung rhythms) of pre- (n = 8) and postmetamorphic tadpoles (n = 8), at physiologic (7.8) and acidic pH (7.4). We analyzed the root mean square of the cranial nerve V or VII neurograms. Development and acidosis had no effect on buccal period. Lung frequency increased with development (P < 0.0001). It also increased with acidosis, but in postmetamorphic tadpoles only (P < 0.05). The noise-titration technique evidenced low-dimensional nonlinearities in all the postmetamorphic brainstems, at both pH. Chaos-like complexity, assessed through the noise limit, increased from pH 7.8 to pH 7.4 (P < 0.01). In contrast, linear models best fitted the ventilatory rhythm in all but one of the premetamorphic preparations at pH 7.8 (P < 0.005 vs. postmetamorphic) and in four at pH 7.4 (not significant vs. postmetamorphic). Therefore, in a lower vertebrate model, the brainstem respiratory central rhythm generator accounts for ventilatory chaos-like complexity, especially in the postmetamorphic stage and at low pH. According to the ventilatory generators homology theory, this may also be the case in mammals. PMID:21325645

Samara, Ziyad; Fiamma, Marie-Noelle; Bautin, Nathalie; Ranohavimparany, Anja; Le Coz, Patrick; Golmard, Jean-Louis; Darre, Pierre; Zelter, Marc; Poon, Chi-Sang; Similowski, Thomas

2011-01-01

380

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

ERIC Educational Resources Information Center

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…

Akmansoy, Vesile; Kartal, Sadik

2014-01-01

381

Expansion of the propagation of chaos for Bird and Nanbu sytems

of the mollified Boltzmann equation. In particular, they have the propagation of chaos property. Following [GM94 of the error in the propagation of chaos in terms of the number of particles, for slightly more general systems, we call it an expansion of the error in the propagation of chaos. In the setting of [DPR09b

382

Chaos Examples Doubling map Logistic map Bifurcation diagram Summary Randomness and determinism of Houston) October 5, 2012 1 / 19 #12;Chaos Examples Doubling map Logistic map Bifurcation diagram Summary) October 5, 2012 2 / 19 #12;Chaos Examples Doubling map Logistic map Bifurcation diagram Summary

Climenhaga, Vaughn

383

Chaos Effect in the Edwards-Anderson Ising Spin Glass: A numerical Domain Wall

Ising spin glass. The first issue we concern is chaos caused by temperature variation (temperature chaos). It is well known that in spin glasses a small change in temperature causes new relaxation process which does the existence of temperature chaos was pre- dicted by a phenomenological theory for short- range spin glasses

Katsumoto, Shingo

384

The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz. PMID:23278100

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

2012-12-01

385

NASA Astrophysics Data System (ADS)

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

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

2012-12-01

386

Chaos based encryption system for encrypting electroencephalogram signals.

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. PMID:24733526

Lin, Chin-Feng; Shih, Shun-Han; Zhu, Jin-De

2014-05-01

387

Behavior modeling through CHAOS for simulation of dismounted soldier operations

NASA Astrophysics Data System (ADS)

One of the major challenges in human behavior modeling for military applications is dealing with all factors that can influence behavior and performance. In a military context, behavior and performance are influenced by the task at hand, the internal (cognitive and physiological) and external (climate, terrain, threat, equipment, etc.) state. Modeling the behavioral effects of all these factors in a centralized manner would lead to a complex rule-base that is difficult to maintain or expand. To better cope with this complexity we have developed the Capability-based Human-performance Architecture for Operational Simulation (CHAOS). CHAOS is a multi-agent system for human behavior modeling that is based on pandemonium theory. Every agent in CHAOS represents a specific part of behavior, such as 'reaction to threat' or 'performing a patrol task'. These agents are competing over a limited set of resources that represent human capabilities. By combining the element of competition with multiple limited resources, CHAOS allows us to model stress, strain and multi-tasking in an intuitive manner. The CHAOS architecture is currently used in firefighter and dismounted soldier simulations and has shown itself to be suitable for human behavior and performance modeling.

Ubink, Emiel; Aldershoff, Frank; Lotens, Wouter; Woering, Arend

2008-04-01

388

Chaos: a bridge from microscopic uncertainty to macroscopic randomness

It is traditionally believed that the macroscopic randomness has nothing to do with the micro-level uncertainty. Besides, the sensitive dependence on initial condition (SDIC) of Lorenz chaos has never been considered together with the so-called continuum-assumption of fluid (on which Lorenz equations are based), from physical and statistic viewpoints. A very fine numerical technique (Liao, 2009) with negligible truncation and round-off errors, called here the "clean numerical simulation" (CNS), is applied to investigate the propagation of the micro-level unavoidable uncertain fluctuation (caused by the continuum-assumption of fluid) of initial conditions for Lorenz equation with chaotic solutions. Our statistic analysis based on CNS computation of 10,000 samples shows that, due to the SDIC, the uncertainty of the micro-level statistic fluctuation of initial conditions transfers into the macroscopic randomness of chaos. This suggests that chaos might be a bridge from micro-level uncertainty to macroscopic randomness, and thus would be an origin of macroscopic randomness. We reveal in this article that, due to the SDIC of chaos and the inherent uncertainty of initial data, accurate long-term prediction of chaotic solution is not only impossible in mathematics but also has no physical meanings. This might provide us a new, different viewpoint to deepen and enrich our understandings about the SDIC of chaos.

S. J. Liao

2011-08-23

389

Topographic variations in chaos on Europa: Implications for diapiric formation

NASA Technical Reports Server (NTRS)

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.

Schenk, Paul M.; Pappalardo, Robert T.

2004-01-01

390

NSDL National Science Digital Library

In this unit, "students explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using links. They also learn that the order property does not hold for subtraction and explore the relation between addition and subtraction. Students write story problems in which subtraction is required and begin to memorize the subtraction facts. A brief bibliography of related books for children is provided." (from NCTM's Illuminations)

Math, Illuminations N.

2008-12-18

391

The author presents two tricks to accelerate depth-first search algorithms\\u000afor a class of combinatorial puzzle problems, such as tiling a tray by a fixed\\u000aset of polyominoes. The first trick is to implement each assumption of the\\u000asearch with reversible local operations on doubly linked lists. By this trick,\\u000aevery step of the search affects the data incrementally.\\u000a The

Donald E. Knuth

2000-01-01

392

NSDL National Science Digital Library

This site was created to provide information, research, and networking for people working in urban and community forestry. It is meant to inform, educate, and inspire the researcher, arborist, community group leader, and volunteer. The site contains: educational materials, how-to guides, a research database, discussion forums, a quarterly web-zine, a comprehensive link list of national and local resources, late-breaking news, interactive tools for tree identification and selection, and an Ask an Arborist section.

393

Nonlinear analysis of correlations in Alu repeat sequences in DNA

NASA Astrophysics Data System (ADS)

We report on a nonlinear analysis of deterministic structures in Alu repeats, one of the richest repetitive DNA sequences in the human genome. Alu repeats contain the recognition sites for the restriction endonuclease AluI, which is what gives them their name. Using the nonlinear prediction method developed in chaos theory, we find that all Alu repeats have novel deterministic structures and show strong nonlinear correlations that are absent from exon and intron sequences. Furthermore, the deterministic structures of Alus of younger subfamilies show panlike shapes. As young Alus can be seen as mutation free copies from the “master genes,” it may be suggested that the deterministic structures of the older subfamilies are results of an evolution from a “panlike” structure to a more diffuse correlation pattern due to mutation.

Xiao, Yi; Huang, Yanzhao; Li, Mingfeng; Xu, Ruizhen; Xiao, Saifeng

2003-12-01

394

NASA Astrophysics Data System (ADS)

This paper discusses nonlinear dynamos where the nonlinearity arises directly via the Lorentz force in the Navier-Stokes equation, and leads to a situation where the Lorentz force and the velocity and the magnetic field are in direct competition over substantial regions of the flow domain. Filamentary and non-filamentary dynamos are contrasted, and the concept of Alfvénic dynamos with almost equal magnetic and kinetic energies is reviewed via examples. So far these remain in the category of toy models; the paper concludes with a discussion of whether similar dynamos are likely to exist in astrophysical objects, and whether they can model the solar cycle.

Galloway, David

2011-08-01

395

In this work, the topologies of networks constructed from time series from an underlying system undergo a period doubling cascade have been explored by means of the prevalence of different motifs using an efficient computational motif detection algorithm. By doing this we adopt a refinement based on the $k$ nearest neighbor recurrence-based network has been proposed. We demonstrate that the refinement of network construction together with the study of prevalence of different motifs allows a full explosion of the evolving period doubling cascade route to chaos in both discrete and continuous dynamical systems. Further, this links the phase space time series topologies to the corresponding network topologies, and thus helps to understand the empirical "superfamily" phenomenon, as shown by Xu.

Ruoxi Xiang; Michael Small

2014-06-18

396

Time-dependent generalized polynomial chaos

Generalized polynomial chaos (gPC) has non-uniform convergence and tends to break down for long-time integration. The reason is that the probability density distribution (PDF) of the solution evolves as a function of time. The set of orthogonal polynomials associated with the initial distribution will therefore not be optimal at later times, thus causing the reduced efficiency of the method for long-time integration. Adaptation of the set of orthogonal polynomials with respect to the changing PDF removes the error with respect to long-time integration. In this method new stochastic variables and orthogonal polynomials are constructed as time progresses. In the new stochastic variable the solution can be represented exactly by linear functions. This allows the method to use only low order polynomial approximations with high accuracy. The method is illustrated with a simple decay model for which an analytic solution is available and subsequently applied to the three mode Kraichnan-Orszag problem with favorable results.

Gerritsma, Marc, E-mail: M.I.Gerritsma@TUDelft.n [Department of Aerospace Engineering, TU Delft (Netherlands); Steen, Jan-Bart van der, E-mail: jan-bart-vander.steen@siemens.co [Siemens Nederland N.V., Prinses Beatrixlaan 800 , P.O. Box 16068, 2500 BB The Hague (Netherlands); Vos, Peter, E-mail: Belgium.peter.vos@vito.b [Flemish Institute for Technological Research (VITO), Unit Environmental Modelling, Boeretang 200, 2400 Mol (Belgium); Karniadakis, George, E-mail: gk@dam.brown.ed [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)

2010-11-01

397

Genotoxicity of drinking water from Chao Lake

Genotoxic activity appears to originate primarily from reactions of chlorine with humic substances in the source waters. Comparisons of extracts of settled versus chlorinated water have confirmed that chlorinating during water treatment produces mutagenic activity in the mutagenicity tests. Present work on XAD-2 extracts of raw, chlorinated (treated), and settled water from the Chao Lake region of China has involved a battery of mutagenicity assays for various genetic endpoints: the Salmonella test, the sister-chromatid exchange (SCE) induction in Chinese hamster lung (CHL) cells, and the micronucleus (MN) induction in the peripheral blood erythrocytes of silver carp. Extracts of raw and treated water but not the settled water are mutagenic in the Salmonella assay. On the other hand, extracts of three water samples show activity in the SCE and MN assays, especially the raw and treated water. These data show that contamination and chlorinating contribute mutagens to drinking water and suggest that the mammalian assays may be more sensitive for detecting mutagenicity in aquatic environment than the Salmonella test.

