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1

Scaling of chaos in strongly nonlinear lattices

NASA Astrophysics Data System (ADS)

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.

Mulansky, Mario

2014-06-01

2

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

3

Bifurcation continuation, chaos and chaos control in nonlinear Bloch system

NASA Astrophysics Data System (ADS)

A detailed analysis is undertaken to explore the stability and bifurcation pattern of the nonlinear Bloch equation known to govern the dynamics of an ensemble of spins, controlling the basic process of nuclear magnetic resonance. After the initial analysis of the parameter space and stability region identification, we utilize the MATCONT package to analyze the detailed bifurcation scenario as the two important physical parameters ? (the normalized gain) and c (the phase of the feedback field) are varied. A variety of patterns are revealed not studied ever before. Next we explore the structure of the chaotic attractor and how the identification of unstable periodic orbit (UPO) can be utilized to control the onset of chaos.

Ghosh, Dibakar; Chowdhury, A. Roy; Saha, Papri

2008-10-01

4

UNSOLVED ECONOMETRIC PROBLEMS IN NONLINEARITY, CHAOS, AND BIFURCATION

In an attempt to resolve the controversies that exist within the field of economics regarding nonlinearity, chaos, and bifurcation, we investigate the relevancy to these controversies of a controlled competition among nonparametric econometric tests for nonlinearity and chaos, and we also report on our results with experiments using parametric macroeconomic models to investigate the implications of bifurcation for macroeconomic policy.

William A. Barnett; Yijun He

2012-01-01

5

Nonlinear internal friction, chaos, fractal and musical instruments.

National Technical Information Service (NTIS)

Nonlinear and structure sensitive internal friction phenomena in materials are used for characterizing musical instruments. It may be one of the most important factors influencing timbre of instruments. As a nonlinear dissipated system, chaos and fractals...

Z. Q. Sun C. W. Lung

1995-01-01

6

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

7

Controlling Spatiotemporal Chaos Using Nonlinear Feedback Functional Method

NASA Astrophysics Data System (ADS)

Nonlinear feedback functional method for controlling spatiotemporal chaos is presented. As a key point, some typical kinds of nonlinear feedback functions are given. The efficiency and robustness of the method based on the flexibility of choices of nonlinear feedback functions are discussed.

Fang, Jin-qing; M, K. Ali; Fang, Qing

1997-11-01

8

Nonlinear waves, chaos and patterns in microwave electronic devices.

We discuss some problems, concerning the application of nonlinear dynamics methods and ideas to vacuum microwave electronics. We consider such phenomena as solitons, deterministic chaos and pattern formation in different models of electron flows and devices. Our results reveal that microwave electronics is an interesting field of application of nonlinear dynamics. (c) 1996 American Institute of Physics. PMID:12780264

Trubetskov, D. I.; McHedlova, E. S.; Anfinogentov, V. G.; Ponomarenko, V. I.; Ryskin, N. M.

1996-09-01

9

A Monomial Chaos Approach for Efficient Uncertainty Quantification in Nonlinear Problems

A monomial chaos approach is presented for efficient uncertainty quantification in nonlinear computational problems. Propagating uncertainty through nonlinear equations can be computationally intensive for existing uncertainty quantification methods. It usually results in a set of nonlinear equations which can be coupled. The proposed monomial chaos approach employs a polynomial chaos expansion with monomials as basis functions. The expansion coefficients are

Jeroen A. S. Witteveen; Hester Bijl

2008-01-01

10

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

11

Linear vs nonlinear and infinite vs finite: An interpretation of chaos

An example of a linear infinite-dimensional system is presented that exhibits deterministic chaos and thus challenges the presumably unquestionable connection between chaos and nonlinearity. Via this example, the roles of, and relationships between, linearity, nonlinearity, infinity and finiteness in the occurrence of chaos are investigated. The analysis of these complementary but related aspects leads to: a new interpretation of chaos as the manifestation of incompressible and thus incompressible information and a conjecture about the nonexistence of operationally accessible linear systems.

Protopopescu, V.

1990-10-01

12

Controlling chaos using nonlinear approximations and delay coordinate embedding

NASA Astrophysics Data System (ADS)

In a previous paper we showed that a chaos control method proposed by Ott, Grebogi and Yorke can be improved by using nonlinear approximations for chaotic dynamical systems and stable manifolds of targets. Here we consider systems whose governing equations are unknown and apply the chaos control method using the nonlinear approximations. Delay coordinate embedding techniques are used, so that approximate saddle points to be stabilized and nonlinear approximations of the systems and stable manifolds are obtained from time series of single variables. We also take into account the fact that the obtained section maps depend on the current and previous parameters. To demonstrate our approach, we give two numerical examples for the Hénon map and a pendulum with feedforward and feedback control. Some influences of noise are also discussed in these examples.

Yagasaki, Kazuyuki; Uozumi, Tomotsugu

1998-10-01

13

Nonlinear response and chaos in semiconductors induced by impact ionization

NASA Astrophysics Data System (ADS)

A review is given of the nonlinear response and chaos induced by impact ionization of neutral shallow donors, observed in n-GaAs. Two kinds of the observation are described; (i) firing wave instability, and (ii) periodically driven current filament. For the firing wave instability, several important aspects are discussed including the selective excitation of the current filaments and the deterministic nature of the firing density wave. The nonlinear response of a periodically driven current filament has been investigated by applying a dc+ac bias of the form of V dc+ V ac sin(2?f 0 t), where f 0˜1 MHz. The carrier dynamics and the bifurcation routes to chaos are discussed in terms of the observed phase diagram and the bifurcation map. The deterministic nature of the strange attractors are described in detail in terms of the correlation dimension and the Kolmogorov entropy.

Aoki, K.; Yamamoto, K.

1989-02-01

14

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

15

Nonlinear dynamics, chaos and complex cardiac arrhythmias

NASA Technical Reports Server (NTRS)

Periodic stimulation of a nonlinear cardiac oscillator in vitro gives rise to complex dynamics that is well described by one-dimensional finite difference equations. As stimulation parameters are varied, a large number of different phase-locked and chaotic rhythms is observed. Similar rhythms can be observed in the intact human heart when there is interaction between two pacemaker sites. Simplified models are analyzed, which show some correspondence to clinical observations.

Glass, L.; Courtemanche, M.; Shrier, A.; Goldberger, A. L.

1987-01-01

16

Fundamental threshold of chaos in some nonlinear oscillators

A technique for predicting chaos arising in a broad class of nonlinear oscillatory systems is proposed. It is based on the notion of running Lyapunov exponents and uses the local stability properties of trajectories for determining the {open_quote}{open_quote}safe{close_quote}{close_quote} areas in the phase space where any trajectory is regular and stable in the sense of Lyapunov. The combination of this approach with harmonic balance method permits to obtain the corresponding {open_quote}{open_quote}safe{close_quote}{close_quote} regions in the control parameter space. The borders of these regions may be considered as threshold lines delimiting the areas of possible chaotic instability. An example of the two-well Duffing oscillator demonstrates good agreement between theoretically predicted values of control parameters where chaos arises with those obtained numerically. The technique is especially effective for rather high dissipation levels when other known methods such as Melnikov{close_quote}s criterion or combination of harmonic balance with analysis of variational equations fail to provide correct results. {copyright} {ital 1996 American Institute of Physics.}

Ryabov, V.B. [Institute of Radio Astronomy, 4 Krasnoznamennaya St., 310002 Kharkov (Ukraine)

1996-06-01

17

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

18

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

19

Chaos control in the nonlinear Schrödinger equation with Kerr law nonlinearity

NASA Astrophysics Data System (ADS)

The nonlinear Schrödinger equation with Kerr law nonlinearity in the two-frequency interference is studied by the numerical method. Chaos occurs easily due to the absence of damping. This phenomenon will cause the distortion in the process of information transmission. We find that fiber-optic transmit signals still present chaotic phenomena if the control intensity is smaller. With the increase of intensity, the fiber-optic signal can stay in a stable state in some regions. When the strength is suppressed to a certain value, an unstable phenomenon of the fiber-optic signal occurs. Moreover we discuss the sensitivities of the parameters to be controlled. The results show that the linear term coefficient and the environment of two quite different frequences have less effects on the fiber-optic transmission. Meanwhile the phenomena of vibration, attenuation and escape occur in some regions.

Yin, Jiu-Li; Zhao, Liu-Wei; Tian, Li-Xin

2014-02-01

20

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

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

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

2012-01-01

21

INTRODUCTION: Introduction to Nonlinear Dynamics and Chaos Theory

NASA Astrophysics Data System (ADS)

Chapters 1-3 of these lectures were given at the University of Oslo during my academic free half-year August l985-January 1986 which I spent at the Institute for Energy Technology (IFE). Chapter 4 was given by T Riste during my journeys to other Scandinavian institutions where I held seminars covering much of what is reflected in Chapter 5. That chapter represents a contribution to chaos theory that was carried out in collaboration with J Palmore. In place of the universal properties of unimodal maps, which are well-treated in the books by Cvitanovic and Schuster, I have instead based my elementary introduction to scaling and universality upon the damped driven pendulum and circle maps, which are of current interest to experimenters at IFE and elsewhere, as is reflected in the literature over the past year. Also, the circle map has not been so well-treated pedagogically in available texts. The discussion in Chapter 3 is not advanced, but it should prepare the reader for a better appreciation of the literature in that field. I should say that these lectures for the most part were written for students, for experimenters, and for curious theorists from other fields in physics, but not for the experts in nonlinear dynamics. For example, Chapter 3 ends where the hardest work begins. Tn preparing the lectures, I drew heavily upon the books by Arnol'd, Jorna, Jordan and Smith, Lichtenberg and Lieberman, and Schuster, and upon numerous journal articles. The level of the lectures is that of a second year graduate course at the University of Houston, but beginning with undergraduate-level topics in ordinary differential equations. Throughout, I have emphasized my interest in the connection of nonlinear dynamics to statistical mechanics, as well as my interest in "computer arithmetic". I hope that the reader will also find these subjects to be of interest since they have provided me with a great deal of intellectual enjoyment. My free-half-year at IFE would have been impossible without the aid and moral support provided by Tormod Riste. Gerd Jarrett helped and befriended me and my family in more ways than I should wish to count, and the entire physics staff at IFE, E Andersen, A F Andresen, G Jarrett, K Otnes, T Riste, A Skjeltorp and O. Steinsvoll helped to slake my heavy thirst for Norwegian history and culture, and agreed from the start to speak Norwegian to me daily in order to help me in my effort to learn to speak that language. Gerd Jarrett performed above and beyond the call of duty by tirelessly typing the original lecture notes, which appear as the internal report IFE/I-86/003 + KGF. I also owe thanks to Lynn Smith for typing the revisions that yielded this final version at the University of Houston. I willingly thank J Fröyland, J Palmore and F Ravndal for several helpful discussions and comments, and M Golubitsky, J Palmore, D Schiller and O Steinsvoll for proof-reading several of the chapters (blame for remaining errors is entirely my own, however). I also wish to thank P Alström, E Aurell, T Bohr, P Cvitanovic, E H Hauge, P C Hemmer, J Hertz, J Ketoja, T Kohonen, J Kurkijärvi, K Lindgren, J Myrheim, R Ritala and S Stenholm for interesting discussions during my journeys to other Scandinavian institutions. I am especially grateful to J Fröyland for guestfriendship at the University of Oslo, and to A K M F Hussain for encouraging in 1984 that I should put my lecture notes into print. Finally, my academic free-year was supported financially by the American Scandinavian Foundation, NORDITA and the University of Houston. All my travel costs within Scandinavia were paid by NORDITA

McCauley, Joseph L.

1988-01-01

22

Influence of nonlinear conductance and coscphi term on the onset of chaos in Josephson junctions

Chaotic behavior in a Josephson junction is investigated. Threshold curves for the onset of chaos in the rf current-frequency plane are computed by means of Kolmogorov entropy. Both the nonlinear dependence of the quasiparticle current I/sub N/(V) and the coscphi term have been considered to account for previously reported experimental results.

Aiello, A.; Barone, A.; Ovsyannikov, G.A.

1984-07-01

23

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

ERIC Educational Resources Information Center

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

Bloch, Deborah P.

2005-01-01

24

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

25

NASA Astrophysics Data System (ADS)

The effect of small nonlinear dissipation on the dynamics of a system with the stochastic web which is linear oscillator driven by pulses is studied. The scenario of coexisting attractors evolution with the increase of nonlinear dissipation is revealed. It is shown that the period-doubling transition to chaos is possible only for the third-order resonance and only hard transitions can be seen for all other resonances.

Felk, E. V.; Kuznetsov, A. P.; Savin, A. V.

2014-09-01

26

IUTAM chaos `97 - symposium on new applications of nonlinear and chaotic dynamics in mechanics

It will be nearly twenty years since Feigenbaum`s landmark papers on period doubling and the modern beginnings of what is now called {open_quotes}Chaos Theory{close_quotes} in the popular press. From the very beginning, mechanics has been a central focus for modern nonlinear dynamical systems, from Lorenz`s pioneering work in 1963 on Rayleigh-Benard flow, to Holmes` theory of strange attractors in the buckling of structures in 1978. Fluid, structural, machine and rigid body dynamics has been a fertile field for nonlinear phenomena and chaos in particular. Early experimental evidence for chaotic phenomena in mechanics gave the new {open_quotes}chaos theory{close_quotes} a mark of credibility, importance, and relevance that its earlier sister catastrophe theory did not achieve. The fact that mechanics straddles both physics and engineering also meant that mechanics became a pathway for direct application of chaos theory to applied problems such as aeroelastic instabilities, ship capsize, rattling and impact in machines, cable dynamics and many others. These applications were the subject of numerous conferences including two predecessors to this Symposium, Stuttgart in 1989 and London in 1993. This document contains abstracts of reports which were presented at the International Union of Theoretical and Applied Mechanics Symposium on Applications of Nonlinear and Chaotic Dynamics in Mechanics. Individual reports have been processed separately for the United States Department of Energy databases.

NONE

1997-12-31

27

Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate

An analysis on the nonlinear dynamics of a simply supported functionally graded materials (FGMs) rectangular plate subjected to the transversal and in-plane excitations is presented in a thermal environment for the first time. Material properties are assumed to be temperature dependent. Based on Reddy's third-order plate theory, the nonlinear governing equations of motion for the FGM plates are derived using

Y. X. Hao; L. H. Chen; W. Zhang; J. G. Lei

2008-01-01

28

On cascades of bifurcations leading to chaos in several nonlinear dissipative systems of ODEs

NASA Astrophysics Data System (ADS)

This paper considers several nonlinear dissipative systems of ordinary differential equations. The studied systems undergo a full analysis of corresponding singular points on a whole set of parameters' values variation. Specifically, types of singular points, boarders of stability regions, as well as presented local bifurcations, are determined. By using numerical methods a consideration of scenarios of transition to chaos in these systems with one bifurcation parameter variation is held. The aim of this research is a confirmation of a Feigenbaum-Sharkovskii-Magnitskii mechanism of transition to chaos unique for all dissipative systems of ODEs. As the result of analysis of one of the systems the lack of any chaotic behavior is shown with the help of Poincare sections.

Trebler, Andrey A.

2010-10-01

29

Nonlinear Dynamics and Chaos in Parametrically Excited Surface Waves

Surface waves in a closed container subject to vertical oscillation are studied. Nonlinear dynamical equations of two nearly degenerate subharmonic modes responding to the external forcing are derived, using the averaged Lagrangian method for slowly varying amplitudes. Stability and bifurcation diagrams are shown for the system with linear damping. Period-doubling bifurcation and chaotic solutions with one positive Lyapunov characteristic exponent

Makoto Umeki; Tsutomu Kambe

1989-01-01

30

BOOK REVIEW: Nonlinear Dynamics: Integrability, Chaos and Patterns

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

M. Lakshmanan; S. Rajaseekar

2004-01-01

31

Chaos in nonlinear dynamic systems: Helicopter vibration mechanisms

The nonlinear dynamic behavior of a helicopter is considered in this paper, using only real-time flight data analysis. The main objective of this study is to characterize the vibration mechanism(s). based on the analysis of the time-series data of the dynamical system, specifically acceleration for two different airspeeds with a sampling rate of 1024 Hz. We explore the possibility of

James H. Taylor; Saied S. Sharif

2007-01-01

32

Global and local chaos in the pumped nonlinear Schroedinger equation

NASA Astrophysics Data System (ADS)

An optical ring cavity is considered in which the propagation of an envelope pulse is described by the nonlinear Schroedinger equation. This cavity is pumped by a coherent train of pulses. As the pump intensity is increased a sequence of period-doubling bifurcations is followed by an inverse sequence (chaotic band structure). The global (moment) and local (field) properties of the pulse sequences have the same dynamical behavior. Bistability and the merging of two chaotic branches have also been observed.

Blow, K. J.; Doran, N. J.

1984-02-01

33

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

Security in information exchange plays a central role in the deployment of modern communication systems. Besides algorithms, chaos is exploited as a real-time high-speed data encryption technique which enhances the security at the hardware level of optical networks. In this work, compact, fully controllable and stably operating monolithic photonic integrated circuits (PICs) that generate broadband chaotic optical signals are incorporated in chaos-encoded optical transmission systems. Data sequences with rates up to 2.5 Gb/s with small amplitudes are completely encrypted within these chaotic carriers. Only authorized counterparts, supplied with identical chaos generating PICs that are able to synchronize and reproduce the same carriers, can benefit from data exchange with bit-rates up to 2.5Gb/s with error rates below 10(-12). Eavesdroppers with access to the communication link experience a 0.5 probability to detect correctly each bit by direct signal detection, while eavesdroppers supplied with even slightly unmatched hardware receivers are restricted to data extraction error rates well above 10(-3). PMID:20389532

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

2010-03-01

34

Hamiltonian chaos in a nonlinear polarized optical beam

This lecture concerns the applications of ideas about temporal complexity in Hamiltonian systems to the dynamics of an optical laser beam with arbitrary polarization propagating as a traveling wave in a medium with cubically nonlinear polarizability. We use methods from the theory of Hamiltonian systems with symmetry to study the geometry of phase space for this optical problem, transforming from C{sup 2} to S{sup 3} {times} S{sup 1}, first, and then 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{sub 2} are classified and displayed graphically. These bifurcations take place when either J (the beam intensity), or the optical parameters of the medium are varied. After this bifurcation analysis has shown the existence of various saddle connections on S{sup 2}, the Melnikov method is used to demonstrate analytically that the traveling-wave dynamics of a polarized optical laser pulse develops chaotic behavior in the form of Smale horseshoes when propagating through spatially periodic perturbations in the optical parameters of the medium. 20 refs., 7 figs.

David, D.; Holm, D.D.; Tratnik, M.V. (Los Alamos National Lab., NM (USA))

1989-01-01

35

Coupled nonlinear oscillators: A paradigm for spatiotemporal chaos and nonequilibrium phenomena

NASA Astrophysics Data System (ADS)

The control of high-dimensional chaos and the thermal nucleation of kink-antikink pairs are investigated in a chain of locally coupled, nonlinear, electronic resonators. Experimental evidence for the universality of spatiotemporal stochastic resonance is given. We also show that recently developed feedback control techniques will not succeed in the presence of certain symmetries. First, we demonstrated the stabilization of complex waveforms embedded within convective spatiotemporal chaos. The employed coupling was unidirectional, giving rise to instabilities and patterns as observed in so- called open flow systems. The stability of the nonlinear waves was associated with the presence of kink-antikink pairs. We measured dynamic properties of the kinks such as speed, shape and width. For the case of (symmetric) diffusive coupling we then examined the interplay between a periodic modulation and spatially distributed thermal noise. The phenomenon of array enhanced stochastic resonance was confirmed and its relation to the nucleation of kink-antikink pairs established. The third part of this work applies mainly to low- dimensional dynamical systems. A new method of local stability analysis was developed and verified for a system of two coupled diode resonators. We found that symmetries generic of homogeneous orbits in systems of coupled oscillators, preclude one-parameter control schemes.

Locher, Markus

1997-12-01

36

NASA Astrophysics Data System (ADS)

This paper studies the chaotic behaviours of a relative rotation nonlinear dynamical system under parametric excitation and its control. The dynamical equation of relative rotation nonlinear dynamical system under parametric excitation is deduced by using the dissipation Lagrange equation. The criterion of existence of chaos under parametric excitation is given by using the Melnikov theory. The chaotic behaviours are detected by numerical simulations including bifurcation diagrams, Poincaré map and maximal Lyapunov exponent. Furthermore, it implements chaotic control using non-feedback method. It obtains the parameter condition of chaotic control by the Melnikov theory. Numerical simulation results show the consistence with the theoretical analysis. The chaotic motions can be controlled to period-motions by adding an excitation term.

Shi, Pei-Ming; Han, Dong-Ying; Liu, Bin

2010-09-01

37

Universal theory of dynamical chaos in nonlinear dissipative systems of differential equations

NASA Astrophysics Data System (ADS)

A new universal theory of dynamical chaos in nonlinear dissipative systems of differential equations including ordinary and partial, autonomous and non-autonomous differential equations and differential equations with delay arguments is presented in this paper. Four corner-stones lie in the foundation of this theory: the Feigenbaum's theory of period doubling bifurcations in one-dimensional mappings, the Sharkovskii's theory of bifurcations of cycles of an arbitrary period up to the cycle of period three in one-dimensional mappings, the Magnitskii's theory of rotor type singular points of two-dimensional non-autonomous systems of differential equations as a bridge between one-dimensional mappings and differential equations and the theory of homoclinic cascade of bifurcations of stable cycles in nonlinear differential equations. All propositions of the theory are strictly proved and illustrated by numerous analytical and computing examples.

Magnitskii, Nikolai A.

2008-03-01

38

Control of bifurcations and chaos in heart rhythms

Cardiac arrhythmias have been closely linked to a variety of bifurcations and chaos. In this paper control of bifurcations and chaos for nonlinear models of cardiac electro-physiologic activity is investigated. Both the Andronov-Hopf bifurcation and period doubling bifurcation are treated. Washout filter aided feedback controllers are employed to control the location and stability of the bifurcations, and the amplitude of

H. O. Wang; Dong Chen; L. G. Bushnell

1997-01-01

39

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.

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

2009-01-01

40

Nonlinear elasticity of cross-linked networks

NASA Astrophysics Data System (ADS)

Cross-linked semiflexible polymer networks are omnipresent in living cells. Typical examples are actin networks in the cytoplasm of eukaryotic cells, which play an essential role in cell motility, and the spectrin network, a key element in maintaining the integrity of erythrocytes in the blood circulatory system. We introduce a simple mechanical network model at the length scale of the typical mesh size and derive a continuous constitutive law relating the stress to deformation. The continuous constitutive law is found to be generically nonlinear even if the microscopic law at the scale of the mesh size is linear. The nonlinear bulk mechanical properties are in good agreement with the experimental data for semiflexible polymer networks, i.e., the network stiffens and exhibits a negative normal stress in response to a volume-conserving shear deformation, whereby the normal stress is of the same order as the shear stress. Furthermore, it shows a strain localization behavior in response to an uniaxial compression. Within the same model we find a hierarchy of constitutive laws depending on the degree of nonlinearities retained in the final equation. The presented theory provides a basis for the continuum description of polymer networks such as actin or spectrin in complex geometries and it can be easily coupled to growth problems, as they occur, for example, in modeling actin-driven motility.