Liu, Q.; Jiao, Q.C. [Nanjing Univ. (China). Dept. of Biological Science and Technology] [Nanjing Univ. (China). Dept. of Biological Science and Technology; Huang, X.M.; Jiang, J.P.; Cui, S.Q.; Yao, G.H.; Jiang, Z.R.; Zhao, H.K.; Wang, N.Y. [Anhui Antiepidemic Station, Hefei (China)] [Anhui Antiepidemic Station, Hefei (China)

1999-02-01

398

Melnikov's criteria and chaos in systems with fractional order deflection

NASA Astrophysics Data System (ADS)

In this paper a qualitative analysis of the dynamic systems described with the second-order differential equation with fractional order deflection function is considered. The existence of fixed points, closed orbits and the unions of fixed points and the trajectories connecting them is shown. The homoclinic orbit which connects a fixed point with itself and the corresponding stable and unstable manifolds are given in the closed analytical form. Melnikov's procedure for defining the criteria for transversal intersection of the stable and unstable manifolds is extended for the systems with fractional order deflection function. The critical parameter values for chaos are obtained analytically and proved numerically using the Lyapunov exponents. The bifurcation diagrams are plotted for various values of fractional order and the transition to chaos by period doubling is shown. The phase plane diagrams and the Poincare maps for certain fractional orders are obtained. The control of chaos and the transformation to periodic motion is considered.

Cveticanin, L.; Zukovic, M.

2009-10-01

399

Regularity and chaos in interacting two-body systems.

We study classical and quantum chaos for two interacting particles on the plane. This is the simplest nontrivial case which sheds light on chaos in interacting many-body systems. The system consists of a confining one-body potential, assumed to be a deformed harmonic oscillator, and a two-body interaction of Coulomb type. In general, the dynamics is mixed with regular and chaotic trajectories. The relative roles of the one-body field and the two-body interaction are investigated. Chaos sets in as the strength of the two-body interaction increases. However, the degree of chaoticity strongly depends on the shape of the one-body potential and, for some shapes of the harmonic oscillator, the dynamics remains regular for all values of the two-body interaction. Scaling properties are found for the classical as well as for the quantum mechanical problem. PMID:15524612

Radionov, Sergey; Aberg, Sven; Guhr, Thomas

2004-09-01

400

Nonlinear Dynamics, Magnitude-Period Formula and Forecasts on Earthquake

Based on the geodynamics, an earthquake does not take place until the momentum-energy excess a faulting threshold value of rock due to the movement of the fluid layer under the rock layer and the transport and accumulation of the momentum. From the nonlinear equations of fluid mechanics, a simplified nonlinear solution of momentum corresponding the accumulation of the energy could be derived. Otherwise, a chaos equation could be obtained, in which chaos corresponds to the earthquake, which shows complexity on seismology, and impossibility of exact prediction of earthquakes. But, combining the Carlson-Langer model and the Gutenberg-Richter relation, the magnitude-period formula of the earthquake may be derived approximately, and some results can be calculated quantitatively. For example, we forecast a series of earthquakes of 2004, 2009 and 2014, especially in 2019 in California. Combining the Lorenz model, we discuss the earthquake migration to and fro. Moreover, many external causes for earthquake are merely the initial conditions of this nonlinear system.

Yi-Fang Chang

2008-02-02

401

Biological Experimental Observations of an Unnoticed Chaos as Simulated by the Hindmarsh-Rose Model

An unnoticed chaotic firing pattern, lying between period-1 and period-2 firing patterns, has received little attention over the past 20 years since it was first simulated in the Hindmarsh-Rose (HR) model. In the present study, the rat sciatic nerve model of chronic constriction injury (CCI) was used as an experimental neural pacemaker to investigate the transition regularities of spontaneous firing patterns. Chaotic firing lying between period-1 and period-2 firings was observed located in four bifurcation scenarios in different, isolated neural pacemakers. These bifurcation scenarios were induced by decreasing extracellular calcium concentrations. The behaviors after period-2 firing pattern in the four scenarios were period-doubling bifurcation not to chaos, period-doubling bifurcation to chaos, period-adding sequences with chaotic firings, and period-adding sequences with stochastic firings. The deterministic structure of the chaotic firing pattern was identified by the first return map of interspike intervals and a short-term prediction using nonlinear prediction. The experimental observations closely match those simulated in a two-dimensional parameter space using the HR model, providing strong evidences of the existence of chaotic firing lying between period-1 and period-2 firing patterns in the actual nervous system. The results also present relationships in the parameter space between this chaotic firing and other firing patterns, such as the chaotic firings that appear after period-2 firing pattern located within the well-known comb-shaped region, periodic firing patterns and stochastic firing patterns, as predicted by the HR model. We hope that this study can focus attention on and help to further the understanding of the unnoticed chaotic neural firing pattern. PMID:24339962

Gu, Huaguang

2013-01-01

402

Biological experimental observations of an unnoticed chaos as simulated by the Hindmarsh-Rose model.

An unnoticed chaotic firing pattern, lying between period-1 and period-2 firing patterns, has received little attention over the past 20 years since it was first simulated in the Hindmarsh-Rose (HR) model. In the present study, the rat sciatic nerve model of chronic constriction injury (CCI) was used as an experimental neural pacemaker to investigate the transition regularities of spontaneous firing patterns. Chaotic firing lying between period-1 and period-2 firings was observed located in four bifurcation scenarios in different, isolated neural pacemakers. These bifurcation scenarios were induced by decreasing extracellular calcium concentrations. The behaviors after period-2 firing pattern in the four scenarios were period-doubling bifurcation not to chaos, period-doubling bifurcation to chaos, period-adding sequences with chaotic firings, and period-adding sequences with stochastic firings. The deterministic structure of the chaotic firing pattern was identified by the first return map of interspike intervals and a short-term prediction using nonlinear prediction. The experimental observations closely match those simulated in a two-dimensional parameter space using the HR model, providing strong evidences of the existence of chaotic firing lying between period-1 and period-2 firing patterns in the actual nervous system. The results also present relationships in the parameter space between this chaotic firing and other firing patterns, such as the chaotic firings that appear after period-2 firing pattern located within the well-known comb-shaped region, periodic firing patterns and stochastic firing patterns, as predicted by the HR model. We hope that this study can focus attention on and help to further the understanding of the unnoticed chaotic neural firing pattern. PMID:24339962

Gu, Huaguang

2013-01-01

403

Distributed source coding using chaos-based cryptosystem

NASA Astrophysics Data System (ADS)

A distributed source coding scheme is proposed by incorporating a chaos-based cryptosystem in the Slepian-Wolf coding. The punctured codeword generated by the chaos-based cryptosystem results in ambiguity at the decoder side. This ambiguity can be removed by the maximum a posteriori decoding with the help of side information. In this way, encryption and source coding are performed simultaneously. This leads to a simple encoder structure with low implementation complexity. Simulation results show that the encoder complexity is lower than that of existing distributed source coding schemes. Moreover, at small block size, the proposed scheme has a performance comparable to existing distributed source coding schemes.

Zhou, Junwei; Wong, Kwok-Wo; Chen, Jianyong

2012-12-01

404

Non-Markovian Quantum Dynamics and Classical Chaos

We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude-a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.

I. Garcia-Mata; C. Pineda; D. A. Wisniacki

2012-04-16

405

Non-Markovian quantum dynamics and classical chaos

NASA Astrophysics Data System (ADS)

We study the influence of a chaotic environment in the evolution of an open quantum system. We show that there is an inverse relation between chaos and non-Markovianity. In particular, we remark on the deep relation of the short time non-Markovian behavior with the revivals of the average fidelity amplitude—a fundamental quantity used to measure sensitivity to perturbations and to identify quantum chaos. The long time behavior is established as a finite size effect which vanishes for large enough environments.

García-Mata, Ignacio; Pineda, Carlos; Wisniacki, Diego

2012-08-01

406

Information Geometry and Chaos on Negatively Curved Statistical Manifolds

A novel information-geometric approach to chaotic dynamics on curved statistical manifolds based on Entropic Dynamics (ED) is suggested. Furthermore, an information-geometric analogue of the Zurek-Paz quantum chaos criterion is proposed. It is shown that the hyperbolicity of a non-maximally symmetric 6N-dimensional statistical manifold M_{s} underlying an ED Gaussian model describing an arbitrary system of 3N non-interacting degrees of freedom leads to linear information-geometric entropy growth and to exponential divergence of the Jacobi vector field intensity, quantum and classical features of chaos respectively.

Carlo Cafaro

2008-10-25

407

Routes to spatiotemporal chaos in Kerr optical frequency combs.

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. PMID:24697375

Coillet, Aurélien; Chembo, Yanne K

2014-03-01

408

Preface to the Focus Issue: Chaos Detection Methods and Predictability

NASA Astrophysics Data System (ADS)

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.

Gottwald, Georg A.; Skokos, Charalampos

2014-06-01

409

Chaos-assisted emission from asymmetric resonant cavity microlasers

We study emission from quasi-one-dimensional modes of an asymmetric resonant cavity that are associated with a stable periodic ray orbit confined inside the cavity by total internal reflection. It is numerically demonstrated that such modes exhibit directional emission, which is explained by chaos-assisted emission induced by dynamical tunneling. Fabricating semiconductor microlasers with an asymmetric resonant cavity, we experimentally demonstrate the selective excitation of the quasi-one-dimensional modes by employing the device structure to preferentially inject currents to these modes and observe directional emission in good accordance with the theoretical prediction based on chaos-assisted emission.