John, Karin; Caillerie, Denis; Peyla, Philippe; Raoult, Annie; Misbah, Chaouqi

2013-04-01

41

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

42

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

43

NASA Astrophysics Data System (ADS)

Detection of possible chaos in hydrological time series can be useful for scientific understanding of the component processes as well as for short-term predictability and predictive modeling. However, the presence of noise and seasonality makes the detection of any nonlinear component, especially chaos, difficult in finite time series. This study utilizes approaches such as correlation dimension (CD), phase space reconstruction (PSR) and artificial neural networks (ANN) for the detection of possible chaos. The results on simulated data generated from the Lorenz system of equations (contaminated with various levels of noise and periodicity) indicate the presence of thresholds in terms of "noise to chaotic-signal" and "seasonality to chaotic-signal", beyond which the currently available set of tools are unable to detect the chaotic component. The simulation results also demonstrate that the underlying chaotic or nonlinear component, if present, may be extractable from a time series contaminated with noise and seasonality. We also show the impacts on predictive modeling, for example we illustrate the possibility that a decomposition of the time series observations into periodic, nonlinear dynamical and noise components can be utilized to improve predictive modeling through a best fit strategy that applies the most suitable methodology to each component. Analysis of monthly streamflow data from the Arkansas River at Little Rock and daily streamflow data from the Colorado River below Parker dam shows that the chaotic component can be detected in the Arkansas data but not in the Colorado data. The extracted chaotic component from the Arkansas data is processed further to generate multi-step ahead predictions. These results suggest that while chaos may be detectable in certain hydrological time series leading in many situations to improved short-term predictability, not all hydrological time series exhibits detectable chaos. Acknowledgment: Auroop R Ganguly gratefully acknowledges the Laboratory Directed Research and Development Program (SEED money funds) of the Oak Ridge National Laboratory (ORNL), managed by UT-Battelle, LLC for the U.S. DOE under Contract No. DE-AC05-00OR22725.

Ganguly, A. R.; Khan, S.; Saigal, S.

2005-12-01

44

NASA Astrophysics Data System (ADS)

It is shown that resonant three-wave coupling equations in plasma physics can be recast in a form which is isomorphic to the Lorenz turbulence equations. The possibility of Lorenz-type chaos is predicted

Feng, Lu; Li, Jianxin; Feng, Qi-yuan; Xingyu, Yang; Liu, Xiumin; Wang, Jing

1997-11-01

45

Photocross-Linked Second Order Nonlinear Optical Polymers.

National Technical Information Service (NTIS)

We report a novel method to obtain stable second order nonlinear optical (NLO) properties in polymeric thin films. Photocross-linking between the NLO active molecules and a photoreactive polymer is achieved by ultraviolet irradiation subsequent to poling....

Y. M. Chen B. K. Mandal J. Y. Lee P. Miller J. Kumar

1991-01-01

46

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

47

An analysis is given of the dynamic of a one-degree-of-freedom oscillator with quadratic and cubic nonlinearities subjected to parametric and external excitations having incommensurate frequencies. A new method is given for constructing an asymptotic expansion of the quasi-periodic solutions. The generalized averaging method is first applied to reduce the original quasi-periodically driven system to a periodically driven one. This method

M. Belhaq; M. Houssni

1999-01-01

48

NSDL National Science Digital Library

US News and World Report has ranked the Maryland Chaos Group number one in the country (tied with University of Texas, Austin) for Non-linear Dynamics, or Chaos. Chaos is an interdisciplinary science founded on the idea that "nonlinear deterministic systems can behave in an apparently unpredictable and chaotic manner." The site includes brief descriptions of the group's research interests as well as a Chaos Pictures Gallery. The publications section will be of most value to researchers as it contains general references, abstracts, and papers. The online papers (which come in a variety of formats) consist of preprints and published articles on bifurcations, fractal basin boundaries, quantum chaos, general chaos, and more. Papers and abstracts are searchable.

49

Nonlinear Control of Asynchronous BTB-Link

The high power self-commutated VSC are the key control devices in HVDC, FACTS and DFACTS systems. The self-commutated voltage source converter back to back (VSC- BTB) link connects two ac power systems asynchronously, can control the active power exchanged between the two ac system and the reactive powers at the both terminals independently. To achieve the expected control objectives suitable

Y. H. Liu; H. W. Wu; N. R. Watson

2011-01-01

50

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

51

Chaos, Topology, and Social Organization.

ERIC Educational Resources Information Center

Applies chaos theory to complex social organization, beginning with a mathematical definition of chaos. Shows how a nonlinear equation might be used to describe organization. The conclusion section identifies three approaches to analyzing chaos in social organization: metaphorical analysis, mathematical modeling, and data collection. (36…

Marion, Russ

1992-01-01

52

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

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

George Sugihara; Robert M. May

1990-01-01

53

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.

54

Chaos-based communications at high bit rates using commercial fibre-optic links

NASA Astrophysics Data System (ADS)

Chaotic signals have been proposed as broadband information carriers with the potential of providing a high level of robustness and privacy in data transmission. Laboratory demonstrations of chaos-based optical communications have already shown the potential of this technology, but a field experiment using commercial optical networks has not been undertaken so far. Here we demonstrate high-speed long-distance communication based on chaos synchronization over a commercial fibre-optic channel. An optical carrier wave generated by a chaotic laser is used to encode a message for transmission over 120km of optical fibre in the metropolitan area network of Athens, Greece. The message is decoded using an appropriate second laser which, by synchronizing with the chaotic carrier, allows for the separation of the carrier and the message. Transmission rates in the gigabit per second range are achieved, with corresponding bit-error rates below 10-7. The system uses matched pairs of semiconductor lasers as chaotic emitters and receivers, and off-the-shelf fibre-optic telecommunication components. Our results show that information can be transmitted at high bit rates using deterministic chaos in a manner that is robust to perturbations and channel disturbances unavoidable under real-world conditions.

Argyris, Apostolos; Syvridis, Dimitris; Larger, Laurent; Annovazzi-Lodi, Valerio; Colet, Pere; Fischer, Ingo; García-Ojalvo, Jordi; Mirasso, Claudio R.; Pesquera, Luis; Shore, K. Alan

2005-11-01

55

NASA Astrophysics Data System (ADS)

The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time ?˜10ps and by a low cutoff frequency with a response time ?˜1?s . Moreover, the optoelectronic feedback also consists of a significant delay ?D of the order of 100ns . Depending on two key physical parameters, the loop gain ? and the nonlinearity operating point ? , a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations (DDEs), which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE (iDDE) that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants ? , ? , and ?D . We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of ? . One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electro-optic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms (chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations).

Peil, Michael; Jacquot, Maxime; Chembo, Yanne Kouomou; Larger, Laurent; Erneux, Thomas

2009-02-01

56

The response of a nonlinear optical oscillator subject to a delayed broadband bandpass filtering feedback is studied experimentally, numerically, and analytically. The oscillator loop is characterized by a high cutoff frequency with a response time tau approximately 10 ps and by a low cutoff frequency with a response time theta approximately 1 micros. Moreover, the optoelectronic feedback also consists of a significant delay tauD of the order of 100 ns. Depending on two key physical parameters, the loop gain beta and the nonlinearity operating point Phi, a large variety of multiple time scale regimes are reported, including slow or fast periodic oscillations with different waveforms, regular or chaotic breathers, slow time envelope dynamics, complex and irregular self-pulsing, and fully developed chaos. Many of these regimes are exhibiting new features that are absent in the classical first-order scalar nonlinear delay differential equations (DDEs), which differ in the modeling by the low cutoff only. Nearly all kinds of solutions are recovered numerically by a new class of integro-DDE (iDDE) that take into account both the high and low cutoff frequencies of the feedback loop. For moderate feedback gain, asymptotic solutions are determined analytically by taking advantage of the relative values of the time constants tau, theta, and tauD. We confirm the experimental observation of two distinct routes to oscillatory instabilities depending on the value of Phi. One route is reminiscent of the square wave oscillations of the classical first-order DDE, but the other route is quite different and allows richer wave forms. For higher feedback gain, these two distinct regimes merge leading to complex nonperiodic regimes that still need to be explored analytically and numerically. Finally, we investigate the theoretical limits of our iDDE model by experimentally exploring phenomena at extreme physical parameter setting, namely, high-frequency locking at strong feedback gain or pulse packages for very large delays. The large variety of oscillatory regimes of our broadband bandpass delay electro-optic oscillator is attractive for applications requiring rich optical pulse sources with different frequencies and/or wave forms (chaos-based communications, random number generation, chaos computing, and generation of stable multiple GHz frequency oscillations). PMID:19391821

Peil, Michael; Jacquot, Maxime; Chembo, Yanne Kouomou; Larger, Laurent; Erneux, Thomas

2009-02-01

57

Chaos and non-linear dynamics of a 1.55?m InGaAsP-InP microring laser

NASA Astrophysics Data System (ADS)

In this paper, numerical investigation is performed for a 1.55?m InGaAsP-InP microring laser as a function of the bus waveguide reflectivity, the injection current and the phase of the backreflected field. The nascent nonlinear instabilities are identified utilizing a multimode rate equation model, originating from the continuous injections of each clockwise to the counterclockwise mode and inverse. The resulted time series are filtered using a 40GHz electrical low pass filter in order to omit the mode beatings. Chaos data analysis revealed high-dimensional chaos by means of the correlation dimension and the metric entropy calculation with continuously testing surrogate data. With increasing the bus waveguide reflectivity, period-doubling and quasiperiodic route to chaos was found and the dimension was found to follow a linear increase. The same dimension increase was found with increasing the injection current, with the system experiencing sudden transitions from chaos to limit cycles. With altering the phase of the backreflected field the dynamics were found to transit from limit cycle (??=0-->?/2) to chaos, maintained chaotic (??=?/2-->2?/3) and finally returning to periodic states (??=2?/3-->2?). Furthermore, the dynamics are investigated with calculating the standardized moments.

Chlouverakis, Konstantinos E.; Mikroulis, Spiros; Syvridis, Dimitris

2008-05-01

58

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.

2006-07-05

59

An algebraic criterion for the onset of chaos in nonlinear dynamic systems

NASA Technical Reports Server (NTRS)

The correspondence between iterated integrals and a noncommutative algebra is used to recast the given dynamical system from the time domain to the Laplace-Borel transform domain. It is then shown that the following algebraic criterion has to be satisfied for the outset of chaos: the limit (as tau approaches infinity and x sub 0 approaches infinity) of ((sigma(k=0) (tau sup k) / (k* x sub 0 sup k)) G II G = 0, where G is the generating power series of the trajectories, the symbol II is the shuffle product (le melange) of the noncommutative algebra, x sub 0 is a noncommutative variable, and tau is the correlation parameter. In the given equation, symbolic forms for both G and II can be obtained by use of one of the currently available symbolic languages such as PLI, REDUCE, and MACSYMA. Hence, the criterion is a computer-algebraic one.

Unal, A.; Tobak, M.

1987-01-01

60

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

61

Application of nonlinear dynamics and chaos to ferroresonance in distribution systems

Ferroresonant overvoltages or undervoltages can occur in cable-fed transformer installations when single phase switching or interrupting is practiced. This paper identifies the ferroresonant circuit as a nonlinear dynamic system. Analysis and classification methods are presented which provide new insight into the global behavior of ferroresonance. The concepts presented offer potential for progress in the areas of transformer model development and evaluation, analysis and prediction of ferroresonance, and distribution system design and operation. Measurements from a typical five-legged core transformer installation are used to illustrate the application of nonlinear dynamics and chaotic systems to the problem of ferroresonance.

Mork, B.A. (Michigan Technological Univ., Houghton, MI (United States). Electrical Engineering Dept.); Stuehm, D.L. (North Dakota State Univ., Fargo, ND (United States). Electrical Engineering Dept.)

1994-04-01

62

Is there chaos in the brain? I. Concepts of nonlinear dynamics and methods of investigation

In the light of results obtained during the last two decades in a number of laboratories, it appears that some of the tools of nonlinear dynamics, first developed and improved for the physical sciences and engineering, are well-suited for studies of biological phenomena. In particular it has become clear that the different regimes of activities undergone by nerve cells, neural

Philippe Faure; Henri Korn

2001-01-01

63

Nonlinear instability and chaos in plasma wave-wave interactions. II. Numerical methods and results.

National Technical Information Service (NTIS)

In Part I of this work and Physics of Plasmas, June 1995, the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. It was shown that explosive instability arises from nonlinear co...

C. S. Kueny P. J. Morrison

1995-01-01

64

Reshaping-induced chaos suppression

We discuss the route for eliminating chaos in nonlinear oscillations by changing only the shape of a periodic force. We consider the Duffing oscillator forced with the Jacobi elliptic function sn and, applying a simple averaging technique, show that the phenomenon of chaos suppression due to reshaping of the driving force may be easily explained as an effect solely arising

Frank Rödelsperger; Yuri S. Kivshar; Hartmut Benner

1995-01-01

65

Linear and Nonlinear Analysis of Spatio-Temporal Chaos in Yttrium Iron Garnet Films

NASA Astrophysics Data System (ADS)

The spatio-temporal chaotic behavior of magnetic spin wave states in Yttrium Iron Garnet films is experimentally studied and analyzed. A 37 micron sample is placed in a DC magnetic field to align the atomic spins, which are then excited at resonant frequencies. Chaotic spin wave states result when surface modes of the film begin to interact above an excitation power threshold. We study the spatial correlation of the chaotic states of the sample by monitoring the magnetic moment at two positions on the film surface. The magnetic moments are detected by using coaxial loops mounted near the film surface and we can obtain time series corresponding to the signals at each position. We have analyzed the correlation between the two signals using both linear methods and a novel nonlinear analysis technique. This nonlinear analysis is non-parametric and is based solely on the statistics of the two time series.

Goodridge, Chris; Carroll, Tom; Pecora, Lou; Rachford, Fred

2000-03-01

66

Spatiotemporal chaos in mixed linear–nonlinear coupled logistic map lattice

NASA Astrophysics Data System (ADS)

We investigate the spatiotemporal dynamics with mixing degrees of nonlinear chaotic maps in coupling connections. Here, the coupling methods between lattices are both linear neighborhood coupling and the nonlinear chaotic map coupling of lattices. While strictly nearest neighborhood coupling is only a special case in the proposed system. We employed the criteria such as Kolmogorov–Sinai entropy density and universality, bifurcation diagrams, space–amplitude and space–time diagrams to investigate the chaotic behaviors of the proposed system in this paper. In fact, the proposed system contains new features for applications of cryptography such as the larger range of parameters for chaotic behaviors, the higher percentage of lattices in chaotic behaviors for most of parameters and less periodic windows in bifurcation diagrams. Furthermore, we also show the parameter ranges of the proposed system which hold those features in cryptography compared with those of the CML system. Finally, we design the encryption scheme based on the proposed system for an explicit illustration.

Zhang, Ying-Qian; Wang, Xing-Yuan

2014-05-01

67

Prediction based chaos control via a new neural network

NASA Astrophysics Data System (ADS)

In this Letter, a new chaos control scheme based on chaos prediction is proposed. To perform chaos prediction, a new neural network architecture for complex nonlinear approximation is proposed. And the difficulty in building and training the neural network is also reduced. Simulation results of Logistic map and Lorenz system show the effectiveness of the proposed chaos control scheme and the proposed neural network.

Shen, Liqun; Wang, Mao; Liu, Wanyu; Sun, Guanghui

2008-11-01

68

Bifurcation to nonlinear polarization dynamics and chaos in vertical-cavity surface-emitting lasers

NASA Astrophysics Data System (ADS)

In this contribution we provide an in depth theoretical analysis of the bifurcations leading to nonlinear polarization dynamics in a free-running vertical-cavity surface-emitting laser (VCSEL). We detail the sequence of bifurcations that occurs when increasing the injection current, and which brings the laser from linear to elliptical polarization emission and then self-pulsating or even more complex chaotic dynamics of the light intensity. Continuation techniques allow us to follow the stable and unstable limit cycle solutions emerging from Hopf bifurcations, and therefore to interpret the frequency of the self-pulsating polarization dynamics. The fundamental frequency of the pulsating dynamics is either close to the laser relaxation oscillation frequency or close to the linear-birefringence-induced polarization mode frequency splitting, depending on the laser parameters. A systematic analysis of the parameter space allows us to identify two scenarios that are in excellent qualitative agreement with those reported in recent experiments. Our results provide, moreover, evidence for an interesting polarization mode hopping mechanism, i.e., a so-called deterministic mode hopping where the laser exhibits a chaotic and therefore random-like hopping between two states that are elliptically polarized and nonorthogonal.

Virte, Martin; Panajotov, Krassimir; Sciamanna, Marc

2013-01-01

69

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

70

In this paper, the problem of dynamics and chaos control of an electromechanical instrument which is used to record the motion of earth during and earthquake is studied. The amplitude of the fifth sub- and super-harmonic oscillations for the resonant states are obtained and discussed using the multiples time scales method. It is found that chaotic and periodic orbits of

M. Siewe Siewe; F. M. Moukam Kakmeni; S. Bowong; C. Tchawoua

2006-01-01

71

Chaos in laser-matter interactions

This is a set of lecture notes given by the authors at the Universities of Rochester, Arkansas and Puerto Rico. This volume introduces the main ideas of chaos and its applications to a broad range of problems in quantum optics, electronics and laser physics. Contents: Introduction; Nonlinearity; The Period Doubling Route to Chaos; The Duffing Oscillator; Strange Attractors; Two-Frequency Route to Chaos; Intermittency; Dimensions of Attractors; Noise, The Lorenz Model and the Single-Mode Laser; Chaotic Lasers: Theory and Experiment; Hamiltonian Systems; The Henon-Heiles System; The Standard Mapping; Fat Fractals; Ergodicity and Mixing; Chaos and the Microwave Ionization of Hydrogen; The Kicked Pendulum: Classical Theory and Quantum Theory; Chaos and Multiple-Photon Excitation of Molecular Vibrations; Chaos and Molecular Rotations; Ideas in Quantum Chaos; Outlook.

Ackerhalt, J.; Milonni, P.; Shih, M.L.

1987-01-01

72

NSDL National Science Digital Library

The American Mathematical Society has made available online the article, "Prime Case of Chaos." The article discusses "conjectural links between the Riemann zeta function and chaotic quantum-mechanical systems."

Cipra, Barry

2003-10-10

73

Deterministic polarization chaos from a laser diode

NASA Astrophysics Data System (ADS)

Fifty years after the invention of the laser diode, and forty years after the butterfly effect signified the unpredictability of deterministic chaos, it is commonly believed that a laser diode behaves like a damped nonlinear oscillator and cannot be driven into chaotic operation without additional forcing or parameter modulation. Here, we counter that belief and report the first example of a free-running laser diode generating chaos. The underlying physics comprises 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 noise-driven mode hopping, but shows opposite statistical properties. Our findings open up new research areas for the creation of controllable and integrated sources of optical chaos.

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

2013-01-01

74

NSDL National Science Digital Library

The American Mathematical Society has made available online the article, "Prime Case of Chaos." The article discusses "conjectural links between the Riemann zeta function and chaotic quantum-mechanical systems." Additional full-text articles and tables of contents from each of the four volumes of What's Happening in the Mathematical Sciences are also available.

Cipra, Barry.

1999-01-01

75

ERIC Educational Resources Information Center

In "Thriving on Chaos," author Tom Peters suggests that future managers will need the quick reactions of video game players. Patient observation may work better. Chaos theory teaches that random happenings cannot be controlled; the toughest, randomly caused problems have no solutions; a leader's vision or moral code cannot be imposed on others;…

Jones, Rebecca

1994-01-01

76

Chaos Theory and the Problem of Change in Family Systems

In spite of the fact that nonlinear dynamical models have been used for almost half a century in the area of family process theory, an appreciation of the potential of chaos models is a relatively recent development. The present paper discusses the shift of focus in our understanding of family processes resulting from Prigogine's chaos framework, and outlines a chaos

Matthijs Koopmans

1998-01-01

77

Strange Attractors: Chaos Theory and Composition Studies.

ERIC Educational Resources Information Center

Chaos theory provides a powerful lens for re-seeing a number of issues in composition studies ranging in scale from achieving a generative model for text production to articulating the very nature of the discipline. Chaos systems are nonlinear, have complex forms, manifest recursive symmetries between scale levels, have feedback mechanisms, and…

Hesse, Doug

78

Sensitivity to initial conditions, entropy production, and escape rate at the onset of chaos

NASA Astrophysics Data System (ADS)

We analytically link three properties of nonlinear dynamical systems, namely sensitivity to initial conditions, entropy production, and escape rate, in z-logistic maps for both positive and zero Lyapunov exponents. We unify these relations at chaos, where the Lyapunov exponent is positive, and at its onset, where it vanishes. Our result unifies, in particular, two already known cases, namely (i) the standard entropy rate in the presence of escape, valid for exponential functionality rates with strong chaos, and (ii) the Pesin-like identity with no escape, valid for the power-law behavior present at points such as the Feigenbaum one.

Fuentes, Miguel Angel; Sato, Yuzuru; Tsallis, Constantino

2011-08-01

79

Chain Link Deformation in the Nonlinear Dynamics of Tracked Vehicles.

National Technical Information Service (NTIS)

In this investigation, a computational finite element procedure for the deformation and stress analysis of the chain links of tracked vehicles is presented and used to examine the validity of using the static approach in the design and stress analysis of ...

M. K. Sarwar T. Nakanishi A. A. Shabana

1995-01-01

80

In this paper we show how the chaotic behavior of two nonlinear gyros can be synchronized via fuzzy logic controller. Based on Lyapunov stability theory and fuzzy rules, the nonlinear controller and some generic sufficient conditions for global asymptotic synchronization are attained. We directly construct the fuzzy rules subject to a common Lyapunov function such that the error dynamics of

Her-Terng Yau

2007-01-01

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

Analysis of nonlinear vibration of a motor linkage mechanism system with composite links

NASA Astrophysics Data System (ADS)

This paper studies the nonlinear vibration of a three-phase AC motor-linkage mechanism system with links fabricated from three-dimensional braided composite materials. Taking the drive motor and the linkage mechanism as an integrated system, the dynamic equations of the system are established by the finite element method. The relation between the nonlinear vibration of the system and the parameters of the system is obtained by the method of multiple scales. Results show that not only the structural parameters, but also the electromagnetic parameters and the material parameters have significant effects on the nonlinear vibration of the system. Finally, a numerical example is presented.

Li, Zhaojun; Cai, Ganwei; Huang, Qibai; Liu, Shiqing

2008-04-01

83

Chaos: A Very Short Introduction

This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is `no more complicated than X=2.'Anyone who ever tried to give a popular

R Klagesh

2007-01-01

84

Chaos: A Very Short Introduction

This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is `no more complicated than X=2.Anyone who ever tried to give a popular

R Klages

2007-01-01

85

ERIC Educational Resources Information Center

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

Pryor, Robert G. L.; Bright, Jim

2003-01-01

86

NASA Astrophysics Data System (ADS)

We have investigated the correlation between the macroscopic physical properties and the microscopic molecular structure for linear rod-like polyamides with different linking structure of nonlinear optical chromophores by in situ corona poling and optical second harmonic generation. These polymers consist of a wholly aromatic rigid backbone poly( p-phenylene terephthalamide), PPTA and nonlinear optical chromophores of various sizes. Though all polymers with different linking structure of chromophores possess similar ?- and ?-glass transition temperatures, their bulk physical properties greatly depend on the microscopic linking structure. Especially the polyamide F-DCVA with a flexibly linked bulky chromophore exhibits a high internal stress due to a thermal contraction of the rigid polyamide backbone, which at room temperature can overcome the orientational force of the externally applied electric field.

Kwon, O.-Pil; Rezzonico, Daniele; Kwon, Seong-Ji; Jazbinsek, Mojca; Tapponnier, Axelle; Günter, Peter; Lee, Suck-Hyun

2007-03-01

87

Non-Linearity Effects of an OFDM-ROF Link Employing RF Amplifier and EAM

In this paper, a close agreement between a developed analytical model and an experimental case is presented to analyze non-linearity effects in terms of adjacent channel power ratio (ACPR) for OFDM signal fed RF amplifier integrated with radio over fibre (RoF) link.