Shinohara, Susumu; Hentschel, Martina [Max-Planck-Institut fuer Physik Komplexer Systeme, Noethnitzer Strasse 38, D-01187 Dresden (Germany); Harayama, Takahisa; Sunada, Satoshi [NTT Communication Science Laboratories, NTT Corporation, 2-4 Hikaridai, Seika-cho, Soraku-gun, Kyoto 619-0237 (Japan); Fukushima, Takehiro [Department of Communication Engineering, Okayama Prefectural University, 111 Kuboki, Soja, Okayama 719-1197 (Japan); Narimanov, Evgenii E. [Birck Nanotechnology Center, Department of Electrical and Computer Engineering, Purdue University, 1205 West State Street, West Lafayette, Indiana 47907-2057 (United States)

2011-05-15

410

FAST TRACK COMMUNICATION: Kac Moody algebras and controlled chaos

NASA Astrophysics Data System (ADS)

Compactification can control chaotic Mixmaster behaviour in gravitational systems with p-form matter: we consider this in light of the connection between supergravity models and Kac Moody algebras. We show that different compactifications define 'mutations' of the algebras associated with the noncompact theories. We list the algebras obtained in this way, and find novel examples of wall systems determined by Lorentzian (but not hyperbolic) algebras. Cosmological models with a smooth pre-big bang phase require that chaos is absent: we show that compactification alone cannot eliminate chaos in the simplest compactifications of the heterotic string on a Calabi Yau, or M theory on a manifold of G2 holonomy.

Wesley, Daniel H.

2007-02-01

411

Chaos in human behavior: the case of work motivation.

This study considers the complex dynamics of work motivation. Forty-eight employees completed a work-motivation diary several times per day over a period of four weeks. The obtained time series were analysed using different methodologies derived from chaos theory (i.e. recurrence plots, Lyapunov exponents, correlation dimension and surrogate data). Results showed chaotic dynamics in 75% of cases. The findings confirm the universality of chaotic behavior within human behavior, challenge some of the underlying assumptions on which work motivation theories are based, and suggest that chaos theory may offer useful and relevant information on how this process is managed within organizations. PMID:20480693

Navarro, José; Arrieta, Carlos

2010-05-01

412

Nonlinear antennas combine advances in nonlinear dynamics, active antenna design, and analog microelectronics to generate beam steering and beam forming across an array of nonlinear oscillators. Nonlinear antennas exploit two phenomena typically shunned in traditional designs: nonlinear unit cells and interelement coupling. The design stems from nonlinear coupled differential equation analysis that by virtue of the dynamic control is far

BRIAN K. MEADOWS; TED H. HEATH; JOSEPH D. NEFF; EDGAR A. BROWN; DAVID W. FOGLIATTI; MICHAEL GABBAY; V. In; P. Hasler; S. P. Deweerth; W. L. Ditto

2002-01-01

413

Chaos Synchronization: a Lagrange Programming Network Approach

simulation examples for identical and nonÂidentical chaotic systems. The schemes are illustrated on Chua have been analysed espeÂ cially for ad hoc examples of general interest such as Chua's circuit and Lorenz attractor or for classes of nonlinear systems, e.g. Lur'e systems [Chen & Dong, 1998; Wu & Chua

414

Bifurcations in a Mathieu equation with cubic nonlinearities: Part II

In a previous paper [Chaos Solitons Fract. 14(2) (2002) 173], the authors investigated the dynamics of the equation:d2xdt2+(?+?cost)x+?Ax3+Bx2dxdt+Cxdxdt2+Ddxdt3=0We used the method of averaging in the neighborhood of the 2:1 resonance in the limit of small forcing and small nonlinearity. We found that a degenerate bifurcation point occurs in the resulting slow flow and some of the bifurcations near this point

Leslie Ng; Richard Rand

2002-01-01

415

In a paper published in this journal in 2001 by Dong et al. [W. G. Dong, X. Y. Huang, and Q. L. Wo, J. Acoust. Soc. Am. 110, 120-126 (2001)] it was claimed that acoustic chaos was obtained experimentally by the nonlinear interaction of two acoustic waves in a duct. In this comment a simple experimental setup and an analytical model is used to show that the dynamics of such systems corresponds to a quasiperiodic motion, and not to a chaotic one. PMID:19045755

Castrejón-Pita, A A; Castrejón-Pita, J R; Huelsz, G; Sarmiento-Galán, A

2008-11-01

416

Theory of weakly nonlinear self sustained detonations

We propose a theory of weakly nonlinear multi-dimensional self sustained detonations based on asymptotic analysis of the reactive compressible Navier-Stokes equations. We show that these equations can be reduced to a model consisting of a forced, unsteady, small disturbance, transonic equation and a rate equation for the heat release. In one spatial dimension, the model simplifies to a forced Burgers equation. Through analysis, numerical calculations and comparison with the reactive Euler equations, the model is demonstrated to capture such essential dynamical characteristics of detonations as the steady-state structure, the linear stability spectrum, the period-doubling sequence of bifurcations and chaos in one-dimensional detonations and cellular structures in multi- dimensional detonations.

Faria, Luiz M; Rosales, Rodolfo R

2014-01-01

417

NSDL National Science Digital Library

Hosted by the Yerkes Regional Primate Research Center at Emory University, the Living Links site specializes in "comparisons of the social life, ecology, cognition, neurology, and molecular genetics of apes and humans." With an emphasis on the four extant great apes (bonobos, chimpanzees, gorillas, and orangutans), this educational site attempts "1) to reconstruct human evolution, 2) pinpoint the differences and similarities between humans and apes, and 3) educate the public about apes, and promote their well-being and conservation." The Info section provides a long (hyperlinked) list of general information on apes, from Allogrooming to Wooly spider monkeys. The Research section gives a brief overview of the Yerkes Center's research questions (and their evolutionary context), and Animals describes the Center's study animals -- three main social groups of chimpanzees -- with a special vocalizations feature. For those interested in learning more about apes and how our ancestry is intertwined with theirs, this site will be of interest.

418

NSDL National Science Digital Library

The JFK Link is an archive of documents relevant to the "life, administration, death, and legacy" of John Fitzgerald Kennedy. Understanding and experiencing the annoyance of trying to locate political speeches, Phil Hopley has produced a Web site that makes JFK's career speeches free and easily accessible to anyone. In its nascent stages, the site currently contains materials of the 1960 Presidential Campaign for then Senator John F. Kennedy and Vice President Richard Nixon. These materials include speeches, remarks, press conferences, study papers, and statements given by both candidates from August 1 - November 7, 1960. Forthcoming are public messages, speeches, and statements of JFK from the dates January 20, 1961 to November 22, 1963; he also plans to offer select speeches made by JFK from 1947 to 1960.

Hopley, Phil.

1999-01-01

419

NSDL National Science Digital Library

Link TV was created in 1999 and it is dedicated to "providing global perspectives on news, events and culture." It is, as its homepage says, "television without borders", and visitors to the site can watch topical documentaries, listen to world music, and check out their podcast series. In the "Watch" area, the site profiles some of the more recent offerings, which include everything from Middle East news digests, a Taarab music festival from Morocco, and a documentary on child rights. Along the bottom of the homepage, visitors can look over the archives of series like "Made in Taiwan" and "World Music Videos". The site is quite media rich, and visitors can also sign up to receive updates via Twitter, Facebook, and MySpace. Finally, visitors can use the "Get Involved" area to learn more about how they can continue the conversations around some of these programs in other venues.

420

Saturn's F Ring Core: Calm Amidst Chaos

NASA Astrophysics Data System (ADS)

Near the edge of Saturn's Roche Zone the F ring is straddled on either side by two small satellites Prometheus and Pandora and as such undergoes perturbations that result in orbital chaos (Scargle et al 1993 DPS 25, #26.04, Winter et al 2007 MNRAS 380, L54; 2010 A&A 523, A67). Even in such an unstable environment the F ring appears to be relatively stable. Thus we postulate there are quiescent stable zones arising from mutual resonant interactions from the two ring moons. It is in one of these zones we believe the F ring has found a stable foothold despite the chaotic orbits in the region. At locations we call "anti-resonances" ring particles have much smaller changes over time in their semi-major axes and eccentricities than particles outside of these anti-resonance zones. We devise an impulse-based perturbation model that explains the orbital outcomes from successive perturbations from two satellites. In addition we compute the orbital evolution of thousands of mass-less test particles with a Bulirsch-Stoer N-body integrator over a narrow radial range covering the F ring core region at high spatial resolution. We find that the variance of the semi-major axes of particles in anti-resonances can be less than ~1km over a period of 32 years, while just a few kilometers away in either radial direction the variance can be tens of kilometers. More importantly, particles outside of these stable zones can migrate into a stable zone due to chaotic orbits, but once they enter an anti-resonance zone they remain there. The anti-resonances act as long-lived sinks for ring particles and explain the location of the F ring core despite its location not being in overall torque balance with ring moons.

Whizin, A.; Cuzzi, J.; Hogan, R.; Dobrovolskis, A.; Colwell, J. E.; Scargle, J.; Dones, L.; Showalter, M.

2012-12-01

421

The Small Saturnian Satellites -- Chaos and Conundrum

NASA Astrophysics Data System (ADS)

From an analysis of Hubble Space Telescope data French et al. (2003 Icarus, 162, 143) found that the orbits of Prometheus and Pandora, which flank Saturn's ring, exhibited unexpected variations in their semimajor axes and mean motions. Goldreich and Rappaport (2003 Icarus, 162, 391) showed that those variations were caused by a chaotic interaction between the satellites. We report on the practical consequences that the chaos has on the production of ephemerides needed to support the Cassini mission and on the post Cassini ephemerides.Recently El Moutamid et al. (2014 Celest. Mech., 118, 235) proposed that the motions of three other satellites, Anthe, Methone, and Aegaeon could also be chaotic as a result of their mean motion resonances with Mimas. Coincidentally, the current orbits of the three satellites are a poor fit to the Cassini imaging data even though the direct perturbation of Mimas is included in the orbit computations. We discuss the status of our attempts to improve the orbit modelling for these satellites and the implications of their possibly chaotic behavior. Daphnis is a small satellite orbiting in the narrow (40 km) Keeler Gap in Saturn's rings. It was discovered in 2004 and found to have a near circular orbit in the ring gap. That orbit fits Cassini imaging data from 2004 to 2010 quite well, but it cannot fit the imaging acquired subsequent to late 2012. To fit the later data requires a circular orbit with a semimajor axis some 3 km larger. Moreover, no observations were made between 2010 and late 2012. We speculate on possible causes for the orbit change.

Jacobson, Robert A.

2014-05-01

422

A closer look at Chaos on Europa

NASA Technical Reports Server (NTRS)

This mosaic of the Conamara Chaos region on Jupiter's moon, Europa, clearly indicates relatively recent resurfacing of Europa's surface. Irregularly shaped blocks of water ice were formed by the break up and movement of the existing crust. The blocks were shifted, rotated, and even tipped and partially submerged within a mobile material that was either liquid water, warm mobile ice, or an ice and water slush. The presence of young fractures cutting through this region indicates that the surface froze again into solid, brittle ice.

The background image in this picture was taken during Galileo's sixth orbit of Jupiter in February, 1997. Five very high resolution images which were taken during the spacecraft's twelfth orbit in December, 1997 provide an even closer look at some of the details. This mosaic shows some of the high resolution data inset into the context of this tumultuous region.

North is to the top of the picture, and the sun illuminates the scene from the east (right). The picture, centered at 9 degrees north latitude and 274 degrees west longitude, covers an area approximately 35 by 50 kilometers (20 by 30 miles). The finest details visible in the very high resolution insets are about 20 meters (22 yards) across, and in the background image, 100 meters (110 yards) across. The insets were taken on December 16, 1997, at ranges as close as 880 kilometers (550 miles) by the Solid State Imaging (SSI) system on NASA's Galileo spacecraft.

The Jet Propulsion Laboratory, Pasadena, CA manages the Galileo mission for NASA's Office of Space Science, Washington, DC. JPL is an operating division of California Institute of Technology (Caltech).

This image and other images and data received from Galileo are posted on the World Wide Web, on the Galileo mission home page at URL http://galileo.jpl.nasa.gov. Background information and educational context for the images can be found at URL http://www.jpl.nasa.gov/galileo/sepo

1998-01-01

423

Nonlinear Analysis of Heartbeat Time Series

NASA Astrophysics Data System (ADS)

The hypothesis that Heart Rate Variability (HRV) may exhibit the features of deterministic low-dimensional chaos (A.L. Goldberger et al., Sci. Am. 262, 42 (1990)) still lacks a clear demonstration. The purpose of the present report is to evaluate the degree of nonlinearity in the interbeat time interval series obtained from healthy subjects in different physiological conditions (daytime, sleeping, relaxation). It is well known, in fact, that HRV is influenced by the activity the subject is performing. Different methods were used: the classical nonlinear prediction (G. Sugihara and R.M. May, Nature 344, 734 (1990)), the S-map method recently proposed (G. Sugihara, Phil. Trans. R. Soc. Lond. A 348, 477 (1994)), and the detection of the Periodic Unstable Fixed Points (PUFPs) (S.J. Schiff et al., Nature 370, 615 (1994)). The first results indicate: 1) a short term predictability, quantified by the normalized prediction error, higher during sleep and relaxation than during daytime activity; 2) a weak, but systematic nonlinearity, present in all the data analyzed. The occurrence of the short term predictability is being further investigated to reject the hypothesis that it depends on external physiological influences other than the intrinsic heartbeat generating process.

di Garbo, A.; Barbi, M.; Chillemi, S.; Balocchi, R.; Michelassi, C.; Carpeggiani, C.; Emdin, M.; Santarcangelo, E.

1996-03-01

424

Chaos in the classroom: Exposing gifted elementary school children to chaos and fractals

NASA Astrophysics Data System (ADS)

A unit of study for gifted 4th and 5th graders is described on the subject of mathematical periodicity and chaos and the underlying physical processes which produce these phenomena. A variety of hands-on experiments and the use of various data analysis tools and computer aids provide students with powerful raw material for their analysis, interpretation, and understanding. The concepts of simple periodic motion (e.g., a pendulum), complex superposition of motions (e.g., the vibrations in musical instruments), and chaotic sequences (e.g., stock prices) are covered, with numerous practical examples. Opportunities to involve related activities emphasizing language arts, history, and graphic art are included. The student response to the material is documented.

Adams, Helen M.; Russ, John C.

1992-09-01

425

Doubly Transient Chaos: The Generic Form of Chaos in Autonomous Dissipative Systems

Chaos is an inherently dynamical phenomenon traditionally studied for trajectories that are either permanently erratic or transiently influenced by permanently erratic ones lying on a set of measure zero. The latter gives rise to the final state sensitivity observed in connection with fractal basin boundaries in conservative scattering systems and driven dissipative systems. Here we focus on the most prevalent case of undriven dissipative systems, whose transient dynamics fall outside the scope of previous studies since no time-dependent solutions can exist for asymptotically long times. We show that such systems can exhibit positive finite-time Lyapunov exponents and fractal-like basin boundaries which nevertheless have codimension one. In sharp contrast with its driven and conservative counterparts, the settling rate to the (fixed-point) attractors grows exponentially in time, meaning that the fraction of trajectories away from the attractors decays super-exponentially. While no invariant chaotic sets exist...

Motter, Adilson E; Karolyi, Gyorgy; Tel, Tamas

2013-01-01

426

Alexander B. Medvinsky \\emph{et al} [A. B. Medvinsky, I. A. Tikhonova, R. R. Aliev, B.-L. Li, Z.-S. Lin, and H. Malchow, Phys. Rev. E \\textbf{64}, 021915 (2001)] and Marcus R. Garvie \\emph{et al} [M. R. Garvie and C. Trenchea, SIAM J. Control. Optim. \\textbf{46}, 775-791 (2007)] shown that the minimal spatially extended reaction-diffusion model of phytoplankton-zooplankton can exhibit both regular, chaotic behavior, and spatiotemporal patterns in a patchy environment. Based on that, the spatial plankton model is furtherly investigated by means of computer simulations and theoretical analysis in the present paper when its parameters would be expected in the case of mixed Turing-Hopf bifurcation region. Our results show that the spiral waves exist in that region and the spatiotemporal chaos emerge, which arise from the far-field breakup of the spiral waves over large ranges of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually involve the whole space within that region. Our results are confirmed by means of computation spectra and nonlinear bifurcation of wave trains. Finally, we give some explanations about the spatially structured patterns from the community level.

Quan-Xing Liu; Gui-Quan Sun; Bai-Lian Li; Zhen Jin

2007-04-03

427

Nonlinear Statistical Modeling of Speech

NASA Astrophysics Data System (ADS)

Contemporary approaches to speech and speaker recognition decompose the problem into four components: feature extraction, acoustic modeling, language modeling and search. Statistical signal processing is an integral part of each of these components, and Bayes Rule is used to merge these components into a single optimal choice. Acoustic models typically use hidden Markov models based on Gaussian mixture models for state output probabilities. This popular approach suffers from an inherent assumption of linearity in speech signal dynamics. Language models often employ a variety of maximum entropy techniques, but can employ many of the same statistical techniques used for acoustic models. In this paper, we focus on introducing nonlinear statistical models to the feature extraction and acoustic modeling problems as a first step towards speech and speaker recognition systems based on notions of chaos and strange attractors. Our goal in this work is to improve the generalization and robustness properties of a speech recognition system. Three nonlinear invariants are proposed for feature extraction: Lyapunov exponents, correlation fractal dimension, and correlation entropy. We demonstrate an 11% relative improvement on speech recorded under noise-free conditions, but show a comparable degradation occurs for mismatched training conditions on noisy speech. We conjecture that the degradation is due to difficulties in estimating invariants reliably from noisy data. To circumvent these problems, we introduce two dynamic models to the acoustic modeling problem: (1) a linear dynamic model (LDM) that uses a state space-like formulation to explicitly model the evolution of hidden states using an autoregressive process, and (2) a data-dependent mixture of autoregressive (MixAR) models. Results show that LDM and MixAR models can achieve comparable performance with HMM systems while using significantly fewer parameters. Currently we are developing Bayesian parameter estimation and discriminative training algorithms for these new models to improve noise robustness.

Srinivasan, S.; Ma, T.; May, D.; Lazarou, G.; Picone, J.

2009-12-01

428

Fundamental Models for Fuel Cell Engineering Chao-Yang Wang*

.4. Electron Transport 4740 3.5. Transient Phenomena 4741 3.6. Large-Scale Simulation 4742 3.7. Liquid WaterFundamental Models for Fuel Cell Engineering Chao-Yang Wang* Departments of Mechanical Engineering Fuel Cell Dynamics 4727 2.1. CFCD Model Equations 4728 2.2. Computational Aspects 4729 2.2.1. General

429

Nonequilibrium pattern formation and spatiotemporal chaos in fluid convection

The final report for grant number DE-FG03-98ER14891 summarizes the application of the unique simulation capabilities developed under DOE support to investigations of important issues in pattern formation and spatiotemporal chaos in Rayleigh-Benard convection, particularly emphasizing quantitative contact with the active experimental programs.

Michael Cross

2006-09-13

430

Security problems with a chaos-based deniable authentication scheme

Recently, a new scheme was proposed for deniable authentication. Its main originality lied on applying a chaos-based encryption-hash parallel algorithm and the semi-group property of the Chebyshev chaotic map. Although original and practicable, its insecurity and inefficiency are shown in this paper, thus rendering it inadequate for adoption in e-commerce.

G. Alvarez

2004-12-09

431

Fractal Patterns and Chaos Games Robert L. Devaney

Fractal Patterns and Chaos Games Robert L. Devaney #3; May 22, 2003 #3; Please address all correspondence to Robert L. Devaney, Department of Mathematics, Boston University, Boston MA 02215, or email bob and Koch curve has been known for many years by a handful of research math- ematicians, it was only

Devaney, Robert L.

432

Introduction to STM induced Luminescence Zhen-Chao Dong

Introduction to STM induced Luminescence Zhen-Chao Dong University of Science and Technology Â· Luminescence from metal-oxide-metal (MOM) tunnel junctions Â· Early studies of photon emission by STM 2. Status of STM Induced Luminescence Â· Metals Â· Semiconductors Â· Molecules and Nanostructures Â· Theoretical

Wang, Wei Hua

433

Hydrothermal plume dynamics on Europa: Implications for chaos formation

a liquid ocean to the base of its ice shell. This process has been implicated in the formation of chaos existing work describing buoyant plumes in a rotating, unstratified environment. We discuss the scaling scaling constants and to visualize plume behavior in a Europa-like parameter regime. We predict

Pierrehumbert, Raymond

434

Short Lyapunov time: a method for identifying confined chaos

NASA Astrophysics Data System (ADS)

Context. The orbital instability of minor solar system bodies (asteroids, small satellites, moonlets, and particles) is frequently studied in terms of the Lyapunov characteristic exponent (LCE). Asteroids interior to Jupiter often exihibit very short Lyapunov times, TL, and very large radial variations, becoming Jupiter's crossers and escapers. However, a few cases of asteroids with very short TL and no significant radial variation have been found. These orbits were called “confined chaos” or even “stable chaos”. This feature also appeared in the case of moonlets embedded in Saturn's F ring and disturbed by the nearby satellites Prometheus and Pandora. Aims: We present a simple approach to estimating the contribution of the radial component of the LCE to identify trajectories in the “confined chaos” regime. Methods: To estimate the radial contribution to the maximum LCE, we considered a rotating reference system in which one of the axis was aligned with the radial direction of the reference trajectory. Measuring the distance in the phase space between the two nearby orbits then allowed us to separate the contribution of the radial component from the others. We applied the method to two different dynamical systems: (a) an asteroid around the Sun disturbed by Jupiter; (b) a moonlet of Saturn's F-ring disturbed by the satellites Prometheus and Pandora. Results: In all cases, we found that the method of comparing the radial contribution of the LCE to the entire contribution allows us to correctly distinguish between confined chaos and escapers.