A. R. Islam; M. R. H. Khan; N. Huda; A. S. Ali

2007-01-01

88

Nonlinear dynamic system identification using Chebyshev functional link artificial neural networks

A computationally efficient artificial neural network (ANN) for the purpose of dynamic nonlinear system identification is proposed. The major drawback of feedforward neural networks, such as multilayer perceptrons (MLPs) trained with the backpropagation (BP) algorithm, is that they require a large amount of computation for learning. We propose a single-layer functional-link ANN (FLANN) in which the need for a hidden

Jagdish Chandra Patra; Alex C. Kot

2002-01-01

89

NSDL National Science Digital Library

This website from the Department of Physics and Astronomy at Johns Hopkins University introduces chaos and describes how it appears in animal populations and weather models. The site also describes fractals and explains the butterfly effect. Images provide representations of chaotic behavior.

Bradley, Larry

2009-06-15

90

Chaos in Environmental Education.

ERIC Educational Resources Information Center

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

Hardy, Joy

1999-01-01

91

The mechanism of the dominance (preponderance) of the 0+ ground state for random interactions is proposed to be the chaotic realization of the highest rotational symmetry. This is a consequence of a general principle on the chaos and symmetry that the highest symmetry is given to the ground state if sufficient mixing occurs in a chaotic way by a random interaction. Under this symmetry-realization mechanism, the ground-state parity and isospin can be predicted so that the positive parity is favored over the negative parity and the isospin T = 0 state is favored over higher isospin. It is further suggested how one can enhance the realization of highest symmetries within random interactions. Thus, chaos and symmetry are shown to be linked deeply.

Otsuka, Takaharu [Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan); Center for Nuclear Study, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan); RIKEN, Hirosawa, Wako-shi, Saitama, 351-0198 (Japan); Shimizu, Noritaka [Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo, 113-0033 (Japan); RIKEN, Hirosawa, Wako-shi, Saitama, 351-0198 (Japan)

2004-09-13

92

Quantum Chaos generates Regularities

The mechanism of the dominance (preponderance) of the 0+ ground state for random interactions is proposed to be the chaotic realization of the highest rotational symmetry. This is a consequence of a general principle on the chaos and symmetry that the highest symmetry is given to the ground state if sufficient mixing occurs in a chaotic way by a random interaction. Under this symmetry-realization mechanism, the ground-state parity and isospin can be predicted so that the positive parity is favored over the negative parity and the isospin T = 0 state is favored over higher isospin. It is further suggested how one can enhance the realization of highest symmetries within random interactions. Thus, chaos and symmetry are shown to be linked deeply.

Otsuka, Takaharu [Department of Physics, University of Tokyo (Japan); RIKEN (Japan); Center for Nuclear Study, University of Tokyo (Japan); Shimizu, Noritaka [Department of Physics, University of Tokyo (Japan); RIKEN (Japan)

2005-07-08

93

NASA Astrophysics Data System (ADS)

Preface; Acknowledgments; Introduction: 1. The legacy of chaos in quantum mechanics G. Casati and B. V. Chirikov; Part I. Classical Chaos and Quantum Localization: 2. Stochastic behaviour of a quantum pendulum under a periodic perturbation G. Casati, B. V. Chirikov, F. M. Izrailev and J. Ford; 3. Quantum dynamics of a nonintegrable system D. R. Grempel, R. E. Prange and S. E. Fishman; 4. Excitation of molecular rotation by periodic microwave pulses. A testing ground for Anderson localization R. Blümel, S. Fishman and U. Smilansky; 5. Localization of diffusive excitation in multi-level systems D. K. Shepelyansky; 6. Classical and quantum chaos for a kicked top F. Haake, M. Kus and R. Scharf; 7. Self-similarity in quantum dynamics L. E. Reichl and L. Haoming; 8. Time irreversibility of classically chaotic quantum dynamics K. Ikeda; 9. Effect of noise on time-dependent quantum chaos E. Ott, T. M. Antonsen Jr and J. D. Hanson; 10. Dynamical localization, dissipation and noise R. F. Graham; 11. Maximum entropy models and quantum transmission in disordered systems J.-L. Pichard and M. Sanquer; 12. Solid state 'atoms' in intense oscillating fields M. S. Sherwin; Part II. Atoms in Strong Fields: 13. Localization of classically chaotic diffusion for hydrogen atoms in microwave fields J. E. Bayfield, G. Casati, I. Guarneri and D. W. Sokol; 14. Inhibition of quantum transport due to 'scars' of unstable periodic orbits R. V. Jensen, M. M. Sanders, M. Saraceno and B. Sundaram; 15. Rubidium Rydberg atoms in strong fields G. Benson, G. Raithel and H. Walther; 16. Diamagnetic Rydberg atom: confrontation of calculated and observed spectra C.-H. Iu, G. R. Welch, M. M. Kash, D. Kleppner, D. Delande and J. C. Gay; 17. Semiclassical approximation for the quantum states of a hydrogen atom in a magnetic field near the ionization limit M. Y. Kuchiev and O. P. Sushkov; 18. The semiclassical helium atom D. Wintgen, K. Richter and G. Tanner; 19. Stretched helium: a model for quantum chaos in two-electron atoms R. Blümel and W. P. Reinhardt; Part III. Semiclassical Approximations: 20. Semiclassical theory of spectral rigidity M. V. Berry; 21. Semiclassical structure of trace formulas R. G. Littlejohn; 22. h-Expansion for quantum trace formulas P. Gaspard; 23. Pinball scattering B. Eckhardt, G. Russberg, P. Cvitanovic, P. E. Rosenqvist and P. Scherer; 24. Logarithm breaking time in quantum chaos G. P. Berman and G. M. Zaslavsky; 25. Semiclassical propagation: how long can it last? M. A. Sepulveda, S. Tomsovic and E. J. Heller; 26. The quantized Baker's transformation N. L. Balazs and A. Voros; 27. Classical structures in the quantized baker transformation M. Saraceno; 28. Quantum nodal points as fingerprints of classical chaos P. Leboeuf and A. Voros; 29. Chaology of action billiards A. M. Ozorio de Almeida and M. A. M. de Aguiar; Part IV. Level Statistics and Random Matrix Theory: 30. Characterization of chaotic quantum spectra and universality of level fluctuation laws O. Bohigas, M. J. Giannono, and C. Schmit; 31. Quantum chaos, localization and band random matrices F. M. Izrailev; 32. Structural invariance in channel space: a step toward understanding chaotic scattering in quantum mechanics T. H. Seligman; 33. Spectral properties of a Fermi accelerating disk R. Badrinarayanan and J. J. José; 34. Spectral properties of systems with dynamical localization T. Dittrich and U. Smilansky; 35. Unbound quantum diffusion and fractal spectra T. Geisel, R. Ketzmerick and G. Petschel; 36. Microwave studies in irregularly shaped billiards H.-J. Stöckmann, J. Stein and M. Kollman; Index.

Casati, Giulio; Chirikov, Boris

1995-04-01

94

Photodetector nonlinearity limitations on a high-dynamic range 3 GHz fiber optic link

The performance of a dc to 3 GHz externally modulated link utilizing balanced high-power photodetection is presented. Nonlinearity measurements of high power photodiodes show 1 dB compression currents in excess of 55 mA and an output third-order intercept point of +32 to +34 dBm. These high current photodetectors permit the use of high power lasers as external modulator sources for

Keith J. Williams; Lee T. Nichols; Ronald D. Esman

1998-01-01

95

Computer modeling of spectral efficiency and sidelobe buildup effects in nonlinear satellite links

Computer modeling results are presented for the bit error rate performance and spectral shaping properties of several modulation techniques in a satellite link containing filtering, nonlinearities (both AM\\/AM and AM\\/PM), onboard processing, and multiple transponder crosslinks. The modulation techniques compared include binary and quaternary PSK, Staggered-QPSK and Serial Minimum Shift Keying. Additional performance criteria investigated include the frequency, bandwidth, and

E. J. Zakrzewski

1982-01-01

96

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

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

Manouchehr S. Rafie; K. Sam Shanmugan

1989-01-01

97

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

98

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

99

Optical chaos; Proceedings of the Meeting, Quebec, Canada, June 3, 4, 1986

Papers on laser instabilities and chaos, which discuss definitions and the measuring of chaos, a general classification of laser instabilities, and the instability modeling of gas lasers, are presented. Consideration is given to dynamical instabilities, noise, chaos, and bistability in lasers; dynamical processes in semiconductors; and four-wave mixing and bistability. Topics discussed include nonlinear media, spatial effects, and lasers with external modulation.

Chrostowski, J.; Abraham, N.B.

1986-01-01

100

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

101

Chaos in voice, from modeling to measurement.

Chaos has been observed in turbulence, chemical reactions, nonlinear circuits, the solar system, biological populations, and seems to be an essential aspect of most physical systems. Chaos may also be central to the interpretation of irregularity in voice disorders. This presentation will summarize the results from a series of our recent studies. These studies have demonstrated the prescence of chaos in computer models of vocal folds, experiments with excised larynges, and human voices. Methods based on nonlinear dynamics can be used to quantify chaos and irregularity in vocal fold vibration. Studies have suggested that disordered voices from laryngeal pathologies such as laryngeal paralysis, vocal polyps, and vocal nodules might exhibit chaotic behaviors. Conventional parameters, such as jitter and shimmer, may be unreliable for analysis of periodic and chaotic voice signals. Nonlinear dynamic methods, however, have differentiated between normal and pathological phonations and can describe the aperiodic or chaotic voice. Chaos theory and nonlinear dynamics can enchance our understanding and therefore our assessment of pathological phonation. PMID:15964740

Jiang, Jack J; Zhang, Yu; McGilligan, Clancy

2006-03-01

102

Chaos synchronization of two stochastic Duffing oscillators by feedback control

This paper addresses chaos synchronization of two identical stochastic Duffing oscillators with bounded random parameters subject to harmonic excitations. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by Gegenbauer polynomial approximation, so that the chaos synchronization problem of stochastic Duffing oscillators can be reduced into that of the equivalent deterministic systems. Then

Cunli Wu; Tong Fang; Haiwu Rong

2007-01-01

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

An LPV framework for chaos synchronization in communication

NASA Astrophysics Data System (ADS)

This paper proposes a unified framework to achieve chaos synchronization of both classes of chaotic discrete-time systems, namely maps involving polynomial nonlinearities and piecewise linear maps. It is shown that all of those chaotic systems can be rewritten as a polytopic Linear Parameter Varying (LPV) system. A unified approach to tackle chaos synchronization problems encountered in communication is derived.

Halimi, M.; Millérioux, G.

2014-05-01

105

The main object in this study concerns to vibration control of a one-link flexible arm system. The robot link manipulators are widely used in various industrial applications. A variable structure system (VSS) non-linear observer has been proposed in order to reduce the oscillation in controlling the angular. The non-linear observer parameters are optimized using a novel version of simultaneous perturbation

J. Martinez; U. Sawut; K. Nakano

2008-01-01

106

Conjugate pair of representations in chaos and quantum mechanics

Being based on the observation that a conjugate pair of representations, or dual logic, is a necessity under the presence of chaos, a new interpretation of quantum theory is proposed as describing proto-chaos. This chaos has to be a result of basic nonlinearity in the dynamic structure, of which, however, the nonchaotic phase seems to lie ourside the reach of experimental technique, thus the term proto-chaos. Nevertheless, assuming no extra degrees of freedom, the interpretation clarifies a number of riddles posed hitherto and throws some light on the overall hierarchical structure of the authors understanding and description of nature.

Tomita, K.

1987-07-01

107

NASA Astrophysics Data System (ADS)

An expression is derived for the symbol error probability (SEP) of coherent M-ary PSK signals (M of greater than 4) transmitted through a bandlimited nonlinear channel. The bandpass nonlinearity considered exhibits AM/AM and AM/PM distortions. Additive white Gaussian noise on both up- and down-links, and intersymbol interference on up-links, only have been taken as the system impairments. SEPs are computed for an onboard TWTA and a phase-compensating receiver. The use of a soft-limiter linearizer to compensate for the nonlinearities is also presented.

Gemikonakli, O.; Aghvami, A. H.

1989-08-01

108

NASA Astrophysics Data System (ADS)

Deterministic dynamics often leads to complex, unpredictable behavior. This randomness or chaos produces information and limits one's ability to predict future events. There are two components to this imposed ignorance. The first arises in a mathematical context from highly convoluted orbit structures in state space. These allow a system to rapidly visit many regions of state space. In a physical context, the second comes from the coupling of the system -under-study to other systems that provide information to it. Extrinsic information sources preclude the exact determination of the system's state. By the mechanism of their complex orbits, chaotic systems amplify this uncertainty into unpredictable macroscopic behavior. The physical study of chaotic dynamical systems is incomplete without an appreciation of how external fluctuations affect their predictability. Using information theory we describe how to measure the unpredictability of (i) deterministic chaotic systems (without extrinsic noise), and (ii) nondeterministic chaotic systems (coupled to extrinsic noise). Scaling concepts are invaluable tools in this. Scaling reveals that extrinsic noise acts as a disordering field for chaos. Furthermore, even for systems with extrinsic noise, scaling captures fundamental features of chaotic behavior. It provides a unified framework for the topological, metric, and Renyi dimensions and entropies. The physical relevance of these concepts lies in their ability to analyze noisy chaotic signals. The information theoretic approach to temporally complex behavior is applied to chaotic signals from two hydrodynamic experiments. In addition, the dynamic aspects of pattern evolution and the possible breakdown of (naive) dynamical systems theory is discussed for experiments with an image processing system. The first appendix contains descriptions of algorithms for dynamical systems studies. The second discusses a movie on the geometric structure of chaotic driven oscillators using animated Poincare sections.

Crutchfield, James Patrick, Jr.

109

Improvement and empirical research on chaos control by theory of ``chaos + chaos = order''

NASA Astrophysics Data System (ADS)

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

Fulai, Wang

2012-12-01

110

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

This paper focuses on advancing the understanding of Parrondian effects and their paradoxical behavior in nonlinear dynamical systems. Some examples are given to show that a dynamics combined by more than two discrete chaotic dynamics in deterministic manners can give rise to order when combined. The chaotic maps in our study are more general than those in the current literatures as far as "chaos + chaos?=?order" is concerned. Some problems left over in the current literatures are solved. It is proved both theoretically and numerically that, given any m chaotic dynamics generated by the one-dimensional real Mandelbrot maps, it is no possible to get a periodic system when all the m chaotic dynamics are alternated in random manner, but for any integer m(m ? 2) a dynamics combined in deterministic manner by m Mandelbrot chaotic dynamics can be found to give rise to a periodic dynamics of m periods. Numerical and mathematical analysis prove that the paradoxical phenomenon of "chaos + chaos?=?order" also exist in the dynamics generated by non-Mandelbrot maps. PMID:23278080

Fulai, Wang

2012-12-01

111

Effective suppressibility of chaos.

Suppression of chaos is a relevant phenomenon that can take place in nonlinear dynamical systems when a parameter is varied. Here, we investigate the possibilities of effectively suppressing the chaotic motion of a dynamical system by a specific time independent variation of a parameter of our system. In realistic situations, we need to be very careful with the experimental conditions and the accuracy of the parameter measurements. We define the suppressibility, a new measure taking values in the parameter space, that allows us to detect which chaotic motions can be suppressed, what possible new choices of the parameter guarantee their suppression, and how small the parameter variations from the initial chaotic state to the final periodic one are. We apply this measure to a Duffing oscillator and a system consisting on ten globally coupled He?non maps. We offer as our main result tool sets that can be used as guides to suppress chaotic dynamics. PMID:23822472

López, Álvaro G; Seoane, Jesús M; Sanjuán, Miguel A F

2013-06-01

112

Effective suppressibility of chaos

NASA Astrophysics Data System (ADS)

Suppression of chaos is a relevant phenomenon that can take place in nonlinear dynamical systems when a parameter is varied. Here, we investigate the possibilities of effectively suppressing the chaotic motion of a dynamical system by a specific time independent variation of a parameter of our system. In realistic situations, we need to be very careful with the experimental conditions and the accuracy of the parameter measurements. We define the suppressibility, a new measure taking values in the parameter space, that allows us to detect which chaotic motions can be suppressed, what possible new choices of the parameter guarantee their suppression, and how small the parameter variations from the initial chaotic state to the final periodic one are. We apply this measure to a Duffing oscillator and a system consisting on ten globally coupled Hénon maps. We offer as our main result tool sets that can be used as guides to suppress chaotic dynamics.

López, Álvaro G.; Seoane, Jesús M.; Sanjuán, Miguel A. F.

2013-06-01

113

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

114

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

115

Quasiperiodic transition to spatiotemporal chaos in weakly ionized magnetoplasmas

NASA Astrophysics Data System (ADS)

The transition to temporal and then spatiotemporal chaos in a weakly ionized magnetoplasma system which supports nonlinear flute-type ionization-drift waves was studied. The system follows a complex quasiperiodic route with strong nonlinear mode-mode competition, a narrow frequency-locking interval, and an unstable third independent frequency to temporal chaos. At the onset of the spatial chaos, the discrete spatiotemporal modes decrease down to the noise floor, the temporal correlation is reduced more than ten times, and the correlation dimension jumps from less than 8 to greater than 12.

Chu, J. H.; I, Lin

1989-01-01

116

ERIC Educational Resources Information Center

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

Huwe, Terence K.

2009-01-01

117

Chaos, brain and divided consciousness.

Modern trends in psychology and cognitive neuroscience suggest that applications of nonlinear dynamics, chaos and self-organization seem to be particularly important for research of some fundamental problems regarding mind-brain relationship. Relevant problems among others are formations of memories during alterations of mental states and nature of a barrier that divides mental states, and leads to the process called dissociation. This process is related to a formation of groups of neurons which often synchronize their firing patterns in a unique spatial maner. Central theme of this study is the relationship between level of moving and oscilating mental processes and their neurophysiological substrate. This opens a question about principles of organization of conscious experiences and how these experiences arise in the brain. Chaotic self-organization provides a unique theoretical and experimental tool for deeper understanding of dissociative phenomena and enables to study how dissociative phenomena can be linked to epileptiform discharges which are related to various forms of psychological and somatic manifestations. Organizing principles that constitute human consciousness and other mental phenomena from this point of view may be described by analysis and reconstruction of underlying dynamics of psychological or psychophysiological measures. These nonlinear methods in this study were used for analysis of characteristic changes in EEG and bilateral electrodermal activity (EDA) during reliving of dissociated traumatic and stressful memories and during psychopathological states. Analysis confirms a possible role of chaotic transitions in the processing of dissociated memory. Supportive finding for a possible chaotic process related to dissociation found in this study represent also significant relationship of dissociation, epileptiform discharges measured by typical psychopathological manifestations and characteristic laterality changes in bilateral EDA in patients with schizophrenia and depression. Increased level of psychopathological symptoms indicates close relationship to the right-left EDA asymmetry and asymmetry of information entropy calculated by non-linear recurrence quantification analysis of EDA records. Because epileptiform activity has specific chaotic behaviour and calculated information entropy from EDA records reflects the complexity of the deterministic structure in the system there is a relevant assumption that unilaterally increased complexity may produce interhemispheric disbalance and increased chaoticity which hypothetically may serve as a dynamic source of epileptiform discharges related to trauma induced kindling mechanism. Specific form of chaotic inner organization which cannot be explained only as a consequence of external causality support also psychophysiological data that lead to the so-called self-organizing theory of dreaming by Kahn and Hobson. This study suggests that self-organizing theory of dreaming is particularly important with respect to problem of memory formation and processing during dissociative states characteristic for dreams. Recent data and also findings of this study support the research utility of chaos theory in psychology and neuroscience, and also its conceptual view of dynamic ordering factors and self-organization underlying psychological processes and brain physiology. PMID:17867519

Bob, Petr

2007-01-01

118

BOOK REVIEW: Chaos: A Very Short Introduction

This book is a new volume of a series designed to introduce the curious reader to anything from ancient Egypt and Indian philosophy to conceptual art and cosmology. Very handy in pocket size, Chaos promises an introduction to fundamental concepts of nonlinear science by using mathematics that is `no more complicated than X=2. Anyone who ever tried to give a

Leonard Smith

2007-01-01

119

Switching manifold approach to chaos synchronization

In this Rapid Communication, a switching manifold approach is proposed for synchronizing chaos. The effectiveness of this nonlinear control strategy is demonstrated by both theoretical analysis and numerical simulations on two typical chaotic systems: the Lorenz and the modified Lorenz systems.

Jin-Qing Fang; Yiguang Hong; Guanrong Chen

1999-01-01

120

Europe Approaches Chaos with Electrical Circuits.

National Technical Information Service (NTIS)

In this report, the underlying concepts for the period-doubling route to chaos are presented, and the scope of recent research in a variety of physical systems is briefly noted. Then European research investigating chaotic behavior in nonlinear, driven el...

D. Mosher

1984-01-01

121

Chaos Theory and the Mayaguez Crisis.

National Technical Information Service (NTIS)

The emerging science of Chaos may be applicable to sciences other than just those that are classical. Characterized by a non-linear notion that a small input can have a disproportionately large output, the phenomenon is referred to as the 'butterfly' effe...

T. H. Mueller

1990-01-01

122

Coherence and chaos in extended dynamical systems

Coherence, chaos, and pattern formation are characteristic elements of the nonequilibrium statistical mechanics controlling mesoscopic order and disorder in many-degree-of-freedom nonlinear dynamical systems. Competing length scales and/or time scales are the underlying microscopic driving forces for many of these aspects of ``complexity.`` We illustrate the basic concepts with some model examples of classical and quantum, ordered and disordered, nonlinear systems.

Bishop, A.R.

1994-12-31

123

NASA Astrophysics Data System (ADS)

We represent results of numerical simulations for upgrade of optical link with SMF by using the DDMS technique based on application of compensating optical cable coiled around of optical closure. We propose this technique for minimization land cost. Nonlinearity management for decreasing of quasi-solitons interaction is considered. Based on NLSE the model of optical link regeneration section with dispersion and nonlinearity management is described. The NLSE was solved numerically. Estimated values for optical system performance were derived by taking into account the amplified spontaneous emission noise, parameters of dispersion map deviations, and the interaction of quasi-solitons.

Burdin, Vladimir A.; Bourdine, Anton V.; Volkov, Kirill A.

2012-01-01

124

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

125

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

126

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.

Oestreicher, Christian

2007-01-01

127

High-dimensional chaos from self-sustained collisions of solitons

NASA Astrophysics Data System (ADS)

We experimentally demonstrate chaos generation based on collisions of electrical solitons on a nonlinear transmission line. The nonlinear line creates solitons, and an amplifier connected to it provides gain to these solitons for their self-excitation and self-sustenance. Critically, the amplifier also provides a mechanism to enable and intensify collisions among solitons. These collisional interactions are of intrinsically nonlinear nature, modulating the phase and amplitude of solitons, thus causing chaos. This chaos generated by the exploitation of the nonlinear wave phenomena is inherently high-dimensional, which we also demonstrate.

Yildirim, O. Ozgur; Ham, Donhee

2014-06-01

128

Reflection-antisymmetric spatiotemporal chaos under field-translational invariance.

We propose a route to spatiotemporal chaos, in which the system is assumed to have spatial reflection antisymmetry and field-translation symmetry. The lowest-order nonlinear equation that satisfies these symmetries is explored with the weak nonlinear analysis around the bifurcation point. We conclude that the nonlinear term ?(x)(2)u?(x)(3)u is important to make a nontrivial dynamics, and show that the nonlinear dynamical equation having this term produces a turbulent dynamics. PMID:22587169

Matsuo, Miki Y; Sano, Masaki

2012-03-01

129

Detecting chaos in heavy-noise environments.