Winter, O. C.; Mourão, D. C.; Giuliatti Winter, S. M.

2010-11-01

435

Chaos in Power Electronics: An Overview Mario di Bernardo

16 Chaos in Power Electronics: An Overview Mario di Bernardo and Chi K. Tse 1 FacoltÂ´a di The Hong Kong Polytechnic University Hong Kong, China encktse@polyu.edu.hk Abstract Power electronics dynamics and bifurcation scenarios observed in power electronics circuits, emphasizing the salient features

Tse, Chi K. "Michael"

436

(Quantum) chaos theory and statistical physics far from equilibrium

(Quantum) chaos theory and statistical physics far from equilibrium: Introducing the group for Non-equilibrium quantum and statistical physics Tomaz Prosen Department of physics, Faculty of mathematics and physics, University of Ljubljana July, 2011 Tomaz Prosen Non-equilibrium quantum and statistical physics group #12

Â?umer, Slobodan

437

Chaos in learning a simple two person game Yuzuru Sato #

Chaos in learning a simple two person game Yuzuru Sato # Brain Science Institute, RIKEN, 2 of learning to play a generalized rockÂpaperÂscissors game. Each player attempts to improve her average score by adjusting the frequency of the three possible responses. For the zeroÂsum case the learning process displays

438

Chaos in learning a simple two person game Yuzuru Sato

Chaos in learning a simple two person game Yuzuru Sato Brain Science Institute, RIKEN, 2-1 Hirosawa Hyde Park Road, Santa Fe, NM 87501 (Dated: September 7, 2001) We investigate the problem of learning by adjusting the frequency of the three possible responses. For the zero-sum case the learning process displays

439

ITERATIVELLY DECODING CHAOS ENCODED BINARY SIGNALS Francisco J. Escribano

28933 MÂ´ostoles, Madrid, Spain ABSTRACT In the present article we propose a new soft-input soft- output Naturaleza Universidad Rey Juan Carlos 28933 MÂ´ostoles, Madrid, Spain Luis LÂ´opez Laboratory of Distributed) decoding of the bit information. We believe that the design of this new chaos based SISO decoding module

Rey Juan Carlos, Universidad

440

On the Origin of Chaos in the Asteroid Belt

We consider the effect of gravitational perturbations from Jupiter on the dynamics of asteroids, when Jupiter is itself perturbed by Saturn. The presence of Saturn introduces a number of additional frequencies into Jupiter's orbit. These frequencies in turn produce chaos in narrow regions on either side of the chaotic zones associated with the mean motion resonances between the asteroids and

N. Murray; M. Holman; M. Potter

1998-01-01

441

Did Celestial Chaos Kill the Dinosaurs? Michael Ghil*

) a unified theory of groups and gaps in the asteroid belt; (ii) a novel source of robust chaos in the motion over more than 15 years. 2. Groups and gaps in the asteroid belt The asteroid belt lies between). In the outer belt, closer to Jupiter, where the overall number of asteroids is much smaller, certain resonances

Ghil, Michael

442

72 09-2011 elektor The Chaos Machine

72 09-2011 elektor retronics The Chaos Machine Analogue computing rediscovered (1) For some of us reliability. Analogue computers are machines that are built to behave as the system we want to compute. They are powerful and engaging computing machines that are cheap and simple to build. This two-part Retronics

Ambaum, Maarten

443

Gaseous Detonation-Driven Fracture of Tubes Tong Wa Chao

literature. Experimental data of this type are useful for studying the fluid- structure-fracture interaction to be consistent with fracture under mixed-mode loading. High-speed movies of the fracture events and blast waveGaseous Detonation-Driven Fracture of Tubes Thesis by Tong Wa Chao In Partial Fulfillment

444

A Truth of Molecular Chaos Yuriy E. Kuzovlev #

A Truth of Molecular Chaos Yuriy E. Kuzovlev # A.A.Galkin Physics and Technology Institute of NASU independent probability distriÂ butions '', and the like, are nothing but `` prejudices '' [2]. Especially in usual sense since almost surely have nothÂ # Electronic address: kuzovlev@kinetic.ac.donetsk.ua ing

445

Fingerprint Indexing Based on LAS Registration , Chao Zhang1

Fingerprint Indexing Based on LAS Registration Tong Liu1 , Chao Zhang1 and Pengwei Hao1,2 1 Fingerprint indexing is an efficient technique that greatly improves the performance of fingerprint based method based on fingerprint registration with a novel feature called local axial symmetry (LAS

Hao, Pengwei

446

Chaos, Poverty, and Parenting: Predictors of Early Language Development

Studies have shown that distal family risk factors like poverty and maternal education are strongly related to children's early language development. Yet, few studies have examined these risk factors in combination with more proximal day-to-day experiences of children that might be critical to understanding variation in early language. Young children's exposure to a chronically chaotic household may be one critical experience that is related to poorer language, beyond the contribution of SES and other demographic variables. In addition, it is not clear whether parenting might mediate the relationship between chaos and language. The purpose of this study was to understand how multiple indicators of chaos over children's first three years of life, in a representative sample of children living in low wealth rural communities, were related to child expressive and receptive language at 36 months. Factor analysis of 10 chaos indicators over five time periods suggested two factors that were named household disorganization and instability. Results suggested that after accounting for thirteen covariates like maternal education and poverty, one of two chaos composites (household disorganization) accounted for significant variance in receptive and expressive language. Parenting partially mediated this relationship although household disorganization continued to account for unique variance in predicting early language. PMID:23049162

Vernon-Feagans, Lynne; Garrett-Peters, Patricia; Willoughby, Mike; Mills-Koonce, Roger

2011-01-01

447

Careers Education: Evolving, Adapting and Building Resilience through Chaos

ERIC Educational Resources Information Center

Career educators' ultimate goal, given the new career management paradigm, should be to ensure that students are career resilient when they leave their studies (from whatever year level). This article outlines the chaos theory of careers and resilience. It then goes on to describe a four-lesson unit of careers education work that attempts to…

Loader, Trent

2011-01-01

448

Has chaos implied by macrovariable equations been justified?

The underlying microscopic dynamics of a deterministic chemical chaos predicted by phenomenological equations is investigated in this paper. Ensemble simulation of the master equation for the chemical Lorenz model was carried out and compared to the deterministic results. Our calculations reveal that in the chaotic regime the mass action law description is related neither to the ensemble mean nor to

Qianshu Li; Hongli Wang

1998-01-01

449

Learning Dialogically: The Art of Chaos-Informed Transformation

ERIC Educational Resources Information Center

A decision to don the chaos lens, adopt dialogue as its primary mode of communication, and to recognize the power of the organizational mind has fundamentally and irreversibly changed the way a Dutch capital-equipment manufacturer operates in its rapidly complexifying global marketplace. Beginning in September 1999, the focus of an ever widening…

van Eijnatten, Frans M.; van Galen, Maarten C.; Fitzgerald, Laurie A.

2003-01-01

450

Quantum Chaos in SU(3) Models with Trapped Ions

NASA Astrophysics Data System (ADS)

A scheme to generate long-range spin-spin interactions between three-level ions in a chain is presented, providing a feasible experimental route to the rich physics of well-known SU(3) models. In particular, we demonstrate different signatures of quantum chaos which can be controlled and observed in experiments with trapped ions.

Graß, Tobias; Juliá-Díaz, Bruno; Ku?, Marek; Lewenstein, Maciej

2013-08-01

451

Ocean Acoustics: a novel laboratory for wave chaos Steven Tomsovic

Ocean Acoustics: a novel laboratory for wave chaos Steven Tomsovic Department of Physics contexts in which it appears. In the late 1980's it was recognized that ocean acoustics was one of the propagating sound. I. INTRODUCTION Acoustic wave propagation through the ocean became a topic of immense

Tomsovic, Steve

452

Constrained Quantum Mechanics: Chaos in Non-Planar Billiards

ERIC Educational Resources Information Center

We illustrate some of the techniques to identify chaos signatures at the quantum level using as guiding examples some systems where a particle is constrained to move on a radial symmetric, but non-planar, surface. In particular, two systems are studied: the case of a cone with an arbitrary contour or "dunce hat billiard" and the rectangular…

Salazar, R.; Tellez, G.

2012-01-01

453

Chaos Modeling: Increasing Educational Researchers' Awareness of a New Tool.

ERIC Educational Resources Information Center

Chaos theory is being used as a tool to study a wide variety of phenomena. It is a philosophical and empirical approach that attempts to explain relationships previously thought to be totally random. Although some relationships are truly random, many data appear to be random but reveal repeatable patterns of behavior under further investigation.…

Bobner, Ronald F.; And Others

454

Decades of Chaos and Revolution: Showdowns for College Presidents

ERIC Educational Resources Information Center

"Decades of Chaos and Revolution: Showdowns for College Presidents" is the story and comparison of two eras in the history of higher education. The first era covers the period of the 1960s through the mid-1970s, and the second is the first decade of the twenty-first century. Both decades were marked by events that shook the foundations of colleges…

Nelson, Stephen J.

2012-01-01

455

High precision module for Chaos Many-Body Engine

In this paper we present a C# high precision relativistic many-body module integrated with Chaos Many-Body Engine. As a direct application, we used it for estimating the butterfly effect involved by the gravitational force in a specific nuclear relativistic collision toy-model.

Grossu, I V; Felea, D; Jipa, Al

2014-01-01

456

Transient chaos in a closed chemical system Stephen K. Scott*)

employed to study the onset and development of oscillations in a very simple model based on chemicalTransient chaos in a closed chemical system Stephen K. Scott*) School of Chemistry, University Virginia 26506-604.5 (Received 5 September 1990, accepted 4 October 1990) Complex oscillations and even

Showalter, Kenneth

457

Quantum Chaos and Quantum Computers D. L. Shepelyansky*

Quantum Chaos and Quantum Computers D. L. Shepelyansky* Laboratoire de Physique Quantique, UMR 5626: 03.67.Lx, 05.45.Mt, 24.10.Cn Abstract The standard generic quantum computer model is studied and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer

Shepelyansky, Dima

458

FOOD WEB CHAOS WITHOUT SUBCHAIN OSCILLATORS BRIAN BOCKELMAN & BO DENG

of the system. It occurs as the result of a period-doubling cascade from a Hopf bifurcation point. The method of singular perturbation is used to determine the Hopf bifurcation involved as well as the parameter values. 1. The prototypical chaos of the logistic map x x(1-x) ([21]) is resulted from changes in the intrinsic growth rate

Logan, David

459

hal00282243, SOME OPEN QUESTIONS IN \\WAVE CHAOS"

investigate the \\macroscopic" spectral distribution. For any surface of unit area, the behaviour of the eigenvalues and eigenstates of the operator. One is thus led, from a time-dependent (dynamical) problem, to a time-independent (spectral) problem, which forms the \\backbone" of quantum chaos: What are the spectral

460

Evolution of Cooperation: Two for Martin Ackermann and Lin Chao

Evolution of Cooperation: Two for One? Martin Ackermann and Lin Chao How can cooperation thrive cooperation a winning strategy. At least in the short term. Cooperation is ubiquitous at many levels of biological organization. Genes within a cell cooperate to replicate in a coordinated manner; cells within

Ackermann, Martin

461

Forcings and chaos in interannual to decadal climate change

We investigate the roles of climate forcings and chaos (unforced variability) in climate change via ensembles of climate simulations in which we add forcings one by one. The experiments suggest that most interannual climate variability in the period 1979-1996 at middle and high latitudes is chaotic. But observed SST anomalies, which themselves are partly forced and partly chaotic, account for

J. Hansen; M. Sato; R. Ruedy; A. Lacis; K. Asamoah; K. Beckford; S. Borenstein; E. Brown; B. Cairns; B. Carlson; B. Curran; S. de Castro; L. Druyan; P. Etwarrow; T. Ferede; M. Fox; D. Gaffen; J. Glascoe; H. Gordon; S. Hollandsworth; X. Jiang; C. Johnson; N. Lawrence; J. Lean; J. Lerner; K. Lo; J. Logan; A. Luckett; M. P. McCormick; R. McPeters; R. Miller; P. Minnis; I. Ramberran; G. Russell; P. Russell; P. Stone; I. Tegen; S. Thomas; L. Thomason; A. Thompson; J. Wilder; R. Willson; J. Zawodny

1997-01-01

462

Random-matrix theories in quantum physics and classical chaos

All the material for my lectures at the Summer School on Quantum and Classical Chaos was taken from a recent review paper (by Guhr et al.(1998), Phys. Rep., 299, 189). To avoid duplication of published material, I give here only a brief summary of the contents of each lecture, rather than a complete set of lecture notes, and I omit

H. A. Weidenmüller

2000-01-01

463

Chaos in the coherence collapse of semiconductor lasers

The authors report on the observation of a quasi-periodic route to chaos in the coherence collapse of a single-mode semiconductor laser subjected to back-reflections from an external cavity. Also, they present a simple deterministic model that correlates well with the data.

Dente, G.C. (G.C.D. Associates, 2100 Alvarado N.E., Albuquerque, NM (US)); Durkin, P.S.; Wilson, K.A.; Moeller, C.E. (US Air Force, Kirtland Air Force Base, NM (US))

1988-12-01

464

Uncertainty and Predictability in Geophysics: Chaos and Multifractal Insights

Uncertainty and Predictability in Geophysics: Chaos and Multifractal Insights Daniel Schertzer Department, McGill University, Montreal, Canada Uncertainty and error growth are crosscutting geophysical extremes. The focus is now on time-space geophysical scaling behavior: their multifractality. It is found

Lovejoy, Shaun

465

Jurassic Management: Chaos and Management Development in Educational Institutions.

ERIC Educational Resources Information Center

Investigates the failure of "Jurassic" management: visioning, consensus value systems, proactively created teams, and development planning. Applied chaos theory can help self-managing schools and colleges avoid disaster and improve their management-development programs. Survival in turbulent times is based on educational managers' capacity to make…

Gunter, Helen

1995-01-01

466

Positive Maladjustment as a Transition from Chaos to Order

ERIC Educational Resources Information Center

Dabrowski's theory of positive disintegration describes patterns and explains mechanisms of human development and has been successfully applied to understanding of gifted individuals. This article shows how the concepts of chaos theory and self-organization such as the sensitivity to initial conditions, positive and negative feedback, bifurcation…

Laycraft, Krystyna

2009-01-01

467

Turbulence and deterministic chaos. [computational fluid dynamics

NASA Technical Reports Server (NTRS)

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low Reynolds number fully developed turbulence are compared. Several flows are noted: fully chaotic, complex periodic, weakly chaotic, simple periodic, and fixed-point. Of these, only fully chaotic is classified as turbulent. Besides the sustained flows, a flow which decays as it becomes turbulent is examined. For the finest grid, 128(exp 3) points, the spatial resolution appears to be quite good. As a final note, the variation of the velocity derivatives skewness of a Navier-Stokes flow as the Reynolds number goes to zero is calculated numerically. The value of the skewness is shown to become small at low Reynolds numbers, in agreement with intuitive arguments that nonlinear terms should be negligible.

Deissler, Robert G.

1992-01-01

468

Linking morphology to ecosystem structure using air-borne sensors for monitoring the Earth System

NASA Astrophysics Data System (ADS)

Coastal Landscape, and how they change over time, provide the template on which the emerging role of Earth system science (ESS) closely linked with the development of space-borne sensors can stand in the center of a newly emerging science of the Earth's surface, where strong couplings links human dynamics, biology, biochemistry, geochemistry, geomorphology, and fluid dynamics including climate change. Modern views on the behavior of complex systems like the coastal one, allow the interpretation of phenomenological coastal landscape as a stationary landscape-state that correspond to a dynamic equilibrium, and to a self-organized exogenic order of the edge of the chaos. Therefore is essential for a thoroughly understanding of spatiotemporal variations in coastal dynamics and habitat distribution for the source of nonlinearity and complexity in geomorphic system make gathering data appropriate for use in developing and testing models of biological and physical process interacting across a wide range of scale. In this paper a physics based approach was applied to MIVIS (Multi-spectral IR and Visible Imaging Spectrometer) and LiDAR (Light Detection and Ranging) airborne data, simultaneously acquired on 12 May 2009 in order to integrate geomorphological and ecological observations into a detailed macrophytes map of Lake Trasimeno (Italy). Shallow water vegetation, in fact, plays an essential role in determining how coastal morphology and ecosystems dynamics respond to feedbacks between biological and physical processes. An accurate field campaign was carried out during the airborne survey and a collection of different biophysical parameter has been achieved. The purposes of the field observations were twofold. First, field observations allowed identification of biophysical habitats and properties associated both to radiometric and limnological features. Secondly, field reconnaissance allowed identifying significant parameters involved in optical interpretation of the shallow water body and macrophytes composition. By means of bio-optical modeling and the Spectral Mixture Analysis (SMA) hyperspectral data has been processed in order to discriminate different types of bottoms and bottom covers. The derived mapswere merged to LiDAR derived bathymetry for generating the preliminary classification and validation of the biophysical habitat. The accuracy of this processing was evaluated using bathymetric single-beam echograms acquired during the airborne campaign using a 200 kHz echosounder. Results indicate that coastal landscape analysis benefit the accurate collection of different ecological and morphological data that can be obtained from multisensory technologies leading to address to main research question of the Earth system science: which is the source of nonlinearity and complexity in coastal geomorphic system?

Taramelli, A.; Giardino, C.; Valentini, E.; Bresciani, M.; Gasperini, L.

2010-12-01

469

Application of non-linear dynamics to the characterization of cardiac electrical instability

NASA Technical Reports Server (NTRS)

Beat-to-beat alternation in the morphology of the ECG has been previously observed in hearts susceptible to fibrillation. In addition, fibrillation has been characterized by some as a chaotic state. Period doubling phenomena, such as alternation, and the onset of chaos have been connected by non-linear dynamical systems theory. In this paper, we describe the use of a technique from nonlinear dynamics theory, the construction of a first return nap, to assess the susceptibility to fibrillation threshhold in canine experiments.

Kaplan, D. T.; Cohen, R. J.

1987-01-01

470

The author presents two tricks to accelerate depth-first search algorithms for a class of combinatorial puzzle problems, such as tiling a tray by a fixed set of polyominoes. The first trick is to implement each assumption of the search with reversible local operations on doubly linked lists. By this trick, every step of the search affects the data incrementally. The second trick is to add a ghost square that represents the identity of each polyomino. Thus puts the rule that each polyomino be used once on the same footing as the rule that each square be covered once. The coding simplifies to a more abstract form which is equivalent to 0-1 integer programming. More significantly for the total computation time, the search can naturally switch between placing a fixed polyomino or covering a fixed square at different stages, according to a combined heuristic. Finally the author reports excellent performance for his algorithm for some familiar puzzles. These include tiling a hexagon by 19 hexiamonds and the N queen...

Knuth, Donald E

2009-01-01

471

SECULAR CHAOS AND THE PRODUCTION OF HOT JUPITERS

In a planetary system with two or more well-spaced, eccentric, inclined planets, secular interactions may lead to chaos. The innermost planet may gradually become very eccentric and/or inclined as a result of the secular degrees of freedom drifting toward equipartition of angular momentum deficit. Secular chaos is known to be responsible for the eventual destabilization of Mercury in our own solar system. Here we focus on systems with three giant planets. We characterize the secular chaos and demonstrate the criterion for it to occur, but leave a detailed understanding of secular chaos to a companion paper. After an extended period of eccentricity diffusion, the inner planet's pericenter can approach the star to within a few stellar radii. Strong tidal interactions and ensuing tidal dissipation extract orbital energy from the planet and pull it inward, creating a hot Jupiter. In contrast to other proposed channels for the production of hot Jupiters, such a scenario (which we term 'secular migration') explains a range of observations: the pile-up of hot Jupiters at 3 day orbital periods, the fact that hot Jupiters are in general less massive than other radial velocity planets, that they may have misaligned inclinations with respect to stellar spin, and that they have few easily detectable companions (but may have giant companions in distant orbits). Secular migration can also explain close-in planets as low in mass as Neptune; and an aborted secular migration can explain the 'warm Jupiters' at intermediate distances. In addition, the frequency of hot Jupiters formed via secular migration increases with stellar age. We further suggest that secular chaos may be responsible for the observed eccentricities of giant planets at larger distances and that these planets could exhibit significant spin-orbit misalignment.