Detecting chaos and estimating the limit of prediction time in heavy-noise environments is an important and challenging task in many areas of science and engineering. An important first step toward this goal is to reduce noise in the signals. Two major types of methods for reducing noise in chaotic signals are chaos-based approaches and wavelet shrinkage. When noise is strong, chaos-based approaches are not very effective, due to failure to accurately approximate the local chaotic dynamics. Here, we propose a nonlinear adaptive algorithm to recover continuous-time chaotic signals in heavy-noise environments. We show that it is more effective than both chaos-based approaches and wavelet shrinkage. Furthermore, we apply our algorithm to study two important issues in geophysics. One is whether chaos exists in river flow dynamics. The other is the limit of prediction time for the Madden-Julian oscillation (MJO), which is one of the most dominant modes of low-frequency variability in the tropical troposphere and affects a wide range of weather and climate systems. Using the adaptive filter, we show that river flow dynamics can indeed be chaotic. We also show that the MJO is weakly chaotic with the prediction time around 50 days, which is considerably longer than the prediction times determined by other approaches. PMID:21599273

Tung, Wen-wen; Gao, Jianbo; Hu, Jing; Yang, Lei

2011-04-01

130

NASA Astrophysics Data System (ADS)

Study of beam halo-chaos has become a key issue of concern for many future important applications. Control of halo-chaos has been researched intensively. This is the first time that the synchronization of beam halo-chaos has been realized in this field so far. Two nonlinear feedback control methods are proposed for the cascading synchronizing halo-chaos in coupled lattices of a periodic focusing channel. The simulation results show that the methods are effective. The realization of the synchronization of beam halo-chaos is significant not only for halo-chaos control itself but also for halo-chaos-based secure communication which may become an innovative technique.

Fang, Jin-Qing; Yu, Xing-Huo

2004-08-01

131

Chaos in oil prices? Evidence from futures markets

We test for the presence of low-dimensional chaotic structure in crude oil, heating oil, and unleaded gasoline futures prices from the early 1980s. Evidence on chaos will have important implications for regulators and short-term trading strategies. While we find strong evidence of non-linear dependencies, the evidence is not consistent with chaos. Our test results indicate that ARCH-type processes, with controls

Bahram Adrangi; Arjun Chatrath; Kanwalroop Kathy Dhanda; Kambiz Raffiee

2001-01-01

132

Invoking the Muse: Dada's Chaos.

Dada, a self-proclaimed (anti)art (non)movement, took shape in 1916 among a group of writers and artists who rejected the traditions of a stagnating bourgeoisie. Instead, they adopted means of creative expression that embraced chaos, stoked instability and undermined logic, an outburst that overturned centuries of classical and Romantic aesthetics. Paradoxically, this insistence on disorder foreshadowed a new order in understanding creativity. Nearly one hundred years later, Nonlinear Dynamical Systems theory (NDS) gives renewed currency to Dada's visionary perspective on chance, chaos and creative cognition. This paper explores commonalities between NDS-theory and this early precursor of the nonlinear paradigm, suggesting that their conceptual synergy illuminates what it means to 'be creative' beyond the disciplinary boundaries of either. Key features are discussed within a 5P model of creativity based on Rhodes' 4P framework (Person, Process, Press, Product), to which I add Participant-Viewer for the interactivity of observer-observed. Grounded in my own art practice, several techniques are then put forward as non-methodical methods that invoke creative border zones, those regions where Dada's chance and design are wedded in a dialectical tension of opposites. PMID:24894264

Rosen, Diane

2014-07-01

133

Decoherence, determinism and chaos

The author claims by now to have made his case that modern work on fractals and chaos theory has already removed the presumption that classical physics is `deterministic`. Further, he claims that in so far as classical relativistic field theory (i.e. electromagnetism and gravitation) are scale invariant, they are self-consistent only if the idea of `test-particle` is introduced from outside the theory. Einstein spent the last years of his life trying to use singularities in the metric as `particles` or to get them out of the non-linearities in a grand unified theory -- in vain. So classical physics in this sense cannot be the fundamental theory. However, the author claims to have shown that if he introduces a `scale invariance bounded from below` by measurement accuracy, then Tanimura`s generalization of the Feynman proof as reconstructed by Dyson allows him to make a consistent classical theory for decoherent sources sinks. Restoring coherence to classical physics via relativistic action-at-a distance is left as a task for the future. Relativistic quantum mechanics, properly reconstructed from a finite and discrete basis, emerges in much better shape. The concept of `particles has to be replaced by NO-YES particulate events, and particle-antiparticle pair creation and annihilation properly formulated.

Noyes, H.P.

1994-01-01

134

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

135

Observational Manifestation of Chaos in Astrophysical Objects

NASA Astrophysics Data System (ADS)

This book addresses a broad range of problems related to observed manifestations of chaotic motions in galactic and stellar objects, by invoking basic theory, numerical modeling, and observational evidence. For the first time, methods of stochastic dynamics are applied to actually observed astronomical objects, e.g. the gaseous disc of the spiral galaxy NGC 3631. In the latter case, the existence of chaotic trajectories in the boundary of giant vortices was recently found by the calculation of the Lyapunov characteristic number of these trajectories. The reader will find research results on the peculiarities of chaotic system behaviour; a study of the integrals of motion in self-consistent systems; numerical modeling results of the evolution process of disk systems involving resonance excitation of the density waves in spiral galaxies; a review of specific formations in stars and high-energy sources demonstrating their stochastic nature; a discussion of the peculiarities of the precessional motion of the accretion disk and relativistic jets in the double system SS 433; etc. This book stands out as the first one that deals with the problem of chaos in real astrophysical objects. It is intended for graduate and post-graduate students in the fields of non-linear dynamics, astrophysics, planetary and space physics; specifically for those dealing with computer modeling of the relevant processes. Link: http://www.wkap.nl/prod/b/1-4020-0935-6

Fridman, A.; Marov, M.; Miller, R.

2002-12-01

136

ERIC Educational Resources Information Center

Before chaos theory, Western society had no "scientific" tools to deal with disorder and unpredictability because science relied on factual evidence. With chaos theory, knowing and believing are now seen as interconnected and both are considered authentic. Counseling should reflect this authenticity with compassion, not control. (LKS)

Gelatt, H. B.

1995-01-01

137

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

138

Harnessing quantum transport by transient chaos

NASA Astrophysics Data System (ADS)

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

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

2013-03-01

139

Bistable solitons and the route to chaos

NASA Astrophysics Data System (ADS)

The paper presents a numerical simulation of an optical ring cavity in which the propagation of an envelope pulse is described by a particular form of the generalized nonlinear Schroedinger equation which admits bistable-soliton solutions. The cavity is synchronously pumped by a train of identical pulses. Some examples of the effect of the bistable solitons on the bifurcation sequence, i.e., the route to chaos, are presented.

McAvity, David M.; Enns, Richard H.; Rangnekar, Sada S.

1988-11-01

140

Chaos control of parametric driven Duffing oscillators

NASA Astrophysics Data System (ADS)

Duffing resonators are typical dynamic systems, which can exhibit chaotic oscillations, subject to certain driving conditions. Chaotic oscillations of resonating systems with negative and positive spring constants are identified to investigate in this paper. Parametric driver imposed on these two systems affects nonlinear behaviours, which has been theoretically analyzed with regard to variation of driving parameters (frequency, amplitude). Systematic calculations have been performed for these two systems driven by parametric pumps to unveil the controllability of chaos.

Jin, Leisheng; Mei, Jie; Li, Lijie

2014-03-01

141

Blind watermarking algorithm based on henon chaos system and lifting scheme wavelet

A new blind watermarking algorithm based on Henon chaos system and lifting scheme wavelet is proposed. Two dimensional reversible nonlinear Henon chaos system that is dealt with mould operation is utilized to scramble the watermarking images by chain type; then the scrambling watermarking is embedded into the lifting scheme wavelet coefficients using the pseudorandom of the two dimensional Henon chaotic

Zheng-Wei Shen; Wei-Wei Liao; Ya-Nan Shen

2009-01-01

142

Chaos Control and Synchronization of Cellular Neural Network with Delays Based on OPNCL Control

NASA Astrophysics Data System (ADS)

The problem of chaos control and complete synchronization of cellular neural network with delays is studied. Based on the open plus nonlinear closed loop (OPNCL) method, the control scheme and synchronization scheme are designed. Both the schemes can achieve the chaos control and complete synchronization of chaotic neural network respectively, and their validity is further verified by numerical simulation experiments.

Tang, Qian; Wang, Xing-Yuan

2010-03-01

143

Energy enhancement and chaos control in microelectromechanical systems

NASA Astrophysics Data System (ADS)

For a resonator in an electrostatic microelectromechanical system (MEMS), nonlinear coupling between applied electrostatic force and the mechanical motion of the resonator can lead to chaotic oscillations. Better performance of the device can be achieved when the oscillations are periodic with large amplitude. We investigate the nonlinear dynamics of a system of deformable doubly clamped beam, which is the core in many MEMS resonators, and propose a control strategy to convert chaos into periodic motions with enhanced output energy. Our study suggests that chaos control can lead to energy enhancement and consequently high performance of MEM devices.

Park, Kwangho; Chen, Qingfei; Lai, Ying-Cheng

2008-02-01

144

Energy enhancement and chaos control in microelectromechanical systems.

For a resonator in an electrostatic microelectromechanical system (MEMS), nonlinear coupling between applied electrostatic force and the mechanical motion of the resonator can lead to chaotic oscillations. Better performance of the device can be achieved when the oscillations are periodic with large amplitude. We investigate the nonlinear dynamics of a system of deformable doubly clamped beam, which is the core in many MEMS resonators, and propose a control strategy to convert chaos into periodic motions with enhanced output energy. Our study suggests that chaos control can lead to energy enhancement and consequently high performance of MEM devices. PMID:18352106

Park, Kwangho; Chen, Qingfei; Lai, Ying-Cheng

2008-02-01

145

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

146

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

147

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

148

NSDL National Science Digital Library

This site describes Ben Tamari's thoughts on dynamical system in economics, fractals and chaos in nature. The site is divided into six sections: Patterns, Attractors, Economics, Stocks, Form, and Metaphors.

Tamari, Ben

2007-06-03

149

NSDL National Science Digital Library

This website introduces chaos and describes how it appears in animal populations and weather models. The site also describes fractals and explains the butterfly effect. Images provide representations of chaotic behavior.

2007-07-18

150

NASA Astrophysics Data System (ADS)

We present evidence that collisionless simulations of galaxy formation can lead to substantial amounts of chaos, and that this chaos can play an important role in driving the galaxy towards a `well-mixed' state. Earlier numerical integrations of orbits in fixed potentials had shown (Kandrup, Vass, & Sideris, MNRAS 341, 927-936, 2003) that a period of time-dependence with a strong, possibly damped, oscillatory component can trigger large amounts of transient chaos, and it had been argued that resonant phase mixing associated with this transient chaos could play a major role in accounting for the speed and efficiency in violent relaxation. Simulations described here corroborate this physical expectation, thereby reinforcing the idea that violent relaxation can be interpreted as a collective process driven (e.g., Terzi{\\' c} & Kandrup, MNRAS, in press, 2003) by resonances between the frequencies of bulk oscillations and the natural frequencies of individual orbits.

Vass, I. M.; Kandrup, H. E.; Terzi{'c}, B.

2003-12-01

151

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

152

NASA Astrophysics Data System (ADS)

We have investigated the "weak chaos" exponent to see if it can be considered as a classification parameter of different sandpile models. Our simulation results show that the (Abelian) BTW sandpile model, the (non-Abelian) Zhang model, and the ("Abelian") Manna model possesses different "weak chaos" exponents, so they may belong to different universality classes. Finally, we show that getting off the critical point destroys this behavior in these models.

Moghimi-Araghi, Saman; Mollabashi, Ali

153

National Technical Information Service (NTIS)

Two numerical methods, Gauss Pseudospectral Method and Generalized Polynomial Chaos Algorithm, were combined to form a hybrid algorithm for solving nonlinear optimal control and optimal path planning problems with uncertain parameters. The algorithm was a...

G. C. Cottrill

2012-01-01

154

Post-detection nonlinear distortion for efficient MLSD in optical links.

In this paper, we investigate the use of nonlinear distortion of the electrical post-detection signal in order to design simple, yet very effective, maximum likelihood sequence detection (MLSD) receivers for optical communications with direct photo-detection. This distortion enables the use of standard Euclidean branch metrics in the Viterbi algorithm which implements MLSD. Our results suggest that the nonlinear characteristic can be optimized with respect to the uncompensated chromatic dispersion and other relevant system parameters, such as the extinction ratio. The proposed schemes with optimized distortion exhibit the same performance of more sophisticated MLSD schemes, still guaranteeing more efficient Viterbi algorithm implementation. PMID:19547536

Franceschini, M; Ferrari, G; Raheli, R; Meli, F; Castoldi, A

2007-09-01

155

NASA Astrophysics Data System (ADS)

Chaos was first discovered in turbulent fluid flow, considered the unsolved problem in classical physics. Fluid flow turns from smooth (laminar) to turbulent as its velocity increases. The classic explanation for this was that new frequencies appeared, one at a time, in the velocity and density profiles. In the early 1960's, a meteorology professor at MIT named Edward Lorenz simulated the actions of an air mass between warm ground and cool clouds, modeled by a simplified version of the Navier-Stokes equations for fluid flow. Mathematically, the definition of chaotic behavior requires: sensitive dependence upon initial conditions topological transitivity and dense periodic points in the Poincare section of the system's state space. Sensitive dependence is illustrated by Smale's horseshoe, the nonlinear transformation.

Bradley, Elizabeth

1990-12-01

156

Menstruation, perimenopause, and chaos theory.

This article argues that menstruation, including the transition to menopause, results from a specific kind of complex system, namely, one that is nonlinear, dynamical, and chaotic. A complexity-based perspective changes how we think about and research menstruation-related health problems and positive health. Chaotic systems are deterministic but not predictable, characterized by sensitivity to initial conditions and strange attractors. Chaos theory provides a coherent framework that qualitatively accounts for puzzling results from perimenopause research. It directs attention to variability within and between women, adaptation, lifespan development, and the need for complex explanations of disease. Whether the menstrual cycle is chaotic can be empirically tested, and a summary of our research on 20- to 40-year-old women is provided. PMID:22643714

Derry, Paula S; Derry, Gregory N

2012-01-01

157

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

158

Self Generation of Chaos From Electrical Solitons

NASA Astrophysics Data System (ADS)

The nonlinear transmission line (NLTL) is a structure that can generate electrical solitons of subpicosecond duration. As an autonomous soliton generator utilizing the NLTL, thus far, only periodic electrical soliton oscillators have been reported. These circuits self generate a periodic train of solitons, where an amplifier with a saturable absorber prevents the generation of multiple solitons and hence their nonlinear collisions. However, if the amplifier encourages the generation of multiple solitons and their collisions, the system can attain chaos, because the position of the soliton modulates after each collision, disrupting the periodicity. In this work, for the first time, we experimentally demonstrate such a chaotic system. Our circuit self generates an aperiodic signal, which has a continuous spectral distribution. We confirm its chaotic behavior by calculating the largest Lyapunov exponent, and show that the dimensionality of the generated chaos is high (d>3) by performing a false-nearest-neighbors analysis. Moreover, we explicitly measure the route from periodic soliton oscillation to chaotic oscillation via decreasing the time constant of the saturable absorber, showing the effect of soliton collisions on period-doubling bifurcations and finally the creation of chaos.

Yildirim, Ozgur; Ham, Donhee

2011-03-01

159

Chaos via Furstenberg family couple

In this paper we define (F1,F2)-chaos via Furstenberg family couple F1 and F2. It turns out that the Li–Yorke chaos and distributional chaos can be treated as chaos in Furstenberg families sense. Some sufficient conditions such that a system is the (F1,F2)-chaotic (Theorems 4.2 and 4.4) are given. In addition, we construct an example as an application. It is showed

Feng Tan; JinCheng Xiong

2009-01-01

160

Optimal and suboptimal chaos receivers

The paper describes the state of the art in the design of receivers for chaos-based digital communication over noisy channels. An information theoretic analysis of the potential of chaos in digital communication schemes is given, underlining that there is no fundamental principle that speaks against the use of chaos in digital communications. The design of the optimal receiver based on

MARTIN HASLER; THOMAS SCHIMMING

2002-01-01

161

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

162

In order to reduce the computational amount and improve computational precision for nonlinear optimizations and pollution source identification in convection–diffusion equation, a new algorithm, chaos gray-coded genetic algorithm (CGGA) is proposed, in which initial population are generated by chaos mapping, and new chaos mutation and Hooke–Jeeves evolution operation are used. With the shrinking of searching range, CGGA gradually directs to

Xiaohua Yang; Zhifeng Yang; Xinan Yin; Jianqiang Li

2008-01-01

163

Existing individual size distribution (ISD) theories assume that the trophic level (TL) of an organism varies as a linear function of its log-transformed body size. This assumption predicts a power-law distribution of the ISD, i.e., a linear relationship between size and abundance in log space. However, the secondary structure of ISD (nonlinear dome shape structures deviating from a power-law distribution) is often observed. We propose a model that extends the metabolic theory to link the secondary structure of ISD to the nonlinear size-TL relationship. This model is tested with empirical data collected from a subtropical reservoir. The empirical ISD and size-TL relationships were constructed by FlowCAM imaging analysis and stable isotope analyses, respectively. Our results demonstrate that the secondary structure of ISD can be predicted from the nonlinear function of size-TL relationship and vice versa. Moreover, these secondary structures arise due to (1) zooplankton omnivory and (2) the trophic interactions within microbial food webs. PMID:24933809

Chang, Chun-Wei; Miki, Takeshi; Shiah, Fuh-Kwo; Kao, Shuh-Ji; Wu, Jiunn-Tzong; Sastri, Akash R; Hsieh, Chih-Hao

2014-04-01

164

NASA Astrophysics Data System (ADS)

A scheme for chaotic synchronization of two mesoscopic shunted resistive-capacitive-inductive Josephson junctions by means of a third common van der Pol oscillator (the master system) is presented in this paper. The output signal from the latter system in its highly nonlinear state is used to drive both junctions (the slave system). Our numerical calculations demonstrate that the junctions are in chaotic states (positive Lyapunov exponent) prior to being coupled to the master drive, and can be synchronized when they are in their periodic states. It is also revealed that the synchronization state of both junctions is controlled by the driving intensity and damping parameter of the van der Pol oscillator. The bifurcation from chaotic to periodic behaviour or vice versa occurs by altering the external dc bias current passing through the system. The complementary role of the damping parameter and the bias current in controlling synchronization is demonstrated.

Al-Khawaja, Sameer

2011-02-01

165

Thinking about Chaos: Non-Quantitative Approaches to Teacher Education.

ERIC Educational Resources Information Center

Explains the chaos theory and its effect on education, relating it to quantum physics. The article suggests implications for education (predictions about student achievement are limited, the brain learns in nonlinear ways, and the knowledge base in teacher education needs modification to account for recent discoveries in science and mathematics).…

Rockler, Michael J.

1991-01-01

166

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

167

The presence of temporal asymmetries in fluctuation paths of nonequilibrium systems has recently been confirmed numerically in nonequilibrium molecular dynamics simulations of particular deterministic systems. Here we show that this is a common feature of homogeneously driven and thermostatted, reversible, deterministic, chaotic, nonequilibrium systems of interacting particles. This is done by expressing fluctuation paths as correlation functions. The theoretical arguments look rather general, and we expect them to easily extend to other forms of driving and thermostats. The emergence of asymmetry is also justified using the transient time correlation function expression of nonlinear response theory. Numerical simulations are used to verify our arguments. PMID:18447467

Paneni, Carlo; Searles, Debra J; Rondoni, Lamberto

2008-04-28

168

NASA Astrophysics Data System (ADS)

The extreme sensitivity to initial conditions that chaotic systems display makes them unstable and unpredictable. Yet that same sensitivity also makes them highly susceptible to control, provided that the developing chaos can be analyzed in real time and that analysis is then used to make small control interventions. This strategy has been used here to stabilize cardiac arrhythmias induced by the drug ouabain in rabbit ventricle. By administering electrical stimuli to the heart at irregular times determined by chaos theory, the arrhythmia was converted to periodic beating.

Garfinkel, Alan; Spano, Mark L.; Ditto, William L.; Weiss, James N.

1992-08-01

169

Application of Chaos Theory to Psychological Models

NASA Astrophysics Data System (ADS)

This dissertation shows that an alternative theoretical approach from physics--chaos theory--offers a viable basis for improved understanding of human beings and their behavior. Chaos theory provides achievable frameworks for potential identification, assessment, and adjustment of human behavior patterns. Most current psychological models fail to address the metaphysical conditions inherent in the human system, thus bringing deep errors to psychological practice and empirical research. Freudian, Jungian and behavioristic perspectives are inadequate psychological models because they assume, either implicitly or explicitly, that the human psychological system is a closed, linear system. On the other hand, Adlerian models that require open systems are likely to be empirically tenable. Logically, models will hold only if the model's assumptions hold. The innovative application of chaotic dynamics to psychological behavior is a promising theoretical development because the application asserts that human systems are open, nonlinear and self-organizing. Chaotic dynamics use nonlinear mathematical relationships among factors that influence human systems. This dissertation explores these mathematical relationships in the context of a sample model of moral behavior using simulated data. Mathematical equations with nonlinear feedback loops describe chaotic systems. Feedback loops govern the equations' value in subsequent calculation iterations. For example, changes in moral behavior are affected by an individual's own self-centeredness, family and community influences, and previous moral behavior choices that feed back to influence future choices. When applying these factors to the chaos equations, the model behaves like other chaotic systems. For example, changes in moral behavior fluctuate in regular patterns, as determined by the values of the individual, family and community factors. In some cases, these fluctuations converge to one value; in other cases, they diverge in still other cases, they oscillate periodically among two or more precise values. At certain values, the equations iterate random results, with no convergence, divergence or periodicity: "chaos." At still other values, the equations behave chaotically for many iterations; then a periodic oscillation emerges from the chaos. These emergent patterns provide a significantly better model fit to the dynamic reality of psychological behavior because qualitatively reorganized behavior is logically possible and incorporated in the model's metaphysical assumptions.

Blackerby, Rae Fortunato

170

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

171

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

172

NASA Astrophysics Data System (ADS)

Brake squeal has become an increasing concern to the automotive industry because of warranty costs and the requirement for continued interior vehicle noise reduction. Most research has been directed to either analytical and experimental studies of brake squeal mechanisms or the prediction of brake squeal propensity using finite element methods. By comparison, there is a lack of systematic analysis of brake squeal data obtained from a noise dynamometer. It is well known that brake squeal is a nonlinear transient phenomenon and a number of studies using analytical and experimental models of brake systems (e.g., pin-on-disc) indicate that it could be treated as a chaotic phenomenon. Data obtained from a full brake system on a noise dynamometer were examined with nonlinear analysis techniques. The application of recurrence plots reveals chaotic structures even in noisy data from the squealing events. By separating the time series into different regimes, lower dimensional attractors are isolated and quantified by dynamic invariants such as correlation dimension estimates or Lyapunov exponents. Further analysis of the recurrence plot of squealing events by means of recurrence quantification analysis measures reveals different regimes of laminar and random behaviour, periodicity and chaos-forming recurrent transitions. These results help to classify brake squeal mechanisms and to enhance understanding of friction-related noise phenomena.

Oberst, S.; Lai, J. C. S.

2011-02-01

173

The existence of quantum billiard chaos is examined for non-stationary states based on expansion of the quantum distribution in the quasi-classical limit. It is shown that this expansion converges asymptotically and leads to the Liouville equation, which in turn implies the Poincaré recurrence theorem. A smoothing procedure is introduced which renders this expansion consistent at the boundary of the billiard.

Richard L. Liboff

2000-01-01

174

The use of chaos to transmit information is described. Chaotic dynamical systems, such as electrical oscillators with very simple structures, naturally produce complex wave forms. We show that the symbolic dynamics of a chaotic oscillator can be made to follow a desired symbol sequence by using small perturbations, thus allowing us to encode a message in the wave form. We

Scott Hayes; Celso Grebogi; Edward Ott

1993-01-01

175

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

176

Chaos: A Mathematical Introduction

NASA Astrophysics Data System (ADS)

This text presents concepts on chaos in discrete time dynamics that are accessible to anyone who has taken a first course in undergraduate calculus. Retaining its commitment to mathematical integrity, the book, originating in a popular one-semester middle level undergraduate course, constitutes the first elementary presentation of a traditionally advanced subject.

Banks, John; Dragan, Valentina; Jones, Arthur

2003-06-01

177

Chaos and The Changing Nature of Science and Medicine. Proceedings

These proceedings represent the lectures given at the workshop on chaos and the changing nature of science and medicine. The workshop was sponsored by the University of South Alabama and the American Association of Physicists in Medicine. The topics discussed covered nonlinear dynamical systems, complexity theory, fractals, chaos in biology and medicine and in fluid dynamics. Applications of chaotic dynamics in climatology were also discussed. There were 8 lectures at the workshop and all 8 have been abstracted for the Energy Science and Technology database.(AIP)

Herbert, D.E. [Department of Radiology, College of Medicine, University of South Alabama, Mobile, AL 36688 (United States); Croft, P. [Department of Geology and Geography, University of South Alabama, Mobile, AL 36688 (United States); Silver, D.S.; Williams, S.G. [Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688 (United States); Woodall, M. [Department of Radiology, College of Medicine, University of South Alabama, Mobile, AL 36688 (United States)

1996-09-01

178

The Chaos Hypertextbook: Mathematics in the Age of the Computer

NSDL National Science Digital Library

Written by Glenn Elert, this online textbook is aimed at "anyone with an interest in chaos, fractals, non-linear dynamics, or mathematics in general." Although it is not extremely technical, the author recommends having a decent mathematical background. Many people will recognize, at least by name, some of the topics covered. Mandelbrot and Julia sets are two well known fractals, and the book explains how they are constructed and gives some images. The fourth and final chapter discusses ways of measuring chaos. Some remarkable images of fractals are given in the Eye Candy appendix.

Elert, Glenn.

1995-01-01

179

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

180

Quasiperiodic graphs at the onset of chaos.

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers. PMID:24483542

Luque, B; Cordero-Gracia, M; Gómez, M; Robledo, A

2013-12-01

181

Quasiperiodic graphs at the onset of chaos

NASA Astrophysics Data System (ADS)

We examine the connectivity fluctuations across networks obtained when the horizontal visibility (HV) algorithm is used on trajectories generated by nonlinear circle maps at the quasiperiodic transition to chaos. The resultant HV graph is highly anomalous as the degrees fluctuate at all scales with amplitude that increases with the size of the network. We determine families of Pesin-like identities between entropy growth rates and generalized graph-theoretical Lyapunov exponents. An irrational winding number with pure periodic continued fraction characterizes each family. We illustrate our results for the so-called golden, silver, and bronze numbers.

Luque, B.; Cordero-Gracia, M.; Gómez, M.; Robledo, A.

2013-12-01

182

A new strategy of chaos control and a unified mechanism for several kinds of chaos control methods

NASA Astrophysics Data System (ADS)

Based on a general principle of physics that a physical system is in the most stable state if it is of the lowest energy state, a new method for chaos control is proposed. A calculable generalized energy function in a nonlinear system is suggested for measuring control process. The Henon map and Lorenz system are taken as two typical examples to demonstrate the method. A series of stabilized periodic orbits as well as inverse sequence of chaotic bands are obtained. At the same time, a unified mechanism of physics for several kinds of current chaos control methods is studied using the idea proposed in this paper.

Xiao-shu, Luo; Jin-qing, Fang; Li-hu, Wang; Ling-jiang, Kong; Feng, Jiang

1999-12-01

183

Deterministic chaos in geomagnetic reversals

NASA Astrophysics Data System (ADS)

In a recent publication Gissinger (Eur. Phys. J. B 85,137, 2012) proposed a new deterministic chaos model for the generation of the Earth's magnetic field and an explanation of the observed statistics of geomagnetic pole reversal occurrences. The new model is described by a system of three coupled non-linear differential equations limited to quadratic terms. If such a low degree of freedom system is adequate for the description of Earth's geomagnetic dynamo, it has to reflect in statistics and non-linear dynamic characteristics of the temporal interval between geomagnetic reversals. We present the results of the extended statistical analysis of the 2012 compilation of magnetic reversal data spanning the last 170 m.yr. We calculate the Grassberger-Procaccia correlation dimension in the context of a single-variable dataset of waiting times between measured geomagnetic reversals in paleomagnetic records to predict the complexity of the underlying geomagnetic dynamo system. First, we inspect if the time series of geomagnetic reversals has the same or a different correlation dimension than a random time series with the same number of points. This allows us to determine whether geomagnetic reversals are indistinguishable from a stochastic process, or are described by a chaotic rather than stochastic process. Next, higher-dimensional vectors are constructed from the time series of geomagnetic reversals, and correlation dimension is calculated for these higher-dimensional vectors to find out if the correlation dimension has a convergence limit as we increase the vector space dimension. If the convergence limit is revealed from the experimental dataset, then the geomagnetic reversals are chaotic rather than stochastic and are described by a system with limited number of degrees of freedom determined by the correlation dimension. If one expects to describe the geomagnetic dynamo by a low-order system of non-linear differential equations, the system should have a low dimension (self-organized) strange attractor in its phase space indicated by a low correlation dimension of observable data.

Sidorovskaia, N.; Richter, C.; Rypina, I.

2013-12-01

184

NASA Astrophysics Data System (ADS)

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.

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

2013-03-01

185

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.

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

2013-01-01

186

Chaos in Josephson tunnel junctions

Experimental data have been obtained confirming the theoretical assumption of chaos existence in superconducting tunnel junctions (STJ) with hysteretic I-V curve (IVC) in the presence of the external microwave radiation for zero bias current. The dynamic of the chaos formation was investigated and the chaos intensity was estimated. Observation of chaotic oscillations for bias current smaller than the critical current are reported and discussed.

Gubankov, V.; Konstantinyan, K.; Koshelets, V.; Ovsyannikov, G.

1983-05-01

187

The Construction of Chaos Theory

This paper aims at a logico-mathematical analysis of the concept of chaos from the point of view of a constructivist philosophy\\u000a of physics. The idea of an internal logic of chaos theory is meant as an alternative to a realist conception of chaos. A brief\\u000a historical overview of the theory of dynamical systems is provided in order to situate the

Yvon Gauthier

2009-01-01

188

Chaos control of cardiac arrhythmias.

Chaos theory has shown that many disordered and erratic phenomena are in fact deterministic, and can be understood causally and controlled. The prospect that cardiac arrhythmias might be instances of deterministic chaos is therefore intriguing. We used a recently developed method of chaos control to stabilize a ouabain-induced arrhythmia in rabbit ventricular tissue in vitro. Extension of these results to clinically significant arrhythmias such as fibrillation will require overcoming the additional obstacles of spatiotemporal complexity. PMID:21232241

Garfinkel, A; Weiss, J N; Ditto, W L; Spano, M L

1995-01-01

189

Tailoring wavelets for chaos control.

Chaos is a class of ubiquitous phenomena and controlling chaos is of great interest and importance. In this Letter, we introduce wavelet controlled dynamics as a new paradigm of dynamical control. We find that by modifying a tiny fraction of the wavelet subspaces of a coupling matrix, we could dramatically enhance the transverse stability of the synchronous manifold of a chaotic system. Wavelet controlled Hopf bifurcation from chaos is observed. Our approach provides a robust strategy for controlling chaos and other dynamical systems in nature. PMID:12513152

Wei, G W; Zhan, Meng; Lai, C-H

2002-12-31

190

The results of extensive computations are presented to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular we follow the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos. As many as 13 period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a self-similar behavior that is demonstrated and used to compute a universal scaling factor, which arises also from the theory of nonlinear maps and can enable continuation of the solution into a chaotic regime. Aperiodic solutions alternate with periodic ones after chaos sets in, and we show the existence of a period six solution separated by chaotic regions. Images

Smyrlis, Y S; Papageorgiou, D T

1991-01-01

191

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

192

Desmoplakin is a cytoplasmic desmosomal protein that plays a vital role in normal intercellular adhesion. Mutations in desmoplakin can result in devastating skin blistering diseases and arrhythmogenic right ventricular cardiomyopathy, a heart muscle disorder associated with ventricular arrhythmias, heart failure, and sudden death. The desmoplakin N-terminal region is a 1056-amino-acid sequence of unknown structure. It mediates interactions with other desmosomal proteins, is found in a variety of plakin proteins, and spans what has been termed the "plakin domain," which includes residues 180-1022 and consists of six spectrin repeats (SRs) and an Src homology 3 domain. Herein we elucidate the architecture of desmoplakin's plakin domain, as well as its constituent tandem SRs. Small-angle X-ray scattering analysis shows that the entire plakin domain has an "L" shape, with a long arm and a short arm held at a perpendicular angle. The long arm is 24.0 nm long and accommodates four stably folded SRs arranged in tandem. In contrast, the short arm is 17.9 nm in length and accommodates two independently folded repeats and an extended C-terminus. We show that mutations linked to arrhythmogenic right ventricular cardiomyopathy (K470E and R808C) cause local conformational alterations, while the overall folded structure is maintained. This provides the first structural and mechanistic insights into an entire plakin domain and provides a basis for understanding the critical role of desmoplakin in desmosome function. PMID:21756917

Al-Jassar, Caezar; Knowles, Timothy; Jeeves, Mark; Kami, Keiichiro; Behr, Elijah; Bikker, Hennie; Overduin, Michael; Chidgey, Martyn

2011-09-01

193

Chaos control for numerical instability of first order reliability method

NASA Astrophysics Data System (ADS)

The HL-RF algorithm of the first order reliability method (FORM) is a kind of popular iterative algorithm for solving the reliability index in structural reliability analysis and reliability-based design optimization. However, there are the phenomena of convergence failure such as periodic oscillation, bifurcation and chaos in the FORM for some nonlinear problems. This paper suggests a novel method to overcome the numerical instabilities of HL-RF algorithm of FORM based on the principle of chaos control. The essential causes of chaotic dynamics for numerical instabilities including periodic oscillation and chaos of iterative solutions of FORM are revealed. Moreover, the geometrical properties of periodic oscillation of the iterative formulas derived from the FORM and performance measure approach are analyzed and compared. Finally, the stability transformation method (STM) of chaos feedback control is proposed to implement the convergence control of FORM. Several numerical examples with explicit or implicit HL-RF iterative formulas illustrate that the STM is effective, simple and versatile, and can control the periodic oscillation, bifurcation and chaos of the FORM iterative algorithm.

Yang, Dixiong

2010-10-01

194

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

195

Wireless communication with chaos.

The modern world fully relies on wireless communication. Because of intrinsic physical constraints of the wireless physical media (multipath, damping, and filtering), signals carrying information are strongly modified, preventing information from being transmitted with a high bit rate. We show that, though a chaotic signal is strongly modified by the wireless physical media, its Lyapunov exponents remain unaltered, suggesting that the information transmitted is not modified by the channel. For some particular chaotic signals, we have indeed proved that the dynamic description of both the transmitted and the received signals is identical and shown that the capacity of the chaos-based wireless channel is unaffected by the multipath propagation of the physical media. These physical properties of chaotic signals warrant an effective chaos-based wireless communication system. PMID:23683198

Ren, Hai-Peng; Baptista, Murilo S; Grebogi, Celso

2013-05-01

196

Self-generation and management of spin-electromagnetic wave solitons and chaos

NASA Astrophysics Data System (ADS)

Self-generation of microwave spin-electromagnetic wave envelope solitons and chaos has been observed and studied. For the investigation, we used a feedback active ring oscillator based on artificial multiferroic, which served as a nonlinear waveguide. We show that by increasing the wave amplification in the feedback ring circuit, a transition from monochromatic auto-generation to soliton train waveform and then to dynamical chaos occurs in accordance with the Ruelle-Takens scenario. Management of spin-electromagnetic-wave solitons and chaos parameters by both dielectric permittivity and magnetic permeability of the multiferroic waveguiding structure is demonstrated.

Ustinov, Alexey B.; Kondrashov, Alexandr V.; Nikitin, Andrey A.; Kalinikos, Boris A.

2014-06-01

197

Chaos concepts as diagnostic tools for assessing rotating machinery vibration signatures

NASA Astrophysics Data System (ADS)

Chaos content in measured vibration signals is of some practical importance in rotordynamical systems. Of particular interest is the relationship between the occurrence of determinsite chaos and the diagnosis of mechanical failures in rotating machinery. Two nonlinear rotordynamical systems were studied using simulation and various forms of subharmonic, quasiperiodic and chaotic vibrations were observed. Different routes into and out of chaos show important signs for wear assessment and failure prediction. Experimental test facilities are currently under development and the next steps involve experimental verification of the simulation results and the development of signal processing techniques for extracting the dynamical features of the vibration signatures from measured time series data.

Adams, Maurice L.; Loparo, Kenneth A.

1996-06-01

198

Introduction to Experimental Nonlinear Dynamics

NASA Astrophysics Data System (ADS)

Nonlinear behavior can be found in such highly disparate areas as population biology and aircraft wing flutter. For this reason, nonlinear dynamics and chaos have become very active fields of research. This work uses an extended case study--an experiment in mechanical vibration--to introduce and explore the subject of nonlinear behavior and chaos from an engineering perspective. After a review of basic principles, the text then describes a cart-on-a-track oscillator and shows what happens when it is gradually subjected to greater excitation, thereby encountering the full spectrum of nonlinear behavior, from simple free decay to chaos. Advanced undergraduate and graduate students, as well as practicing engineers, will find this book a lively, accessible introduction to the subject.

Virgin, Lawrence N.

2000-03-01

199

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

200

NASA Astrophysics Data System (ADS)

Polynomiography is the algorithmic visualization of iterative systems for computing roots of a complex polynomial. It is well known that iterations of a rational function in the complex plane result in chaotic behavior near its Julia set. In one scheme of computing polynomiography for a given polynomial p(z), we select an individual member from the Basic Family, an infinite fundamental family of rational iteration functions that in particular include Newton's. Polynomiography is an excellent means for observing, understanding, and comparing chaotic behavior for variety of iterative systems. Other iterative schemes in polynomiography are possible and result in chaotic behavior of different kinds. In another scheme, the Basic Family is collectively applied to p(z) and the iterates for any seed in the Voronoi cell of a root converge to that root. Polynomiography reveals chaotic behavior of another kind near the boundary of the Voronoi diagram of the roots. We also describe a novel Newton-Ellipsoid iterative system with its own chaos and exhibit images demonstrating polynomiographies of chaotic behavior of different kinds. Finally, we consider chaos for the more general case of polynomiography of complex analytic functions. On the one hand polynomiography is a powerful medium capable of demonstrating chaos in different forms, it is educationally instructive to students and researchers, also it gives rise to numerous research problems. On the other hand, it is a medium resulting in images with enormous aesthetic appeal to general audiences.

Kalantari, Bahman

201

We study the control of chaos in an experiment on a parametrically excited pendulum whose excitation mechanism is not perfect. This imperfection leads to a weakly excited degree of freedom with an associated small eigenvalue. Although the state of the pendulum could be characterized well and although the perturbation is weak, we fail to control chaos. From a numerical model we learn that the small eigenvalue cannot be ignored when attempting control. However, the estimate of this eigenvalue from an (experimental) time series is elusive. The reason is that points in an experimental time series are distributed according to the natural measure. It is this extremely uneven distribution of points that thwarts attempts to measure eigenvalues that are very different. Another consequence of the phase-space distribution of points for control is the occurrence of logarithmic-oscillations in the waiting time before control can be attempted. We come to the conclusion that chaos needs to be destroyed before the information needed for its control can be obtained. PMID:11101975

van De Water W; de Weger J

2000-11-01

202

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

203

A nonlinear dynamic problem of stall induced flutter oscillation subject to physical uncertainties is analyzed using arbitrary polynomial chaos. A single-degree-of-freedom stall flutter model with torsional oscillation is considered subject to nonlinear aerodynamic loads in the dynamic stall regime and nonlinear structural stiffness. The analysis of the deterministic aeroelastic response demonstrated that the problem is sensitive to variations in structural

Jeroen A. S. Witteveen; Sunetra Sarkar; Hester Bijl

2007-01-01

204

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

205

Chaos and unpredictability in evolution.

The possibility of complicated dynamic behavior driven by nonlinear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility of long-term evolutionary chaos is rarely considered. The concept of "survival of the fittest" is central to much evolutionary thinking and embodies a perspective of evolution as a directional optimization process exhibiting simple, predictable dynamics. This perspective is adequate for simple scenarios, when frequency-independent selection acts on scalar phenotypes. However, in most organisms many phenotypic properties combine in complicated ways to determine ecological interactions, and hence frequency-dependent selection. Therefore, it is natural to consider models for evolutionary dynamics generated by frequency-dependent selection acting simultaneously on many different phenotypes. Here we show that complicated, chaotic dynamics of long-term evolutionary trajectories in phenotype space is very common in a large class of such models when the dimension of phenotype space is large, and when there are selective interactions between the phenotypic components. Our results suggest that the perspective of evolution as a process with simple, predictable dynamics covers only a small fragment of long-term evolution. PMID:24433364

Doebeli, Michael; Ispolatov, Iaroslav

2014-05-01

206

Regularization of chaos by noise in electrically driven nanowire systems

NASA Astrophysics Data System (ADS)

The electrically driven nanowire systems are of great importance to nanoscience and engineering. Due to strong nonlinearity, chaos can arise, but in many applications it is desirable to suppress chaos. The intrinsically high-dimensional nature of the system prevents application of the conventional method of controlling chaos. Remarkably, we find that the phenomenon of coherence resonance, which has been well documented but for low-dimensional chaotic systems, can occur in the nanowire system that mathematically is described by two coupled nonlinear partial differential equations, subject to periodic driving and noise. Especially, we find that, when the nanowire is in either the weakly chaotic or the extensively chaotic regime, an optimal level of noise can significantly enhance the regularity of the oscillations. This result is robust because it holds regardless of whether noise is white or colored, and of whether the stochastic drivings in the two independent directions transverse to the nanowire are correlated or independent of each other. Noise can thus regularize chaotic oscillations through the mechanism of coherence resonance in the nanowire system. More generally, we posit that noise can provide a practical way to harness chaos in nanoscale systems.

Hessari, Peyman; Do, Younghae; Lai, Ying-Cheng; Chae, Junseok; Park, Cheol Woo; Lee, GyuWon

2014-04-01

207

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

208

ON DEVANEY'S DEFINITION OF CHAOS

Chaotic dynamical systems have received a great deal of attention in recent years (see for instance [2],[3]). Although there has been no universally accepted mathematical definition of chaos, the popular text by Devaney [1] isolates three components as being the essential features of chaos. They are formulated for a continuous map f : X X on some metric space X

J. Banks; J. Brooks; G. Cairns; G. Davis; P. Stacey

1992-01-01

209

From strong chaos via weak chaos to regular behaviour: Optimal interplay between chaos and order

NASA Astrophysics Data System (ADS)

We investigate the interplay between chaotic and integrable Hamiltonian systems. In detail, a fully connected four-site lattice system associated with the discrete nonlinear Schrödinger equation is studied. On an embedded two-site segment (dimer) of the four-site system (tetramer) the coupling element between its two sites is time-periodically modified by an external driving term rendering the dimer dynamics chaotic, along with delocalisation of initially single-site excitations. Starting from an isolated dimer system the strength of the coupling to the remaining two sites of the tetramer is treated as a control parameter. It is striking that when the dimer interacts globally with the remaining two sites, thus constituting a fully connected tetramer, a non-trivial dependence of the degree of localisation on the strength of the coupling is found. There even exist ranges of optimal coupling strengths for which the driven tetramer dynamics becomes not only regular but also restores complete single-site localisation. We relate the re-establishment of complete localisation with transitions from permanent chaos via regular transients to permanent stable motion on a torus in the higher-dimensional phase space. In conclusion, increasing the dimension of a system can have profound effects on the character of the dynamics in higher-dimensional mixed phase spaces such that even full stabilisation of motion can be accomplished.

Hennig, D.; Mulhern, C.; Burbanks, A. D.

2013-06-01

210

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

211

Temporal and spectral responses of a softening Duffing oscillator undergoing route-to-chaos

NASA Astrophysics Data System (ADS)

Because nonlinear responses are oftentimes transient and consist of complex amplitude and frequency modulations, linearization would inevitably obscure the temporal transition attributable to the nonlinear terms, thus also making all inherent nonlinear effects inconspicuous. It is shown that linearization of a softening Duffing oscillator underestimates the variation of the frequency response, thereby concealing the underlying evolution from bifurcation to chaos. In addition, Fourier analysis falls short of capturing the time evolution of the route-to-chaos and also misinterprets the corresponding response with fictitious frequencies. Instantaneous frequency along with the empirical mode decomposition is adopted to unravel the multi-components that underlie the bifurcation-to-chaos transition, while retaining the physical features of each component. Through considering time and frequency responses simultaneously, a better understanding of the particular Duffing oscillator is achieved.

Liu, Meng-Kun; Steve Suh, C.

2012-12-01

212

Chaos supported stochastic resonance in a metal-ferroelectric-semiconductor heterostructure

NASA Astrophysics Data System (ADS)

An experimental study is presented on a complex nonlinear system showing a particular type of dynamics that can be interpreted as stochastic resonance. The system consists of a metal-ferroelectric-semiconductor structure, which plays the role of a nonlinear element in an electric circuit with linear resistance, inductance, and capacitance connected in series ( RLC series circuit) driven externally by a high-amplitude harmonic voltage source. The system presents various kinds of nonlinear behavior, of which the simplest, consisting of a period-doubling evolution to chaos, is of interest to this study. The broadband intrinsic chaos emerging after a period-doubling sequence exists for a large range of frequencies of the driving voltage. The appearance of the chaotic dynamics is associated with the promotion of a low-frequency harmonic spectral component. This is interpreted as stochastic resonance with intrinsic chaos replacing noise, the usual variable in regular SR.

Mereu, B.; Cristescu, C. P.; Alexe, M.

2005-04-01

213

Particle chaos in the Earth's magnetotail.

Nonlinear particle dynamics is studied both in current sheets and near neutral lines. The parameter governing particle chaos in a current sheet with a constant normal component, B(n), is kappa=(R(min)/rho(max))(1/2), where R(min) is the minimum field line radius of curvature and rho(max) is the maximum gyroradius. In such a current sheet, motion can be viewed as a combination of a component normal to the current sheet and a tangential component. The parameter kappa represents the ratio of the characteristic time scale of the normal component to the tangential, and thus, particle chaos is maximized for kappa approximately 1. For kappa<1, the slow motion preserves the action integral of the fast motion, J(z), except near the separatrix, the phase space boundary separating motion that crosses the current sheet midplane from that which does not. Near a linear neutral line, it is found that the parameter b(n), which is the ratio of the characteristic vertical and horizontal field strengths, rather than kappa governs particle chaos. In the limit b(n)<1, the slow motion again preserves J(z), and J(z) has the same analytic form as in a constant B(n) current sheet. In the limit of b(n)<1, the structure of x-p(x) phase space is controlled by the stable and unstable manifolds associated with the unstable fixed point orbit at (x,p(x))=(0,0), and this structure lies along a contour of constant J(z). PMID:12779993

Dusenbery, Paul B.; Martin, Richard F.; Burkhart, Grant R.

1992-07-01

214

Stalling chaos control accelerates convergence

NASA Astrophysics Data System (ADS)

Since chaos control has found its way into many applications, the development of fast, easy-to-implement and universally applicable chaos control methods is of crucial importance. Predictive feedback control has been widely applied but suffers from a speed limit imposed by highly unstable periodic orbits. We show that this limit can be overcome by stalling the control, thereby taking advantage of the stable directions of the uncontrolled chaotic map. This analytical finding is confirmed by numerical simulations, giving a chaos-control method that is capable of successfully stabilizing periodic orbits of high period.