Wu Yanqin [Department of Astronomy and Astrophysics, University of Toronto, Toronto, ON (Canada); Lithwick, Yoram [Canadian Institute of Theoretical Astrophysics, Toronto, ON (Canada)

2011-07-10

472

A High Capacity 3D Steganography Algorithm Min-Wen Chao, Chao-hung Lin, Cheng-Wei Yu, and Tong steganography scheme. Our steganography approach is based on a novel multilayered embedding scheme to hide-of-the-art approaches, while obeying the low distortion and security basic requirements for steganography on 3D models

Chen, Sheng-Wei

473

Following an introduction on analytical mechanics, canonical transformations, and perturbation theory, a description is given of nonlinear effects for near-integrable systems associated with resonances, amplitude variations with multiple crossings, adiabatic changes of the parameters, and time variation of the perturbation. Examples of applications coming from observations and calculations related to CERN accelerators concern coupling measurements, intra-beam scattering, beam-beam effects magnetic imperfections, two-beam overlap knockout, and synchro-betatron resonances. Finally, the notions of invariant distortion and aperture of bounded motion in the presence of multipoles are introduced.

Guignard, G.

1989-04-01

474

Nonhyperbolicity in Classical and Quantum Chaos

NASA Astrophysics Data System (ADS)

This thesis concerns the problem of nonhyperbolicity in classical and quantum chaos. In Part I, we investigate how often nonhyperbolic chaotic saddles occur in chaotic dynamical systems. We numerically investigate the fraction of nonhyperbolic parameter values for the Henon map in the parameter range where there exist only chaotic saddles. Newhouse and Robinson proved that the existence of one nonhyperbolic parameter value typically implies the existence of an interval ("a Newhouse interval") of nonhyperbolic parameter values. We also compute the size of the Newhouse intervals. Our results strongly suggest that (1) nonhyperbolic chaotic saddles are common in chaotic dynamical systems; and (2) the Newhouse interval can be quite large in the parameter space. In Part II, we study classically the microwave ionization of hydrogen Rydberg atoms using the standard one-dimensional model. We find that the survival probability of an electron decays algebraically for long exposure times. Furthermore, as the microwave field-strength increases, we find that the asymptotic algebraic decay exponent can decrease due to phase-space metamorphoses in which new layers of KAM islands are exposed when KAM surfaces are destroyed. We also find that after such phase-space metamorphoses, the survival probability of an electron in time can have a crossover region with different decay exponents. We argue that this phenomenon is typical for nonhyperbolic Hamiltonian systems. In Part III, we investigate the quantum manifestations of chaotic scattering for the two cases where the classical dynamics is hyperbolic and nonhyperbolic. A previous semiclassical argument for hyperbolic chaotic scattering suggested that the energy autocorrelation function C(varepsilon ) (varepsilon is the energy difference) of the quantum S-matrix elements is Lorentzian. However, we find numerically that there are cases of hyperbolic chaotic scattering in which C(varepsilon ) deviates from the predicted Lorentzian even at small varepsilon. We argue that the non-Lorentzian behavior might be due to the breakdown of the long time limit of the semiclassical analysis. For nonhyperbolic chaotic scattering, we find that the same semiclassical analysis indicates that the quantum fingerprint is a cusp in C(varepsilon) near varepsilon = 0. Our numerical experiment appears to be consistent with the expected cusp behavior. Finally, in Part IV, we discuss the critical time scaling for the breakdown of the semiclassical analysis.

Lai, Ying-Cheng

475

NASA Technical Reports Server (NTRS)

NASA's Spitzer and Hubble Space Telescopes have teamed up to expose the chaos that baby stars are creating 1,500 light-years away in a cosmic cloud called the Orion nebula.

This striking infrared and visible-light composite indicates that four monstrously massive stars at the center of the cloud may be the main culprits in the familiar Orion constellation. The stars are collectively called the 'Trapezium.' Their community can be identified as the yellow smudge near the center of the image.

Swirls of green in Hubble's ultraviolet and visible-light view reveal hydrogen and sulfur gas that have been heated and ionized by intense ultraviolet radiation from the Trapezium's stars. Meanwhile, Spitzer's infrared view exposes carbon-rich molecules called polycyclic aromatic hydrocarbons in the cloud. These organic molecules have been illuminated by the Trapezium's stars, and are shown in the composite as wisps of red and orange. On Earth, polycyclic aromatic hydrocarbons are found on burnt toast and in automobile exhaust.

Together, the telescopes expose the stars in Orion as a rainbow of dots sprinkled throughout the image. Orange-yellow dots revealed by Spitzer are actually infant stars deeply embedded in a cocoon of dust and gas. Hubble showed less embedded stars as specks of green, and foreground stars as blue spots.

Stellar winds from clusters of newborn stars scattered throughout the cloud etched all of the well-defined ridges and cavities in Orion. The large cavity near the right of the image was most likely carved by winds from the Trapezium's stars.

Located 1,500 light-years away from Earth, the Orion nebula is the brightest spot in the sword of the Orion, or the 'Hunter' constellation. The cosmic cloud is also our closest massive star-formation factory, and astronomers believe it contains more than 1,000 young stars.

The Orion constellation is a familiar sight in the fall and winter night sky in the northern hemisphere. The nebula is invisible to the unaided eye, but can be resolved with binoculars or small telescopes.

This image is a false-color composite where light detected at wavelengths of 0.43, 0.50, and 0.53 microns is blue. Light at wavelengths of 0.6, 0.65, and 0.91 microns is green. Light at 3.6 microns is orange, and 8.0 microns is red.

2006-01-01

476

Order Amidst Chaos of Star's Explosion

NASA Technical Reports Server (NTRS)

[figure removed for brevity, see original site] Click on the image for movie of Order Amidst Chaos of Star's Explosion

This artist's animation shows the explosion of a massive star, the remains of which are named Cassiopeia A. NASA's Spitzer Space Telescope found evidence that the star exploded with some degree of order, preserving chunks of its onion-like layers as it blasted apart.

Cassiopeia A is what is known as a supernova remnant. The original star, about 15 to 20 times more massive than our sun, died in a cataclysmic 'supernova' explosion viewable from Earth about 340 years ago. The remnant is located 10,000 light-years away in the constellation Cassiopeia.

The movie begins by showing the star before it died, when its layers of elements (shown in different colors) were stacked neatly, with the heaviest at the core and the lightest at the top. The star is then shown blasting to smithereens. Spitzer found evidence that the star's original layers were preserved, flinging outward in all directions, but not at the same speeds. In other words, some chunks of the star sped outward faster than others, as illustrated by the animation.

The movie ends with an actual picture of Cassiopeia A taken by Spitzer. The colored layers containing different elements are seen next to each other because they traveled at different speeds.

The infrared observatory was able to see the tossed-out layers because they light up upon ramming into a 'reverse' shock wave created in the aftermath of the explosion. When a massive star explodes, it creates two types of shock waves. The forward shock wave darts out quickest, and, in the case of Cassiopeia A, is now traveling at supersonic speeds up to 7,500 kilometers per second (4,600 miles/second). The reverse shock wave is produced when the forward shock wave slams into a shell of surrounding material expelled before the star died. It tags along behind the forward shock wave at slightly slower speeds.

Chunks of the star that were thrown out fastest hit the shock wave sooner and have had more time to heat up to scorching temperatures previously detected by X-ray and visible-light telescopes. Chunks of the star that lagged behind hit the shock wave later, so they are cooler and radiate infrared light that was not seen until Spitzer came along. These lagging chunks are seen in false colors in the Spitzer picture of Cassiopeia A. They are made up of gas and dust containing neon, oxygen and aluminum -- elements from the middle layers of the original star.

2006-01-01

477

Forecasting of one-dimensional time series previously has been used to help distinguish periodicity, chaos, and noise. This paper presents two-dimensional generalizations for making such distinctions for spatial patterns. The techniques are evaluated using synthetic spatial patterns and then are applied to a natural example: ripples formed in sand by blowing wind. Tests with the synthetic patterns demonstrate that the forecasting techniques can be applied to two-dimensional spatial patterns, with the same utility and limitations as when applied to one-dimensional time series. One limitation is that some combinations of periodicity and randomness exhibit forecasting signatures that mimic those of chaos. For example, sine waves distorted with correlated phase noise have forecasting errors that increase with forecasting distance, errors that, are minimized using nonlinear models at moderate embedding dimensions, and forecasting properties that differ significantly between the original and surrogates. Ripples formed in sand by flowing air or water typically vary in geometry from one to another, even when formed in a flow that is uniform on a large scale; each ripple modifies the local flow or sand-transport field, thereby influencing the geometry of the next ripple downcurrent. Spatial forecasting was used to evaluate the hypothesis that such a deterministic process - rather than randomness or quasiperiodicity - is responsible for the variation between successive ripples. This hypothesis is supported by a forecasting error that increases with forecasting distance, a greater accuracy of nonlinear relative to linear models, and significant differences between forecasts made with the original ripples and those made with surrogate patterns. Forecasting signatures cannot be used to distinguish ripple geometry from sine waves with correlated phase noise, but this kind of structure can be ruled out by two geometric properties of the ripples: Successive ripples are highly correlated in wavelength, and ripple crests display dislocations such as branchings and mergers. ?? 1992 American Institute of Physics.

Rubin, D. M.

1992-01-01

478

BOOK REVIEW: Microscopic Dynamics of Plasmas and Chaos

NASA Astrophysics Data System (ADS)

Some of the key intellectual foundations of plasma physics are in danger of becoming a lost art. Fortunately, however, this threat recedes with the publication of this valuable book. It renders accessible those aspects of theoretical plasma physics that are best approached from the perspectives of classical mechanics, in both its early nineteenth century and late twentieth century manifestations. Half a century has elapsed since the publication of seminal papers such as those by Bohm and Pines (1951), van Kampen (1955), and Bernstein, Greene and Kruskal (1957). These papers served to address a fundamental question of physics - namely the relation between degrees of freedom that exist at the individual particle level of description, and those that exist at the collective level - in the plasma context. The authors of the present book have played a major role in the investigation of this question from an N-body standpoint, which can be divided into two linked themes. First, those topics that can be illuminated by analytical methods that lie in the tradition of classical mechanics that stretches back to Lagrange, Legendre and Hamilton. Second, those topics that benefit from the insights developed following the redevelopment of classical mechanics in relation to chaos theory in the 1980s and subsequently. The working plasma physicist who wishes to dig more deeply in this field is faced at present with a number of challenges. These may include a perception that this subfield is of limited relevance to mission-oriented questions of plasma performance; a perception of the research literature as being self-contained and inaccessible; and, linked to this, unfamiliarity with the mathematical tools. The latter problem is particularly pressing, given the limited coverage of classical mechanics in many undergraduate physics courses. The book by Elskens and Escande meets many of the challenges outlined above. The rewards begin early, by the end of the second chapter, with beautiful derivations of the self-consistent Lagrangian for wave-particle interactions, followed by an equivalent Hamiltonian formulation in terms of action-angle variables. In the following two chapters, these and related techniques are used to explore the deepest topics of plasma dynamics and wave theory, often from a beam-plasma perspective. The book begins afresh at chapter 5, which is an ambitious attempt to summarise modern classical dynamics. This chapter begins well, with a nice introduction to action-angle variables (these have already been extensively exploited in the preceding chapters, however!), but the account eventually became too compressed for the present reviewer. There follow two further chapters on both diffusion and the single-wave-particle system. Perhaps this book is best considered as a companion to the research literature (indeed there is a useful and extensive bibliography), rather than as a conventionally structured textbook. Certainly it is a book that should be read backwards and sideways, as well as forwards. Most readers, for example, will be more familiar with the Vlasov-Poisson system than with the N-body approach to particles and fields that is developed here: their natural starting point will perhaps be appendix G.4 of the present volume. Nor does the book provide a free-standing account of plasma dynamics from the chosen perspective. For example, prior familiarity with van Kampen modes in the Vlasov--Poisson description would greatly assist understanding of chapter 3. Challenging exercises are embedded in the text throughout (even in the otherwise excellent appendices), with answers not necessarily provided. Altogether, this book provides a wealth of theoretical information that is not easily accessible from any other source. It is a book with character, written from a definite viewpoint, but it also facilitates the development of the reader's own perspective by offering a clear path to the original research literature. R O Dendy

Elskens, Y.; Escande, D.

2003-04-01

479

New Nonlinear Multigrid Analysis

NASA Technical Reports Server (NTRS)

The nonlinear multigrid is an efficient algorithm for solving the system of nonlinear equations arising from the numerical discretization of nonlinear elliptic boundary problems. In this paper, we present a new nonlinear multigrid analysis as an extension of the linear multigrid theory presented by Bramble. In particular, we prove the convergence of the nonlinear V-cycle method for a class of mildly nonlinear second order elliptic boundary value problems which do not have full elliptic regularity.

Xie, Dexuan

1996-01-01

480

Sulfates and phyllosilicates in Aureum Chaos, Mars

NASA Astrophysics Data System (ADS)

Many Martian regions show a hydrated mineralogy indicating that aqueous processes played a major role in the planet's past. This study combines short wave infrared data, imagery and elevation data to identify these minerals in an equatorial chaotic terrain region and to find out their stratigraphy and geological context. Local Interior Layered Deposits (ILD) display three stratigraphic units: The lowest unit shows massive and also layered, monohydrated sulfate (MHS, best matching kieserite; 20-650 m thick), intercalated hydroxylated ferric sulfates (HFS, best matching jarosite) and ferric oxides. The overlying polyhydrated sulfate (PHS) is commonly layered (20-40 m thick), smooth to heavily fractured, partially with ferric oxides. Spectrally neutral, distinctly layered, bumpy cap rock (40-300 m thick) forms the top. Units are spectrally and morphologically similar to deposits of Aram Chaos (PHS, MHS, ferric oxides; texture of ILD and cap rock) and Juventae Chasma (HFS). Here, the phyllosilicate nontronite is found attributed to chaotic terrain as a light-toned fractured exposure but also within dark, smooth mantling. Coexisting sulfates and phyllosilicates demonstrate geochemical variations in the aqueous environment. Conversions between sulfates and iron oxides are considered, since we might be looking at alteration products instead of the parent rock material. Here, PHS occurs along mantling edges and flat surfaces of MHS without showing textural differences; making it a potential alteration product of MHS (e.g. due to surface exposure). Since the facies and timing of sulfate formation remain undefined, two different formation models are considered: contemporaneous ILD and PHS deposition with diagenetic sulfate conversion due to overburden (into MHS, iron oxides) later on; and groundwater evaporation. The first is less likely since a (sharp) PHS-MHS boundary is required that would indicate a diagenetic formation. The second is more consistent with our observations concerning the potential anhydrous cap rock. Groundwater would have penetrated into a pre-existing sulfate-free ILD whose permeability and porosity would have defined the rate of water absorption and sulfate precipitation that finally lead to its cementation. The surface ages of chaotic terrain (late Hesperian) and mantling deposits (mid to late Amazonian) further constrain the ILD age and potentially the emplacement of sulfates. We suggest that phyllosilicates in the mantling are allochthonous. In contrast, determining the deposition of in-situ phyllosilicates is theoretical; they could be Noachian (excavated material, following the 'phyllosian' era), or instead late Hesperian or even younger (syn- or post-chaotic). Alternatives, as known from Australian saline lakes, combine groundwater alteration with the observed mineralogy. There, close spatial and temporal associations of both mineral groups are explained by vertically separated geochemical environments (phyllosilicates in deep-, sulfates in shallow evaporitic facies). The preservation of nontronite, HFS and MHS displays that since their deposition a relatively dry environment with intermittent aqueous activity must have prevailed.

Sowe, M.; Wendt, L.; McGuire, P. C.; Neukum, G.

2012-12-01

481

Nonlinear Schrodinger Dynamics and Nonlinear Observables

It is is explained why physical consistency requires substituting linear ob- servables by nonlinear ones for quantum systems with nonlinear time evolution of pure states. The exact meaning and the concrete physical interpretation are described in full detail for a special case of the nonlinear Doebner-Goldin equation.

W. Lucke

482

LDRD final report on using chaos for ultrasensitive coherent signal detection.

A quantum optical approach is proposed and analyzed as a solution to the problem of detecting weak coherent radiation in the presence of a strong incoherent background. The approach is based on the extreme sensitivity of laser dynamical nonlinearities to the coherence of external perturbation. This sensitivity leads to dynamical phase transitions that may be employed for detecting the presence of external coherent radiation. Of particular interest are the transitions between stable and chaotic states of laser operation. Using a baseline scheme consisting of a detector laser operating with a Fabry-Perot cavity, we demonstrated significant qualitative and quantitative differences in the response of the detector laser to the intensity and coherence of the external signal. Bifurcation analysis revealed that considerable modification to the extension of chaotic regions is possible by tailoring active medium and optical resonator configurations. Our calculations showed that with semiconductor lasers, destabilization can occur with a coherent external signal intensity that is over six orders of magnitude smaller than the detector laser's intracavity intensity. Discrimination between coherent and incoherent external signal also looks promising because of the over four orders of magnitude difference in intensity required for inducing chaos-like behavior. These results suggest that the proposed approach may be useful in laser sensor applications, such as satellite Laser Threat Warning Receivers (LTWR).

Chow, Weng Wah Dr. (; .); Wieczorek, Sebastian Maciej; Torrington, Geoffrey Kenneth

2006-11-01

483

Chaotic behavior can be produced from difference equations with unstable fixed points. Difference equations can be used for algorithms to control the chaotic behavior by perturbing a system parameter using feedback based on the first difference of the system value. This results in a system of nonlinear first order difference equations whose stable fixed point is the controlled chaotic behavior. Basing the feedback on the first difference produces distinctly different transient responses than when basing feedback on the error from the fixed point. Analog electronic circuits provide the experimental system for testing the chaos control algorithm. The circuits are low-cost, relatively easy to construct, and therefore provide a useful transition towards more specialized real-world applications. Here we present predictions and experimental results for the transient responses of a first difference based feedback control method applied to a chaotic finite difference 1-dimensional map. The experimental results are in good agreement with predictions, showing a variety of behaviors for the transient response, including erratic appearing non-steady convergence.

Edward H. Hellen; J. Keith Thomas

2008-07-16

484

Long-time uncertainty propagation using generalized polynomial chaos and flow map composition

NASA Astrophysics Data System (ADS)

We present an efficient and accurate method for long-time uncertainty propagation in dynamical systems. Uncertain initial conditions and parameters are both addressed. The method approximates the intermediate short-time flow maps by spectral polynomial bases, as in the generalized polynomial chaos (gPC) method, and uses flow map composition to construct the long-time flow map. In contrast to the gPC method, this approach has spectral error convergence for both short and long integration times. The short-time flow map is characterized by small stretching and folding of the associated trajectories and hence can be well represented by a relatively low-degree basis. The composition of these low-degree polynomial bases then accurately describes the uncertainty behavior for long integration times. The key to the method is that the degree of the resulting polynomial approximation increases exponentially in the number of time intervals, while the number of polynomial coefficients either remains constant (for an autonomous system) or increases linearly in the number of time intervals (for a non-autonomous system). The findings are illustrated on several numerical examples including a nonlinear ordinary differential equation (ODE) with an uncertain initial condition, a linear ODE with an uncertain model parameter, and a two-dimensional, non-autonomous double gyre flow.

Luchtenburg, Dirk M.; Brunton, Steven L.; Rowley, Clarence W.

2014-10-01

485

Foraging at the edge of chaos: internal clock versus external forcing.

Activity rhythms in animal groups arise both from external changes in the environment, as well as from internal group dynamics. These cycles are reminiscent of physical and chemical systems with quasiperiodic and even chaotic behavior resulting from "autocatalytic" mechanisms. We use nonlinear differential equations to model how the coupling between the self-excitatory interactions of individuals and external forcing can produce four different types of activity rhythms: quasiperiodic, chaotic, phase locked, and displaying over or under shooting. At the transition between quasiperiodic and chaotic regimes, activity cycles are asymmetrical, with rapid activity increases and slower decreases and a phase shift between external forcing and activity. We find similar activity patterns in ant colonies in response to varying temperature during the day. Thus foraging ants operate in a region of quasiperiodicity close to a cascade of transitions leading to chaos