Bick, Christian; Kolodziejski, Christoph; Timme, Marc

2013-06-01

215

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

216

Route to chaos for combustion instability in ducted laminar premixed flames

NASA Astrophysics Data System (ADS)

Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario.

Kabiraj, Lipika; Saurabh, Aditya; Wahi, Pankaj; Sujith, R. I.

2012-06-01

217

Route to chaos for combustion instability in ducted laminar premixed flames.

Complex thermoacoustic oscillations are observed experimentally in a simple laboratory combustor that burns lean premixed fuel-air mixture, as a result of nonlinear interaction between the acoustic field and the combustion processes. The application of nonlinear time series analysis, particularly techniques based on phase space reconstruction from acquired pressure data, reveals rich dynamical behavior and the existence of several complex states. A route to chaos for thermoacoustic instability is established experimentally for the first time. We show that, as the location of the heat source is gradually varied, self-excited periodic thermoacoustic oscillations undergo transition to chaos via the Ruelle-Takens scenario. PMID:22757536

Kabiraj, Lipika; Saurabh, Aditya; Wahi, Pankaj; Sujith, R I

2012-06-01

218

Chaos Game Representation of Genomes and their Simulation by Recurrent Iterated Function Systems

Chaos game representation (CGR) of DNA sequences and linked protein sequences from genomes was proposed by Jeffrey (Nucleic Acid Research 18 (1990) 2163-2170) and Yu et al. (J. Theor. Biol, 226 (2004) 341-348), respectively. In this paper, we consider the CGR of three kinds of sequences from complete genomes: whole genome DNA sequences, linked coding DNA sequences and linked protein

Zu-Guo Yu; Long Shi; Qian-Jun Xiao; Vo Anh

2008-01-01

219

Generation of Pseudo-Random Numbers by Chaos-Type Function and Its Application to Cryptosystems

NASA Astrophysics Data System (ADS)

The logistic map is known to be one of nonlinear difference equations as a chaos map, and to generate pseudo-random numbers. However, since the chaos has a high sensitive dependency on initial conditions and accumulates inevitable round-off errors caused by iterating the map, the numerical generation of exact chaotic time series is said to be impossible. The aim of this paper is, first, to propose the algorithm to generate exact chaotic time series of a chaos-type function derived from the exact chaos solution. Next, the pseudo-random numbers are evaluated by the four tests and the accumulation of chi-square values. Also, an application to cryptosystems, which do not need the synchronization in usual computer environment, is considered.

Toyama, Junichiro; Kawamoto, Shunji

220

Chaos in hydrodynamic BL Herculis models

NASA Astrophysics Data System (ADS)

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.

Smolec, R.; Moskalik, P.

2014-06-01

221

Order and chaos in soft condensed matter

NASA Astrophysics Data System (ADS)

Soft matter, like colloidal suspensions and surfactant gels, exhibit strong response to modest external perturbations. This paper reviews our recent experiments on the nonlinear flow behaviour of surfactant worm-like micellar gels. A rich dynamic behaviour exhibiting regular, quasi-periodic, intermittency and chaos is observed. In particular, we have shown experimentally that the route to chaos is via Type-II intermittency in shear thinning worm-like micellar solution of cetyltrimethylammonium tosylate where the strength of flow-concentration coupling is tuned by the addition of sodium chloride. A Poincaré first return map of the time series and the probability distribution of laminar length between burst events show that our data are consistent with Type-II intermittency. The existence of a `Butterfly' intensity pattern in small angle light scattering (SALS) measurements performed simultaneously with the rheological measurements confirms the coupling of flow to concentration fluctuations in the system under study. The scattered depolarised intensity in SALS, sensitive to orientational order fluctuations, shows the same time-dependence (like intermittency) as that of shear stress.

Sood, A. K.; Ganapathy, Rajesh

2006-07-01

222

Chaos Theory: A Brief Introduction

NSDL National Science Digital Library

This article explains the concept of chaos theory, starting with the work of meteorologist Edward Lorenz on the impact of small initial conditions on a larger system. The page includes several helpful diagrams.

Rae, Greg

2011-06-08

223

NASA Astrophysics Data System (ADS)

A critical question for the habitability of Europa remains: how does the ice shell work? The detection of shallow subsurface lenses below Europa’s chaos implies that the ice shell is recycled rapidly and that Europa may be currently active. While this is not the first time liquid water has been implicated for Europa, the location of these features combined with new perspective on their dynamics frames the question in a new way. Melt lenses are intriguing potential habitats. Moreover, their formation requires the existence of impurities within the upper ice shell that may be sources of energy for microorganisms. Geomorphic evidence also exists for hydraulic redistribution of fluids both vertically and horizontally through pores and fractures. This process, observed in terrestrial ice shelves, may preserve liquid water within the ice matrix over many kilometers from the source. Horizontal transport of material may produce interconnectivity between distinct regions of Europa, thus preserving habitable conditions within the ice over a longer duration. At a surface age of 40-90 Myr, with 25-50% covered by chaos terrain, Europa's resurfacing rate is very high and water likely plays a significant role. Because of the vigor of overturn implied by this new work, it is likely that surface and subsurface materials are well-mixed within the largest and deepest lenses, providing a mechanism for bringing oxidants and other surface contaminants to the deeper ice shell where it can reach the ocean by convective or compositional effects. The timescales over which large lenses refreeze are large compared to the timescales for vertical transport, while the timescales for smaller lenses are comparable to or shorter than convective timescales. Moreover, marine ice accretion at the bottom of the ice shell may be contributing to a compositional buoyancy engine that would change the makeup of the ice shell. From this point of view, we evaluate the habitability of Europa’s ice and ocean in light of active processes that may form a “chaos conveyor belt” that drives material exchange on Europa.

Schmidt, Britney E.

2013-10-01

224

NSDL National Science Digital Library

As any physicist will tell you, managing chaos is difficult, if not impossible. Fortunately, this type of Ã¢ÂÂchaosÃ¢ÂÂ refers primarily to the chaotic nature of maintaining an orderly and logical desktop calendar on oneÃ¢ÂÂs computer. With Chaos Manager, users can create their own organizer, which includes an Internet sync feature, a notebook, pop-up appointment reminders and so on. This particular version is compatible with all computers running Windows 98, Me, NT, 2000, and XP.

Bresson, Martin

2006-01-01

225

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.

226

Chaos-Based Spreading in DS-UWB Sensor Networks Increases Available Bit Rate

A chaos-based sequence generation method for reducing multiple access interference in direct sequence ultra-wide-band wireless-sensor networks (WSN) is presented. With this it is possible to increase the expected bit rate (BR) at which each user may transmit given a certain link quality, measured as the signal-to-interference ratio. When compared with traditional random sequences, chaos-based spreading results in a BR increase

Giampaolo Cimatti; Riccardo Rovatti; Gianluca Setti

2007-01-01

227

The mathematical structure of Sudoku puzzles is akin to hard constraint satisfaction problems lying at the basis of many applications, including protein folding and the ground-state problem of glassy spin systems. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by this system. We also show that the escape rate ?, an invariant of transient chaos, provides a scalar measure of the puzzle's hardness that correlates well with human difficulty ratings. Accordingly, ? = ?log10 ? can be used to define a “Richter”-type scale for puzzle hardness, with easy puzzles having 0 < ? ? 1, medium ones 1 < ? ? 2, hard with 2 < ? ? 3 and ultra-hard with ? > 3. To our best knowledge, there are no known puzzles with ? > 4.

Ercsey-Ravasz, Maria; Toroczkai, Zoltan

2012-01-01

228

NASA Technical Reports Server (NTRS)

11 January 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned, layered rock outcrops in Eos Chaos, located near the east end of the Valles Marineris trough system. The outcrops occur in the form of a distinct, circular butte (upper half of image) and a high slope (lower half of image). The rocks might be sedimentary rocks, similar to those found elsewhere exposed in the Valles Marineris system and the chaotic terrain to the east of the region.

*Location near*: 12.9oS, 49.5oW *Image width*: 3 km (1.9 mi) *Illumination from*: lower left *Season*: Southern Summer

2006-01-01

229

Optical digital chaos cryptography

NASA Astrophysics Data System (ADS)

In this work we present a new way to mask the data in a one-user communication system when direct sequence - code division multiple access (DS-CDMA) techniques are used. The code is generated by a digital chaotic generator, originally proposed by us and previously reported for a chaos cryptographic system. It is demonstrated that if the user's data signal is encoded with a bipolar phase-shift keying (BPSK) technique, usual in DS-CDMA, it can be easily recovered from a time-frequency domain representation. To avoid this situation, a new system is presented in which a previous dispersive stage is applied to the data signal. A time-frequency domain analysis is performed, and the devices required at the transmitter and receiver end, both user-independent, are presented for the optical domain.

Arenas-Pingarrón, Álvaro; González-Marcos, Ana P.; Rivas-Moscoso, José M.; Martín-Pereda, José A.

2007-10-01

230

NASA Astrophysics Data System (ADS)

Chaotic maps can mimic random behavior in a quite impressive way. In particular, those possessing a generating partition can produce any symbolic sequence by properly choosing the initial state. We study in this Letter the ability of chaotic maps to generate order patterns and come to the conclusion that their performance in this respect falls short of expectations. This result reveals some basic limitation of a deterministic dynamic as compared to a random one. This being the case, we propose a non-statistical test based on ‘forbidden’ order patterns to discriminate chaotic from truly random time series with, in principle, arbitrarily high probability. Some relations with discrete chaos and chaotic cryptography are also discussed.

Amigó, José M.; Kocarev, Ljupco; Szczepanski, Janusz

2006-06-01

231

Chaos in a neural network circuit

NASA Astrophysics Data System (ADS)

We have constructed a neural network circuit of four clipped, high-grain, integrating operational amplifiers coupled to each other through an array of digitally programmable resistor ladders (MDACs). In addition to fixed-point and cyclic behavior, the circuit exhibits chaotic behavior with complex strange attractors which are approached through period doubling, intermittent attractor expansion and/or quasiperiodic pathways. Couplings between the nonlinear circuit elements are controlled by a computer which can automatically search through the space of couplings for interesting phenomena. We report some initial statistical results relating the behavior of the network to properties of its coupling matrix. Through these results and further research the circuit should help resolve fundamental issues concerning chaos in neural networks.

Kepler, Thomas B.; Datt, Sumeet; Meyer, Robert B.; Abott, L. F.

1990-12-01

232

Chaos and structures in the magnetosphere.

NASA Astrophysics Data System (ADS)

The nonlinear plasma transport mechanisms that control the collisionless heating in the Earth's magnetosphere and the onset of geomagnetic substorms are reviewed. In the high-pressure plasma trapped in the reversed magnetic field loops on the nightside of the magnetosphere, the key issue of the role of the ion orbital chaos as the mechanism for the plasma sheet energization is examined. The energization rate is governed by a collisionless conductance and the solar wind driven dawn-to-dusk electric field. The low-frequency response function is derived and the fluctuation dissipation theorem is given for the system. Returning to the global picture the collisionless energization rate from the transport physics is the basis for a low-dimensional energy-momentum-conserving dynamical model of magnetospheric substorms.

Horton, W.

1997-04-01

233

On the chaos in gene networks.

The methods for constructing "chaotic" nonlinear systems of differential equations modeling gene networks of arbitrary structure and dimensionality with various types of symmetry are considered. It has been shown that an increase in modality of the functions describing the control of gene expression efficiency allows for a decrease in the dimensionality of these systems with retention of their chaotic dynamics. Three-dimensional "chaotic" cyclic systems are considered. Symmetrical and asymmetrical attractors with "narrow" chaos having a Moebius-like structure have been detected in such systems. As has been demonstrated, a complete symmetry of the systems with respect to permutation of variables does not prevent the emergence of their chaotic dynamics. PMID:23427991

Likhoshvai, Vitaly A; Fadeev, Stanislav I; Kogai, Vladislav V; Khlebodarova, Tamara M

2013-02-01

234

Dynamical properties and chaos synchronization of improved Colpitts oscillators

NASA Astrophysics Data System (ADS)

In this paper, the dynamics and synchronization of improved Colpitts oscillators designed to operate in ultrahigh frequency range are considered. The model is described by a continuous time four-dimensional autonomous system with an exponential nonlinearity. The system is integrated numerically and various bifurcation diagrams and corresponding graphs of largest 1D Lyapunov exponent are plotted to summarize different scenarios leading to chaos. It is found that the oscillator moves from the state of fixed point motion to chaos via the usual paths of period-doubling, intermittency and interior crisis routes when monitoring the bias (i.e. power supply) in tiny ranges. In order to promote chaos-based synchronization designs of this type of oscillators, a synchronization strategy based upon the design of a nonlinear state observer is successfully adapted. The suggested approach enables synchronization to be achieved via a scalar transmitted signal which represents a suitable feature for communication applications. Numerical simulations are performed to demonstrate the effectiveness and feasibility of the proposed technique.

Kengne, J.; Chedjou, J. C.; Kenne, G.; Kyamakya, K.

2012-07-01

235

Parametrization of Chaos in the Beam-Wave Interactions

NASA Astrophysics Data System (ADS)

When a high energy beam flows through a bulk plasma, there are nonlinear interactions between the beam and the waves in the plasma, triggering a self oscillation and various routes to chaos. In this study, the period-doubling routes to chaos in several undriven beam-plasma systems are simulated with fluid and particle codes. In this bifurcation, a comprehensive parameter which is defined as the ratio of bounce to oscillation frequencies divided by the velocity slippage is used for the deterministic parameter of limit-cycle, period-doubled, period-quadrupled, and chaotic oscillations independent of input parameters. For different systems such as extended Pierce-diode (B.B. Godfrey, Phys. Fluids 30), 1553 (1987). and infinite homogeneous beam-plasma interaction (J.K. Lee and S.J. Hahn, IEEE Trans. Plasma Sci. 19), 52 (1991)., the larger value of the parameter makes the system more chaotic in analogy with free-electron-laser chaos (S.J. Hahn and J.K. Lee, Phys. Rev. E, 2162 (1993).). This single parameter represents the role of many input parameters, thus suitable for a simplifying and diagnostic measure of nonlinear dynamical and chaotic phenomena for various systems of particle-wave interactions. For the driven extended Pierce-diode system, the quasiperiodic oscillations are also observed.

Lee, Hae June; Lee, Jae Koo; Hur, Min Sup

1997-11-01

236

Chaos in the quasiperiodically forced duffing oscillator

We study chaotic dynamics of the quasiperiodically forced Duffing oscillator. We find that the mechanism for chaos is transverse homoclinic tori. Utilizing a generalization of a global perturbation technique of Melnikov we are able to give a criterion for the existence of chaos and we demonstrate the effect of the number of forcing frequencies on the region of chaos in

Stephen Wiggins

1987-01-01

237

Chaos theory suggests a new paradigm for nursing science.

The traditional approach to science is an empirical or cause-and-effect one, where answers to research questions come about deductively. Nursing has followed this path in its attempt to establish a knowledge base. Difficulty occurs when nurses attempt to develop strategies to solve nursing problems involving human systems using this reductionistic approach. Human systems are complex, dynamic and individual. Traditional scientific models often fall short of providing adequate frameworks for describing, explaining and predicting the behaviour of these complex systems. Many scientific communities have been searching for a flexible more three-dimensional model to describe non-traditional system behaviours. Chaos theory may provide science with the new paradigm for the study of these complex systems. This paper suggests Thomas Kuhn's philosophy of science to use as a foundation for the application of chaos theory or the theory of non-linear dynamics to the science of nursing. PMID:8320396

Coppa, D F

1993-06-01

238

Suppression of spatiotemporal chaos under a constant electric potential signal

NASA Astrophysics Data System (ADS)

Suppression of spatiotemporal chaos in a one-dimensional nonlinear drift-wave equation driven by a sinusoidal wave is considered. Using a constant electric potential signal we demonstrate numerically that the spatiotemporal chaos can be effectively suppressed if the control parameters are properly chosen. The threshold and the controllable range of the control parameters are given. By establishing the kinetic equation of the system energy we find theoretically that an additional driving term in the energy equation is produced by the control signal and it can lead up to the frequency entrainment. Moreover, when the regular state is reached under the control, the system energy oscillates quasi-periodically, while the additional driving term decays to zero.

Yang, Chao-Yu; Tang, Guo-Ning; Liu, Jun-Xian

2008-03-01

239

Hybrid electronic/optical synchronized chaos communication system.

A hybrid electronic/optical system for synchronizing a chaotic receiver to a chaotic transmitter has been demonstrated. The chaotic signal is generated electronically and injected, in addition to a constant bias current, to a semiconductor laser to produce an optical carrier for transmission. The optical chaotic carrier is photodetected to regenerate an electronic signal for synchronization in a matched electronic receiver The system has been successfully used for the transmission and recovery of a chaos masked message that is added to the chaotic optical carrier. Past demonstrations of synchronized chaos based, secure communication systems have used either an electronic chaotic carrier or an optical chaotic carrier (such as the chaotic output of various nonlinear laser systems). This is the first electronic/optical hybrid system to be demonstrated. We call this generation of a chaotic optical carrier by electronic injection. PMID:19399134

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

2009-04-27

240

A simple electronic circuit is described which can be used in the student laboratory to demonstrate and study nonlinear effects and chaos. The circuit shows the changes to the dynamical properties of the system with respect to three control parameters: the applied voltage amplitude and frequency and the circuit damping. The response voltage and its derivative can be displayed to

B. K. Jones; G. Trefan

2001-01-01

241

Strange attractors and chaos control in periodically forced complex Duffing's oscillators

An interesting and challenging research subject in the field of nonlinear dynamics is the study of chaotic behavior in systems of more than two degrees of freedom. In this work we study fixed points, strange attractors, chaotic behavior and the problem of chaos control for complex Duffing's oscillators which represent periodically forced systems of two degrees of freedom. We produce

Gamal M. Mahmoud; Ahmed A. Mohamed; Shaban A. Aly

2001-01-01

242

Study on Weigh-in-Motion System Based on Chaos Immune Algorithm and RBF Network

Aiming at the complexity of data processing in Weigh-In-Motion (WIM) system, a nonlinear system model is built for the WIM system with radical basic function (RBF) neural network. To achieve more accurate network weights of RBF and improve the model detection precision, a novel chaos immune algorithm is presented to optimize the RBF network weights. In this paper, the logistic

Yi Shen; Yunfeng Bu; Mingxin Yuan

2008-01-01

243

Route out of chaos by hf parametric perturbations in spin-wave instabilities

Chaotic behaviour of a nonlinear system can be suppressed by fast parametric modulation. Analytical and numerical investigations show that the increase of the modulation amplitude corresponds to an effective variation of the modulated parameter and results in a scenario ‘out of chaos’. Applying this method to a spin-wave experiment in YIG, the dynamics is changed from chaotic to periodic via

F. Rödelsperger; Y. S. Kivshar; H. Benner

1995-01-01

244

Efficient uncertainty quantification with the polynomial chaos method for stiff systems

The polynomial chaos (PC) method has been widely adopted as a computationally feasible approach for uncertainty quantification (UQ). Most studies to date have focused on non-stiff systems. When stiff systems are considered, implicit numerical integration requires the solution of a non-linear system of equations at every time step. Using the Galerkin approach the size of the system state increases from

Haiyan Cheng; Adrian Sandu

2009-01-01

245

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.

246

This paper demonstrates that an artificial neural network training on time-series data from the logistic map at the onset of chaos trains more effectively when it is weakly chaotic. This suggests that a modest amount of chaos in the brain in addition to the ever present random noise might be beneficial for learning. In such a case, human subjects might exhibit an increased Lyapunov exponent in their EEG recordings during the performance of creative tasks, suggesting a possible line of future research. PMID:23517607

Sprott, J C

2013-04-01

247

Channeling chaos by building barriers.

Chaotic diffusion often represents a severe obstacle for the setup of experiments, e.g., in fusion plasmas or particle accelerators. We present a complete test of a method of control of Hamiltonian chaos, with both its numerical test and its first experimental realization on a paradigm for wave-particle interaction, i.e., a travelling wave tube. The core of our approach is a small apt modification of the system which channels chaos by building barriers to diffusion. Its experimental realization opens the possibility to practically achieve the control of a wide range of systems at a low additional cost of energy. PMID:15783819

Chandre, C; Ciraolo, G; Doveil, F; Lima, R; Macor, A; Vittot, M

2005-02-25

248

Enhancing chaoticity of spatiotemporal chaos.

In some practical situations strong chaos is needed. This introduces the task of chaos control with enhancing chaoticity rather than suppressing chaoticity. In this paper a simple method of linear amplifications incorporating modulo operations is suggested to make spatiotemporal systems, which may be originally chaotic or nonchaotic, strongly chaotic. Specifically, this control can eliminate periodic windows, increase the values and the number of positive Lyapunov exponents, make the probability distributions of the output chaotic sequences more homogeneous, and reduce the correlations of chaotic outputs for different times and different space units. The applicability of the method to practical tasks, in particular to random number generators and secure communications, is briefly discussed. PMID:15697707

Li, Xiaowen; Zhang, Heqiao; Xue, Yu; Hu, Gang

2005-01-01

249

Oscillators with asymmetric single and double well potentials: transition to chaos revisited

Summary We study the Melnikov criterion for a global homoclinic bifurcation and possible transition to chaos for a single degree of\\u000a freedom nonlinear oscillator. This provides a systematic method of treatment for an arbitrary potential expressed as a fourth\\u000a order polynomial. The equation of motion has external excitation and a Duffing type nonlinearity with one or two unsymmetric\\u000a potential wells.

G. Litak; M. Borowiec

2006-01-01

250

Utilization of Nonlinear Dynamics in the Converter Design Process

Due to their exhibition of nonlinearities, electrical power systems, such as shipboard power systems, provide an interesting research environment. Nonlinear systems are characterized by properties such as highly interdependent components and thus it is not hard to observe that power systems may display such phenomena. Nonlinear dynamics, such as bifurcations and chaos, have been shown to cause voltage collapse, angle

Michael Scott Sattler

2011-01-01

251

Chaos Synchronisation and Message Extraction in Optical Chaos Communications

NASA Astrophysics Data System (ADS)

This paper provides an overview of experimental and theoretical work undertaken in the authors' laboratory and directed at the development of optical chaos communications technology. The specific focus of the paper is on the use of external cavity edge-emitting semiconductor lasers for this purpose.

Shore, K. A.; Lee, M. W.; Paul, J.; Hong, Y.; Murakami, A.; Pierce, I.; Spencer, P. S.

2007-05-01

252

Nonlinear systems in medicine.

Many achievements in medicine have come from applying linear theory to problems. Most current methods of data analysis use linear models, which are based on proportionality between two variables and/or relationships described by linear differential equations. However, nonlinear behavior commonly occurs within human systems due to their complex dynamic nature; this cannot be described adequately by linear models. Nonlinear thinking has grown among physiologists and physicians over the past century, and non-linear system theories are beginning to be applied to assist in interpreting, explaining, and predicting biological phenomena. Chaos theory describes elements manifesting behavior that is extremely sensitive to initial conditions, does not repeat itself and yet is deterministic. Complexity theory goes one step beyond chaos and is attempting to explain complex behavior that emerges within dynamic nonlinear systems. Nonlinear modeling still has not been able to explain all of the complexity present in human systems, and further models still need to be refined and developed. However, nonlinear modeling is helping to explain some system behaviors that linear systems cannot and thus will augment our understanding of the nature of complex dynamic systems within the human body in health and in disease states.

Higgins, John P.

2002-01-01

253

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

254

The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its Kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield,

Myron Lecar; Fred A. Franklin; Matthew J. Holman; Norman J. Murray

2001-01-01

255

NASA Technical Reports Server (NTRS)

The physical basis of chaos in the solar system is now better understood: In all cases investigated so far, chaotic orbits result from overlapping resonances. Perhaps the clearest examples are found in the asteroid belt. Overlapping resonances account for its kirkwood gaps and were used to predict and find evidence for very narrow gaps in the outer belt. Further afield, about one new "short-peroid" comet is discovered each year. They are believed to come from the "Kuiper Belt" (at 40 AU or more) via chaotic orbits produced by mean-motion and secular resonances with Neptune. Finally, the planetary system itself is not immune from chaos. In the inner solar system, overlapping secular resonances have been identified as the possible source of chaos. For example, Mercury in 1012 years, may suffer a close encounter with Venus or plunge into the Sun. In the outer solar system, three-body resonances have been identified as a source of chaos, but on an even longer time scale of 109 times the age of the solar system. On the human time scale, the planets do follow their orbits in a stately procession, and we can predict their trajectories for hundreds of thousands of years. That is because the mavericks, with shorter instability times, have long since been ejected. The solar system is not stable; it is just old!

Lecar, Myron; Franklin, Fred A.; Holman, Matthew J.; Murray, Norman J.

2001-01-01

256

Chaos game representation of proteins

The present report proposes a new method for the chaos game representation (CGR) of different families of proteins. Using concatenated amino acid sequences of proteins belonging to a particular family and a 12-sided regular polygon, each vertex of which represents a group of amino acid residues leading to conservative substitutions, the method can generate the CGR of the family and

Soumalee Basu; Archana Pan; Chitra Dutta; Jyotirmoy Das

1997-01-01

257

Quantum chaos and dynamical entropy

We review the notion of dynamical entropy by Connes, Narnhoferand Thirring and relate it to Quantum Chaos. A particle in a periodicpotential is used as an example. This is worked out in the classical andthe quantum mechanical framework, for the single particle as well as forthe corresponding gas.

F Benatti; T Hudetz; A Knauf

1997-01-01

258

Quantum Chaos and Its Application

NASA Astrophysics Data System (ADS)

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 discussed. The second part of this lecture note is devoted to introduce my recent work. Within the framework of the Interacting Boson Model (IBM), we discuss rotational damping, which has a close relation to the transition from order to chaos at high spin states. We discuss the basic mechanism of its appearance by showing, the global properties of the level density and electromagnetic transitions, including their fluctuation properties in the system governed by the quadrupole-quadrupole interaction at highly excited, high spin states. It is demonstrated that an unexpected regularity arises due to a quadrupole-quadrupole interaction at high spin state. We present an articulate elucidation on the importance of the higher multipole interactions, which cause the mixing among highly excited rotational bands. For the damping width of the rotational bands, an explanation based on the SU(3) limit of the IBM is suggested. This work is done under the collaboration with T. Otsuka and P.~von Brentano.

Mizusaki, T.

259

New Features about Chaos in Bianchi I non-Abelian Born-Infeld cosmology

When the action is replaced by the Born-Infeld-type non-Abelian action (NBI), a chaos-order transition is observed in the high energy region for a Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field. This is interpreted as a smothering effect due to (non-perturbative in {alpha}') string corrections to the classical EYM action. We give a numerical evidence for the chaos-order transition and present an analytical proof of regularity of color oscillations in the limit of strong Born-Infeld non-linearity.

Dyadichev, Vladimir V.; Gal'tsov, Dmitri V. [Theoretical Physics, Moscow State University, 119899, Moscow (Russian Federation); Moniz, Paulo Vargas [Astronomy Unit, Mathematical Sciences, University of London, Mile End Road, London E1 4NS (United Kingdom)

2006-11-03

260

Control of chaos in permanent magnet synchronous motor by using optimal Lyapunov exponents placement

NASA Astrophysics Data System (ADS)

Permanent Magnet Synchronous Motor (PMSM) experiences chaotic behavior for a certain range of its parameters. In this case, since the performance of the PMSM degrades, the chaos should be eliminated. In this Letter, the control of the undesirable chaos in PMSM using Lyapunov exponents (LEs) placement is proposed that is also improved by choosing optimal locations of the LEs in the sense of predefined cost function. Moreover, in order to provide the physical realization of the method, nonlinear parameter estimator for the system is suggested. Finally, to show the effectiveness of the proposed methodology, the simulation results for applying this control strategy are provided.

Ataei, Mohammad; Kiyoumarsi, Arash; Ghorbani, Behzad

2010-09-01

261

Bistability and chaos at low levels of quanta.

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. PMID:24032904

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

2013-08-01

262

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

263

Observing chaos for quantum-dot microlasers with external feedback.

Chaos presents a striking and fascinating phenomenon of nonlinear systems. A common aspect of such systems is the presence of feedback that couples the output signal partially back to the input. Feedback coupling can be well controlled in optoelectronic devices such as conventional semiconductor lasers that provide bench-top platforms for the study of chaotic behaviour and high bit rate random number generation. Here we experimentally demonstrate that chaos can be observed for quantum-dot microlasers operating close to the quantum limit at nW output powers. Applying self-feedback to a quantum-dot microlaser results in a dramatic change in the photon statistics wherein strong, super-thermal photon bunching is indicative of random-intensity fluctuations associated with the spiked emission of light. Our experiments reveal that gain competition of few quantum dots in the active layer enhances the influence of self-feedback and will open up new avenues for the study of chaos in quantum systems. PMID:21694714

Albert, Ferdinand; Hopfmann, Caspar; Reitzenstein, Stephan; Schneider, Christian; Höfling, Sven; Worschech, Lukas; Kamp, Martin; Kinzel, Wolfgang; Forchel, Alfred; Kanter, Ido

2011-01-01

264

ICPP: Chaos Control and Taming of Turbulence in Plasma Devices

NASA Astrophysics Data System (ADS)

Chaos and turbulence are often considered as troublesome features of plasma devices. Recently, in the general framework of nonlinear dynamical systems, a number of strategies have been developed to achieve active control over complex temporal or spatiotemporal behaviour. Many of these techniques apply to plasma instabilities (T. Klinger in H.G. Schuster (ed.) Handbook of Chaos Control), Wiley-VCH, Weinheim (1999).. In the present contribution, we discuss recent progress in chaos control, stochastic resonance, and taming of turbulence in different plasma experiments. Successful control of plasma instabilities is typically a three-step procedure. In the first step, the physics of the plasma instability mechanism is investigated in its detail. This provides a most useful tool, the control parameter. In the second step, an appropriate control algorithm is selected, where we distinguish open-loop and closed-loop control. The third step is the technical implementation of the control scheme. Experimental and simulation results of four different plasma problems are discussed: (i) Chaotic oscillations in simple Plasma diodes are controlled using a discrete feedback scheme. (ii) Stochastically induced mode jumps in thermionic plasma diodes are phase-synchronized by a weak periodic driver force, so-called stochastic resonance.(iii) Phase turbulence of ionization waves in glow discharges is successfully controlled by purely temporal, discrete and continuous feedback schemes. (iv) Electrostatic drift wave turbulence is synchronized (`tamed') by application of a rotating electric field with a preselected mode structure and frequency.

Klinger, Thomas

2000-10-01

265

Hyperbolic chaos at blinking coupling of noisy oscillators

NASA Astrophysics Data System (ADS)

We study an ensemble of identical noisy phase oscillators with a blinking mean-field coupling, where one-cluster and two-cluster synchronous states alternate. In the thermodynamic limit the population is described by a nonlinear Fokker-Planck equation. We show that the dynamics of the order parameters demonstrates hyperbolic chaos. The chaoticity manifests itself in phases of the complex mean field, which obey a strongly chaotic Bernoulli map. Hyperbolicity is confirmed by numerical tests based on the calculations of relevant invariant Lyapunov vectors and Lyapunov exponents. We show how the chaotic dynamics of the phases is slightly smeared by finite-size fluctuations.

Kuptsov, Pavel V.; Kuznetsov, Sergey P.; Pikovsky, Arkady

2013-03-01

266

Relaxation Dynamics of Spatiotemporal Chaos in the Nematic Liquid Crystal

NASA Astrophysics Data System (ADS)

We are working on the electroconvection of nematic liquid crystals, in which a kind of spatiotemporal chaos called as a soft-mode turbulence (SMT) is observed. The SMT is caused by the nonlinear interaction between the convective modes and the Nambu--Goldstone (NG) modes. By applying an external magnetic field H, the NG mode is suppressed and an ordered pattern can be observed. By removing the suppression effect the ordered state relax to its original SMT pattern. We revealed two types of instability govern the relaxation process: the zigzag instability and the free rotation of wavevector q(r).

Nugroho, Fahrudin; Ueki, Tatsuhiro; Hidaka, Yoshiki; Kai, Shoichi

2011-11-01

267

Nonlinear optics and materials; Proceedings of the Meeting, Dallas, TX, May 8-10, 1991

NASA Astrophysics Data System (ADS)

Topics of current interest in nonlinear optics and materials are discussed, including the theory of nonlinear interactions in microdroplets, fundamental droplet experiments and comparisons with theory, droplet diagnostics and vaporization, transverse effects in nonlinear optics, propagation effects, and quantum fluctuations. Further, the discussion covers noninversion and correlated-emission lasers, nonlinearities and chaos in lasers, laser acceleration of particles, composites, polymers, and semiconductors.

Cantrell, Cyrus D.; Bowden, Charles M.

268

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

269

NASA Technical Reports Server (NTRS)

The results of extensive computations are presented in order to accurately characterize transitions to chaos for the Kuramoto-Sivashinsky equation. In particular, the oscillatory dynamics in a window that supports a complete sequence of period doubling bifurcations preceding chaos is followed. As many as thirteen period doublings are followed and used to compute the Feigenbaum number for the cascade and so enable, for the first time, an accurate numerical evaluation of the theory of universal behavior of nonlinear systems, for an infinite dimensional dynamical system. Furthermore, the dynamics at the threshold of chaos exhibit a fractal behavior which is demonstrated and used to compute a universal scaling factor that enables the self-similar continuation of the solution into a chaotic regime.

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1991-01-01

270

Recurrence-based detection of the hyperchaos-chaos transition in an electronic circuit

NASA Astrophysics Data System (ADS)

Some complex measures based on recurrence plots give evidence about hyperchaos-chaos transitions in coupled nonlinear systems [E. G. Souza et al., ``Using recurrences to characterize the hyperchaos-chaos transition,'' Phys. Rev. E 78, 066206 (2008)]. In this paper, these measures are combined with a significance test based on twin surrogates to identify such a transition in a fourth-order Lorenz-like system, which is able to pass from a hyperchaotic to a chaotic behavior for increasing values of a single parameter. A circuit analog of the mathematical model has been designed and implemented and the robustness of the recurrence-based method on experimental data has been tested. In both the numerical and experimental cases, the combination of the recurrence measures and the significance test allows to clearly identify the hyperchaos-chaos transition.

Ngamga, E. J.; Buscarino, A.; Frasca, M.; Sciuto, G.; Kurths, J.; Fortuna, L.

2010-12-01

271

On chaos control and synchronization of the commensurate fractional order Liu system

NASA Astrophysics Data System (ADS)

In this work, we study chaos control and synchronization of the commensurate fractional order Liu system. Based on the stability theory of fractional order systems, the conditions of local stability of nonlinear three-dimensional commensurate fractional order systems are discussed. The existence and uniqueness of solutions for a class of commensurate fractional order Liu systems are investigated. We also obtain the necessary condition for the existence of chaotic attractors in the commensurate fractional order Liu system. The effect of fractional order on chaos control of this system is revealed by showing that the commensurate fractional order Liu system is controllable just in the fractional order case when using a specific choice of controllers. Moreover, we achieve chaos synchronization between the commensurate fractional order Liu system and its integer order counterpart via function projective synchronization. Numerical simulations are used to verify the analytical results.

Hegazi, A. S.; Ahmed, E.; Matouk, A. E.

2013-05-01

272

Chaos in rf-driven long Josephson junctions in the presence of an external field

Chaotic responses induced by an applied rf signal on the long Josephson junction influenced by a constant dc-driven field are investigated by means of a model based on the sine-Gordon equation. We assume that the localized nonlinear excitations present in the system as initial data are the breatherlike mode. Thus, in order to analyze in detail the onset of the complicated irregular behavior (chaos), we employ collective coordinate theory to derive the total Hamiltonian and the dissipative function in terms of the breather width. The appearance of chaos in this system is predicted by the Melnikov theory and a few numerical treatments. A threshold for chaos as a function of the physical parameters of the system is found. Finally, the Poincare sections, which allow us to see clearly the phenomenon in the nondissipative case, is compared to the analytical prediction and good agreement is obtained.

Kenfack, A.; Kofane, T.C. [Laboratoire de Mecanique, Faculte des Sciences, Universite de Yaounde I, B.P. 812, Yaounde, Cameroun (??)] [Laboratoire de Mecanique, Faculte des Sciences, Universite de Yaounde I, B.P. 812, Yaounde, Cameroun (??)

1995-10-01

273

Chaos concepts as diagnostic tools for assessing rotating machinery vibration signatures

Chaos content in measured vibration signals is of some practical importance in rotordynamical systems. Of particular interest is the relationship between the occurrence of determinsite chaos and the diagnosis of mechanical failures in rotating machinery. Two nonlinear rotordynamical systems were studied using simulation and various forms of subharmonic, quasiperiodic and chaotic vibrations were observed. Different routes into and out of chaos show important signs for wear assessment and failure prediction. Experimental test facilities are currently under development and the next steps involve experimental verification of the simulation results and the development of signal processing techniques for extracting the dynamical features of the vibration signatures from measured time series data. {copyright} {ital 1996 American Institute of Physics.}

Adams, M.L. [Department of Mechanical and Aerospace Engineering, The Case School of Engineering, Case Western Reserve University, Cleveland, Ohio 44106 (United States); Loparo, K.A. [Department of Systems Engineering, The Case School of Engineering, Case Western Reserve University, Cleveland, Ohio 44106 (United States)

1996-06-01

274

The equilibrium states of an inverted two-link simple pendulum with an asymmetric follower force are classified depending\\u000a on the characteristics of the springs (hard, soft, or linear) at the upper end and at the hinges. Phase portraits are plotted.\\u000a The bifurcation points on the equilibrium curves are identified. Emphasis is on fold and cusp catastrophes

L. G. Lobas; V. V. Koval’chuk; O. V. Bambura

2007-01-01

275

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

276

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

277

NASA Technical Reports Server (NTRS)

Nonlinear equations of motion for a cantilever rotor blade are derived for the hovering flight condition. The blade is assumed to have twist, precone, droop, sweep, torque offset and blade root offset, and the elastic axis and the axes of center of mass, tension, and aerodynamic center coincident at the quarter chord. The blade is cantilevered in bending, but has a torsional root spring to simulate pitch link flexibility. Aerodynamic forces acting on the blade are derived from strip theory based on quasi-steady two-dimensional airfoil theory. The equations are hybrid, consisting of one integro-differential equation for root torsion and three integro-partial differential equations for flatwise and chordwise bending and elastic torsion. The equations are specialized for a uniform blade and reduced to nonlinear ordinary differential equations by Galerkin's method. They are linearized for small perturbation motions about the equilibrium operating condition. Modal analysis leads to formulation of a standard eigenvalue problem where the elements of the stability matrix depend on the solution of the equilibrium equations. Two different forms of the root torsion equation are derived that yield virtually identical numerical results. This provides a reasonable check for the accuracy of the equations.

Hodges, D. H.

1976-01-01

278

Fighting Chaos: Applications of Breeding

NASA Astrophysics Data System (ADS)

I will discuss basic concepts of chaos, and describe techniques that have allowed taking advantage of chaos and improve forecasts and their information. One example is "breeding of instabilities" a very simple technique to estimate the fastest growing instabilities. Breeding allows predicting when a regime change will take place and how long will the new regime last in the famous Lorenz (1963) "unpredictable chaotic model", something that surprised Lorenz himself. These techniques can be applied to any dynamic chaotic system. Some examples include detection of ocean instabilities and their physical origin, breeding in coupled ocean-atmosphere systems, detecting instabilities in the atmosphere of Mars, and breeding on the phase-space reconstructed from single time series using the time-delay embedding method. Finally I'll discuss the implications of these results for data assimilation.

Kalnay, E.

2012-12-01

279

Outflow channel sources, reactivation, and chaos formation, Xanthe Terra, Mars

NASA Astrophysics Data System (ADS)

The undulating, warped, and densely fractured surfaces of highland regions east of Valles Marineris (located north of the eastern Aureum Chaos, east of the Hydraotes Chaos, and south of the Hydaspis Chaos) resulted from extensional surface warping related to ground subsidence, caused when pressurized water confined in subterranean caverns was released to the surface. Water emanations formed crater lakes and resulted in channeling episodes involved in the excavation of Ares, Tiu, and Simud Valles of the eastern part of the circum-Chryse outflow channel system. Progressive surface subsidence and associated reduction of the subsurface cavernous volume, and/or episodes of magmatic-driven activity, led to increases of the hydrostatic pressure, resulting in reactivation of both catastrophic and non-catastrophic outflow activity. Ancient cratered highland and basin materials that underwent large-scale subsidence grade into densely fractured terrains. Collapse of rock materials in these regions resulted in the formation of chaotic terrains, which occur in and near the headwaters of the eastern circum-Chryse outflow channels. The deepest chaotic terrain in the Hydaspis Chaos region resulted from the collapse of pre-existing outflow channel floors. The release of volatiles and related collapse may have included water emanations not necessarily linked to catastrophic outflow. Basal warming related to dike intrusions, thermokarst activity involving wet sediments and/or dissected ice-enriched country rock, permafrost exposed to the atmosphere by extensional tectonism and channel incision, and/or the injection of water into porous floor material, may have enhanced outflow channel floor instability and subsequent collapse. In addition to the possible genetic linkage to outflow channel development dating back to at least the Late Noachian, clear disruption of impact craters with pristine ejecta blankets and rims, as well as preservation of fine tectonic fabrics, suggest that plateau subsidence and chaos formation may have continued well into the Amazonian Period. The geologic and paleohydrologic histories presented here have important implications, as new mechanisms for outflow channel formation and other fluvial activity are described, and new reactivation mechanisms are proposed for the origin of chaotic terrain as contributors to flooding. Detailed geomorphic analysis indicates that subterranean caverns may have been exposed during chaos formation, and thus chaotic terrains mark prime locations for future geologic, hydrologic, and possible astrobiologic exploration.

Rodriguez, Jose A. P.; Sasaki, Sho; Kuzmin, Ruslan O.; Dohm, James M.; Tanaka, Ken L.; Miyamoto, Hideaki; Kurita, Kei; Komatsu, Goro; Fairén, A. G.; Ferris, Justin C.

2005-05-01

280

Outflow channel sources, reactivation, and chaos formation, Xanthe Terra, Mars

The undulating, warped, and densely fractured surfaces of highland regions east of Valles Marineris (located north of the eastern Aureum Chaos, east of the Hydraotes Chaos, and south of the Hydaspis Chaos) resulted from extensional surface warping related to ground subsidence, caused when pressurized water confined in subterranean caverns was released to the surface. Water emanations formed crater lakes and resulted in channeling episodes involved in the excavation of Ares, Tiu, and Simud Valles of the eastern part of the circum-Chryse outflow channel system. Progressive surface subsidence and associated reduction of the subsurface cavernous volume, and/or episodes of magmatic-driven activity, led to increases of the hydrostatic pressure, resulting in reactivation of both catastrophic and non-catastrophic outflow activity. Ancient cratered highland and basin materials that underwent large-scale subsidence grade into densely fractured terrains. Collapse of rock materials in these regions resulted in the formation of chaotic terrains, which occur in and near the headwaters of the eastern circum-Chryse outflow channels. The deepest chaotic terrain in the Hydaspis Chaos region resulted from the collapse of pre-existing outflow channel floors. The release of volatiles and related collapse may have included water emanations not necessarily linked to catastrophic outflow. Basal warming related to dike intrusions, thermokarst activity involving wet sediments and/or dissected ice-enriched country rock, permafrost exposed to the atmosphere by extensional tectonism and channel incision, and/or the injection of water into porous floor material, may have enhanced outflow channel floor instability and subsequent collapse. In addition to the possible genetic linkage to outflow channel development dating back to at least the Late Noachian, clear disruption of impact craters with pristine ejecta blankets and rims, as well as preservation of fine tectonic fabrics, suggest that plateau subsidence and chaos formation may have continued well into the Amazonian Period. The geologic and paleohydrologic histories presented here have important implications, as new mechanisms for outflow channel formation and other fluvial activity are described, and new reactivation mechanisms are proposed for the origin of chaotic terrain as contributors to flooding. Detailed geomorphic analysis indicates that subterranean caverns may have been exposed during chaos formation, and thus chaotic terrains mark prime locations for future geologic, hydrologic, and possible astrobiologic exploration. ?? 2004 Elsevier Inc. All rights reserved.

Rodriguez, J. A. P.; Sasaki, S.; Kuzmin, R. O.; Dohm, J. M.; Tanaka, K. L.; Miyamoto, H.; Kurita, K.; Komatsu, G.; Fairen, A. G.; Ferris, J. C.

2005-01-01

281

The physical basis of chaos in the solar system is now better understood: in\\u000aall cases investigated so far, chaotic orbits result from overlapping\\u000aresonances. Perhaps the clearest examples are found in the asteroid belt.\\u000aOverlapping resonances account for its Kirkwood gaps and were used to predict\\u000aand find evidence for very narrow gaps in the outer belt. Further afield,

Myron Lecar; Fred A. Franklin; Matthew J. Holman; Norman W. Murray

2001-01-01

282

Temperature chaos and quenched heterogeneities

NASA Astrophysics Data System (ADS)

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.

Barucca, Paolo; Parisi, Giorgio; Rizzo, Tommaso

2014-03-01

283

Characterizing the Morphology of Chaos on Europa

NASA Astrophysics Data System (ADS)

Chaos terrain represents a type of feature unique to Europa and covers approximately one third of the satellite's surface. Two endmember models have been proposed for its formation: one suggests it forms through melting of the surface by liquid water from the subsurface ocean; the second suggests that chaos forms from the upwelling of thermally or compositionally buoyant diapirs. The formation of chaos disrupts preexisting surfaces and it has been observed that the magnitude of this disruption varies from one feature to another. Based on the morphological characteristics of different prominent and well-imaged regions of chaos (i.e., Conamara and Murias), this feature-type has been subdivided into endmember classes (Greeley et al., 2000). Conamara chaos is defined by kilometer-scale blocks of preexisting ridged plains material that have been tilted, translated and rotated with respect to one another within a generally lower-albedo matrix of hummocky material. Approximately 60% of the preexisting terrain has been replaced with or converted into matrix material (Spaun et al., 1998). In contrast, Murias chaos appears to be comprised purely of matrix material, with no hint of blocks of preexisting material or tectonic structure (Figueredo et al. 2002). The morphological characteristics of these two types of chaos have been commonly used to establish criteria for examining formation models. However, additional distinct morphologies of chaos have been proposed and the abundance/distribution of chaos morphologies is not well known. Understanding the importance of these various morphologies could provide valuable insight regarding the formation and evolution of this unique feature-type. To that end, we have systematically mapped the global distribution of chaos using image data at resolutions from ~1 km/pixel to 10 m/pixel and covering a range of viewing geometries. From this, we have categorized variations in morphology using the relative abundance of plates within a given feature as a defining characteristic and, using this map, we examine potential trends in the distribution of chaos morphologies.

Quick, L. C.; Patterson, G. W.; Prockter, L. M.

2008-12-01

284

Dissipative nonlinear dynamics in holography

NASA Astrophysics Data System (ADS)

We look at the response of a nonlinearly coupled scalar field in an asymptotically AdS black brane geometry and find a behavior very similar to that of known dissipative nonlinear systems like the chaotic pendulum. Transition to chaos proceeds through a series of period-doubling bifurcations. The presence of dissipation, crucial to this behavior, arises naturally in a black hole background from the ingoing conditions imposed at the horizon. AdS/CFT translates our solution to a chaotic response of O, the operator dual to the scalar field. Our setup can also be used to study quenchlike behavior in strongly coupled nonlinear systems.

Basu, Pallab; Ghosh, Archisman

2014-02-01

285

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

286

Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos game representation (CGR) of randomly-linked functional protein sequences, then propose the use of the recurrent iterated function systems (RIFS) in fractal theory to simulate the measure based on

Zu-Guo Yu; Qian-Jun Xiao; Long Shi; Jun-Wu Yu; Anh Vo

2010-01-01

287

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

288

Suppression of chaos by nonresonant parametric perturbations

It is shown analytically and numerically that the suppression of chaos may be effectively achieved by applying a high-frequency parametric force to a chaotic dynamical system. Such a periodic nonresonant force may decrease or even completely eliminate chaos. Taking the Duffing oscillator as a concrete but rather general example, an analytical approach is elaborated to demonstrate how such a suppression

Yuri S. Kivshar; Frank Rödelsperger; Hartmut Benner

1994-01-01

289

Applied chaos theory - A paradigm for complexity

It is still not entirely clear, whether chaos theory will furnish solutions to problems posed by complex systems upon the development of a mathematics that is descriptive of complexity, in the same way that calculus is descriptive of continuously-varying processes. The present survey of the current understanding of chaos discusses the characteristics of complexity, the metaquantification of complexity, the anatomy

Ali B. Cambel

1993-01-01

290

Structures of chaos in open reaction systems.

By numerically simulating the Bray-Liebhafsky (BL) reaction (the hydrogen peroxide decomposition in the presence of hydrogen and iodate ions) in a continuously fed well stirred tank reactor (CSTR), we find "structured" types of chaos emerging in regular order with respect to flow rate as the control parameter. These chaotic "structures" appear between each two successive periodic states, and have forms and evolution resembling to the neighboring periodic dynamics. More precisely, in the transition from period-doubling route to chaos to the arising periodic mixture of different mixed-mode oscillations, we are able to recognize and qualitatively and quantitatively distinguish the sequence of "period-doubling" chaos and chaos consisted of mixed-mode oscillations (the "mixed-mode structured" chaos), both appearing in regular order between succeeding periodic states. Additionally, between these types of chaos, the chaos without such recognizable "structures" ("unstructured" chaos) is also distinguished. Furthermore, all transitions between two successive periodic states are realized through bifurcation of chaotic states. This scenario is a universal feature throughout the whole mixed-mode region, as well as throughout other mixed-mode regions obtained under different initial conditions. PMID:21993658

Ivanovi?-Šaši?, A Z; Markovi?, V M; Ani?, S R; Kolar-Ani?, Lj Z; Cupi?, Ž D

2011-12-01

291

Dynamic Equilibrium, Self-Organizing Systems, and Chaos Theory

NSDL National Science Digital Library

It is commonly thought that the behavior of physical systems is controlled by deterministic laws, yet physical processes appear to be unpredictable. This Topic in Depth discusses how the concepts of self-regulating systems, dynamic equilibrium, and chaos theory help to rectify this conundrum. The first website ({1--http://dbhs.wvusd.k12.ca.us/Equilibrium/Dynamic-Equilibrium.html}), developed by John L. Park at Chem Team, addresses dynamic equilibrium as it applies to chemical systems. High school students will find two equilibrium examples illustrating how, by means of forward and reverse reactions, the system becomes constant. In the next website (2), the MadSci Network discusses the issue of dynamic equilibrium in terms of the components of earth systems. Visitors can learn how the carbon dioxide cycle in the atmosphere has been disrupted by humans and how the system copes with this change. The Chaos Group at the University of Maryland developed the third website 3) to promote its research in chaotic dynamics. Visitors can learn about the group's work in Pattern Formation and Granular Dynamics, magnetic and fluid dynamics, and more. The next website (4) is an online articleby Donald Turcotte and John Rundle discussing the difficulty in addressing self-organizing complexity. This website, made available by PubMed Central, provides examples of complexities in systems such as drainage networks and global climate. Visitors can also learn about deterministic and stochastic components in systems. A. Mary Selvam at the Indian Institute of Tropical Meteorology teaches users about the relationship atmospheric flows have with quantumlike mechanics and determinist chaos in the fifth website (5). In this online scientific article, visitors can learn how the author's conclusions may be applicable to the design of artificial intelligence systems. The last website (6) discusses the research efforts of Mercer University Physics Department concerning nonlinear phenomena that are the fundamentals of chaos and complexity. This extensive website provides visitors with explanations of the group's research efforts in neurodynamics, granular physics, and mind body dynamics. Students can also find out about the history of the synchronization of chaos.

Enright, Rachel

292

A conceptualization of death from a perspective of chaos order

This paper asserts that physical death is a condition which results from chaos overwhelming ordered physiological systems of the body. The argument utilizes Genesis 1:1-2:17 in the development of the relationship between chaos and primal order. Within this relationship, chaos is associated with two conditions sufficient to produce death. First, when God removes the human spirit, chaos overwhelms the harmony

Jerome R. Wernow

1987-01-01

293

Topological chaos in cavities and channels

NASA Astrophysics Data System (ADS)

Moving three or more stirrers around in a two-dimensional fluid domain can generate topological chaos, that is, chaos that cannot be removed by continuous deformation of the fluid with the boundaries and stirrers held fixed. Those stirrer motions that generate topological chaos are determined using the Thurston Nielsen classification theorem, which also predicts a lower bound on the fluid stretching rate. Equivalent motions can be produced in a lid-driven cavity without stirrers by using periodic, piecewise constant motion of the top and/or bottom boundaries. We explore the properties of topological chaos in lid-driven cavities. Lid-driven cavity flow can also be combined with rectangular Poiseuille flow as a model of either pressure-driven flow in a channel with surface grooves or electro-osmotic flow in a channel with variations in surface potential. We demonstrate that this combination can be used to generate topological chaos in three-dimensional steady channel flow.

Chen, Jie; Stremler, Mark A.

2006-11-01

294

Class, chaos, and the construction of community.

Chaotic conditions are a prevalent and threatening feature of social life. Five studies examined whether social class underlies divergent responses to perceptions of chaos in one's social environments and outcomes. The authors hypothesized that when coping with perceptions of chaos, lower class individuals tend to prioritize community, relative to upper class individuals, who instead tend to prioritize material wealth. Consistent with these predictions, when personally confronting chaos, lower class individuals were more communally oriented (Study 1), more connected with their community (Study 2), and more likely to volunteer for a community-building project (Study 3), compared to upper class individuals. In contrast, perceptions of chaos caused upper class individuals to express greater reliance on wealth (Study 4) and prefer financial gain over membership in a close-knit community (Study 5), relative to lower class individuals. These findings suggest that social class shapes how people respond to perceptions of chaos and cope with its threatening consequences. PMID:22889070

Piff, Paul K; Stancato, Daniel M; Martinez, Andres G; Kraus, Michael W; Keltner, Dacher

2012-12-01

295

Discretization chaos - Feedback control and transition to chaos

NASA Technical Reports Server (NTRS)

Problems in the design of feedback controllers for chaotic dynamical systems are considered theoretically, focusing on two cases where chaos arises only when a nonchaotic continuous-time system is discretized into a simpler discrete-time systems (exponential discretization and pseudo-Euler integration applied to Lotka-Volterra competition and prey-predator systems). Numerical simulation results are presented in extensive graphs and discussed in detail. It is concluded that care must be taken in applying standard dynamical-systems methods to control systems that may be discontinuous or nondifferentiable.

Grantham, Walter J.; Athalye, Amit M.

1990-01-01

296

Nonlinear dynamics, fractals, cardiac physiology and sudden death

NASA Technical Reports Server (NTRS)

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Goldberger, Ary L.

1987-01-01

297

Hong Kong Polytechnic University: Nonlinear Circuits and Systems

NSDL National Science Digital Library

Hong Kong Polytechnic University's project on Nonlinear Circuits and Systems began in 1991 with a focus on switching power electronics systems. The project has expanded its focus to include signal processing and chaos communications, with an emphasis on practical systems and applications. Seminar slides and Flash movies on chaos and circuit theories and Life Phenomena (such as fireflies, the pendulum and the butterfly effect) are informative. Other graphs represent the SARS virus propagation, the Hong Kong Coast, and the Koch Curve.

298

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

299

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

300

Overview of nonlinear dynamical systems and complexity theory

A brief overview is presented of the principal elements of {open_quote}{open_quote}nonlinear dynamics{close_quote}{close_quote}: catastrophes, fractals, chaos, solitary waves, and coherent and dissipative structures. The text is followed by a set of 10 portraits of the strange and violent world of nonlinear dynamics. {copyright} {ital 1996 American Institute of Physics.}

Herbert, D.E. [Department of Radiology, College of Medicine, University of South Alabama, Mobile, Alabama 36688 (United States)

1996-06-01

301

Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices

Bifurcations, chaos, and extensive periodic windows in the chaotic regime are observed for a driven LRC circuit, the capacitive element being a nonlinear varactor diode. Measurements include power spectral analysis; real time amplitude data; phase portraits; and a bifurcation diagram, obtained by sampling methods. The effects of added external noise are studied. These data yield experimental determinations of several of the universal numbers predicted to characterize nonlinear systems having this route to chaos.

Testa, J.; Perez, J.; Jeffries, C.

1982-01-01

302

Monohydrated Sulfates in Aurorae Chaos

NASA Technical Reports Server (NTRS)

This image of sulfate-containing deposits in Aurorae Chaos was taken by the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) at 0653 UTC (2:53 a.m. EDT) on June 10, 2007, near 7.5 degrees south latitude, 327.25 degrees east longitude. CRISM's image was taken in 544 colors covering 0.36-3.92 micrometers, and shows features as small as 40 meters (132 feet) across. The region covered is roughly 12 kilometers (7.5 miles) wide at its narrowest point.

Aurorae Chaos lies east of the Valles Marineris canyon system. Its western edge extends toward Capri and Eos Chasmata, while its eastern edge connects with Aureum Chaos. Some 750 kilometers (466 miles) wide, Aurorae Chaos is most likely the result of collapsed surface material that settled when subsurface ice or water was released.

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 covers an area featuring several knobs of erosion-resistant material at one end of what appears to be a large teardrop shaped plateau. Similar plateaus occur throughout the interior of Valles Marineris, and they are formed of younger, typically layered rocks that post-date formation of the canyon system. Many of the deposits contain sulfate-rich layers, hinting at ancient saltwater.

The center left image, an infrared false color image, reveals a swath of light-colored material draped over the knobs. The center right image unveils the mineralogical composition of the area, with yellow representing monohydrated sulfates (sulfates with one water molecule incorporated into each molecule of the mineral).

The lower two images are renderings of data draped over topography with 5 times vertical exaggeration. These images provide a view of the topography and reveal how the monohydrated sulfate-containing deposits drape over the knobs and also an outcrop in lower-elevation parts of the plateau.

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

303

Quantum Chaos and Effective Thermalization

NASA Astrophysics Data System (ADS)

We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber Q or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a “quantum smoothened” approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows.

Altland, Alexander; Haake, Fritz

2012-02-01

304

Quantum chaos and effective thermalization.

We demonstrate effective equilibration for unitary quantum dynamics under conditions of classical chaos. Focusing on the paradigmatic example of the Dicke model, we show how a constructive description of the thermalization process is facilitated by the Glauber Q or Husimi function, for which the evolution equation turns out to be of Fokker-Planck type. The equation describes a competition of classical drift and quantum diffusion in contractive and expansive directions. By this mechanism the system follows a "quantum smoothened" approach to equilibrium, which avoids the notorious singularities inherent to classical chaotic flows. PMID:22401203

Altland, Alexander; Haake, Fritz

2012-02-17

305

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

306

Interdisciplinary application of nonlinear time series methods

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of

Thomas Schreiber

1998-01-01

307

Interdisciplinary application of nonlinear time series methods

This paper reports on the application to field measurements of time series methods developed on the basis of the theory of deterministic chaos. The major difficulties are pointed out that arise when the data cannot be assumed to be purely deterministic and the potential that remains in this situation is discussed. For signals with weakly nonlinear structure, the presence of

Thomas Schreiber

1999-01-01

308

Modeling and optimization of the claw-pole alternator based on support vector machines and chaos

A novel way about nonlinear regression modeling of the claw-pole alternator oriented to the computer-aided design (CAD) with the support vector machines (SVM) is presented in this paper. The training samples are rooted in the severe finite element model (FEM) simulation. Parameter optimization of the claw-pole alternator is also presented, which is based on chaos and uses the SVM regression

Xiao-Hua Bao; Qun-Jing Wang; You-Yuan Ni

2005-01-01

309

Chaos and Hyperchaos in the post-breakdown regime of p-germanium

NASA Astrophysics Data System (ADS)

As a highly nonlinear system, p-doped germanium electrically driven into the post-breakdown regime at liquid-helium temperatures shows spontaneous current oscillations. Varying the control parameters, namely the electric and the magnetic field, we observed a sequence of different routes to chaos. Moreover, we found a transition from an ordinary chaotic state to a hyperchaotic state with a sequence of strange attractors apparently having different dimensionality.

Röhricht, B.; Wessely, B.; Peinke, J.; Mühlbach, A.; Parisi, J.; Huebener, R. P.

1985-11-01

310

Markov transitions and the propagation of chaos

The propagation of chaos is a central concept of kinetic theory that serves to relate the equations of Boltzmann and Vlasov to the dynamics of many-particle systems. Propagation of chaos means that molecular chaos, i.e., the stochastic independence of two random particles in a many-particle system, persists in time, as the number of particles tends to infinity. We establish a necessary and sufficient condition for a family of general n-particle Markov processes to propagate chaos. This condition is expressed in terms of the Markov transition functions associated to the n-particle processes, and it amounts to saying that chaos of random initial states propagates if it propagates for pure initial states. Our proof of this result relies on the weak convergence approach to the study of chaos due to Sztitman and Tanaka. We assume that the space in which the particles live is homomorphic to a complete and separable metric space so that we may invoke Prohorov's theorem in our proof. We also s how that, if the particles can be in only finitely many states, then molecular chaos implies that the specific entropies in the n-particle distributions converge to the entropy of the limiting single-particle distribution.

Gottlieb, A.

1998-12-01

311

Transitions to chaos in squeeze-film dampers

NASA Astrophysics Data System (ADS)

This work reports on a numerical study undertaken to investigate the imbalance response of a rigid rotor supported by squeeze-film dampers. Two types of damper configurations were considered, namely, dampers without centering springs, and eccentrically operated dampers with centering springs. For a rotor fitted with squeeze-film dampers without centering springs, the study revealed the existence of three regimes of chaotic motion. The route to chaos in the first regime was attributed to a sequence of period-doubling bifurcations of the period-1 (synchronous) rotor response. A period-3 (one-third subharmonic) rotor whirl orbit, which was born from a saddle-node bifurcation, was found to co-exist with the chaotic attractor. The period-3 orbit was also observed to undergo a sequence of period-doubling bifurcations resulting in chaotic vibrations of the rotor. The route to chaos in the third regime of chaotic rotor response, which occurred immediately after the disappearance of the period-3 orbit due to a saddle-node bifurcation, was attributed to a possible boundary crisis. The transitions to chaotic vibrations in the rotor supported by eccentric squeeze-film dampers with centering springs were via the period-doubling cascade and type 3 intermittency routes. The type 3 intermittency transition to chaos was due to an inverse period-doubling bifurcation of the period-2 (one-half subharmonic) rotor response. The unbalance response of the squeeze-film-damper supported rotor presented in this work leads to unique non-synchronous and chaotic vibration signatures. The latter provide some useful insights into the design and development of fault diagnostic tools for rotating machinery that operate in highly nonlinear regimes.

Inayat-Hussain, Jawaid I.; Mureithi, Njuki W.

2006-09-01

312

The route to chaos for the Kuramoto-Sivashinsky equation

NASA Technical Reports Server (NTRS)

The results of extensive numerical experiments of the spatially periodic initial value problem for the Kuramoto-Sivashinsky equation. This paper is concerned with the asymptotic nonlinear dynamics at the dissipation parameter decreases and spatio-temporal chaos sets in. To this end the initial condition is taken to be the same for all numerical experiments (a single sine wave is used) and the large time evolution of the system is followed numerically. Numerous computations were performed to establish the existence of windows, in parameter space, in which the solution has the following characteristics as the viscosity is decreased: a steady fully modal attractor to a steady bimodal attractor to another steady fully modal attractor to a steady trimodal attractor to a periodic attractor, to another steady fully modal attractor, to another periodic attractor, to a steady tetramodal attractor, to another periodic attractor having a full sequence of period-doublings (in parameter space) to chaos. Numerous solutions are presented which provide conclusive evidence of the period-doubling cascades which precede chaos for this infinite-dimensional dynamical system. These results permit a computation of the length of subwindows which in turn provide an estimate for their successive ratios as the cascade develops. A calculation based on the numerical results is also presented to show that the period doubling sequences found here for the Kuramoto-Sivashinsky equation, are in complete agreement with Feigenbaum's universal constant of 4,669201609 .... Some preliminary work shows several other windows following the first chaotic one including periodic, chaotic, and a steady octamodal window; however, the windows shrink significantly in size to enable concrete quantitative conclusions to be made.

Papageorgiou, Demetrios T.; Smyrlis, Yiorgos S.

1991-01-01

313

Applied chaos theory - A paradigm for complexity

NASA Astrophysics Data System (ADS)

It is still not entirely clear, whether chaos theory will furnish solutions to problems posed by complex systems upon the development of a mathematics that is descriptive of complexity, in the same way that calculus is descriptive of continuously-varying processes. The present survey of the current understanding of chaos discusses the characteristics of complexity, the metaquantification of complexity, the anatomy of open and closed systems and structures, fixed-point and strange attractors, the mathematics of rapid growth, the discrete logistic equation, the role of entropy considerations, and the diagnostics and control of chaos.

Cambel, Ali B.

314

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

315

The Significance of Higher Modes for Evolution of Chaos in Structural Mechanics Systems

NASA Astrophysics Data System (ADS)

Even though chaotic vibrations have been observed in many structural mechanics systems, their analysis has almost always been limited to single-degree-of-freedom (SDOF) approximations. A typical example is the magnetoelastic beam studied by Moon and Holmes [1], which is reported to be the first experimental evidence of chaotic vibrations in structural mechanics. However, the authors have not come across any detailed structural analysis of the system. The present paper reports a structural dynamic analysis of the problem through a finite element formulation and the integration of the resulting equations of motion by a variable time stepping Newmark method (trapezoidal rule). The solution scheme has built-in algorithms for equilibrium interaction of the non-linear forces and check of the temporal solution trajectory. It is shown that the direct integration and mode superposition schemes are equally applicable for problems with chaotic response. The authors have the following conclusions: (1) the SODF approximation with a high accuracy integration scheme may not reveal the regime of chaos even coarsely; (2) the manifestation of chaos is significantly influenced by the higher modes; (3) a spatially discrete model which represents the beam accurately could reveal regimes of chaos reasonably well even with second order schemes such as the trapezoidal rule, but it is essential for the model to be fine enough to represent the motion in higher modes accurately; (4) computationally efficient methods such as the mode superposition method, with an adequate number of modes included, could give accurate solutions to vibration problems involving chaos.

Moorthy, R. I. K.; Kakodkar, A.; Srirangarajan, H. R.

1996-12-01

316

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

317

Adapted polynomial chaos expansion for failure detection

In this paper, we consider two methods of computation of failure probabilities by adapted polynomial chaos expansions. The performance of the two methods is demonstrated by a predator-prey model and a chemical reaction problem.

Paffrath, M. [Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, D81730 Munich (Germany)], E-mail: meinhard.paffrath@siemens.com; Wever, U. [Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, D81730 Munich (Germany)], E-mail: utz.wever@siemens.com

2007-09-10

318

Connectionist Networks Learn to Transmit Chaos.

National Technical Information Service (NTIS)

The activity of some neurons during the generation of coordinated motor patterns may be attributable to chaos. Because even simple biological systems are difficult to control, connectionist networks are used to inquire into the question of whether a chaot...

G. J. Mpitsos R. M. Burton H. C. Creech

1988-01-01

319

Optimized chaos control with simple limiters.

We present an elementary derivation of chaos control with simple limiters using the logistic map and the Henon map as examples. This derivation provides conditions for optimal stabilization of unstable periodic orbits of a chaotic attractor. PMID:11304392

Wagner, C; Stoop, R

2001-01-01

320

NASA Astrophysics Data System (ADS)

Magnetic Flux Ropes Immersed in a uniform magnetoplasma are observed to twist about themselves, writhe about each other and rotate about a central axis. They are kink unstable and smash into one another as they move. Full three dimensional magnetic field and flows are measured at thousands of time steps. Each collision results in magnetic field line generation and the generation of a quasi-seperatrix layer and induced electric fields. Three dimensional magnetic field lines are computed by conditionally averaging the data using correlation techniques. The permutation entropy1 ,which is related to the Lyapunov exponent, can be calculated from the the time series of the magnetic field data (this is also done with flows) and used to calculate the positions of the data on a Jensen Shannon complexity map2. The location of data on this map indicates if the magnetic fields are stochastic, or fall into regions of minimal or maximal complexity. The complexity is a function of space and time. The complexity map, and analysis will be explained in the course of the talk. Other types of chaotic dynamical models such as the Lorentz, Gissinger and Henon process also fall on the map and can give a clue to the nature of the flux rope turbulence. The ropes fall in the region of the C-H plane where chaotic systems lie. The entropy and complexity change in space and time which reflects the change and possibly type of chaos associated with the ropes. The maps give insight as to the type of chaos (deterministic chaos, fractional diffusion , Levi flights..) and underlying dynamical process. The power spectra of much of the magnetic and flow data is exponential and Lorentzian structures in the time domain are embedded in them. Other quantities such as the Hurst exponent are evaluated for both magnetic fields and plasma flow. Work Supported by a UC-LANL Lab fund and the Basic Plasma Science Facility which is funded by DOE and NSF. 1) C. Bandt, B. Pompe, Phys. Rev. Lett., 88,174102 (2007) 2) O. Russo et al., Phys. Rev. Lett., 99, 154102 (2007), J. Maggs, G.Morales, 55, 085015 (2013)

Gekelman, W. N.; DeHaas, T.; Van Compernolle, B.

2013-12-01

321

Weak chaos and quasi-regular structures

NASA Astrophysics Data System (ADS)

The book presents the theory of chaos origin in Hamiltonian systems. In particular, attention is given to the fundamentals of the theory of a stochastic layer and a stochastic web. The discussion is illustrated by numerous examples from various fields of physics. Consideration is also given to applications of the methods of weak chaos theory to the problem of continuum structures and that of particle acceleration by electromagnetic waves.

Zaslavskii, Georgii M.; Sagdeev, Roal'd. Z.; Usikov, Daniel'a.; Chernikov, Aleksandr A.

322

Control of collective network chaos

NASA Astrophysics Data System (ADS)

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

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

2014-06-01

323

Control of collective network chaos.

Under certain conditions, the collective behavior of a large globally-coupled heterogeneous network of coupled oscillators, as quantified by the macroscopic mean field or order parameter, can exhibit low-dimensional chaotic behavior. Recent advances describe how a small set of "reduced" ordinary differential equations can be derived that captures this mean field behavior. Here, we show that chaos control algorithms designed using the reduced equations can be successfully applied to imperfect realizations of the full network. To systematically study the effectiveness of this technique, we measure the quality of control as we relax conditions that are required for the strict accuracy of the reduced equations, and hence, the controller. Although the effects are network-dependent, we show that the method is effective for surprisingly small networks, for modest departures from global coupling, and even with mild inaccuracy in the estimate of network heterogeneity. PMID:24985441

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

2014-06-01

324

Chaos Theory and Protein Dynamics

NASA Astrophysics Data System (ADS)

Chaos theory, commonly known as the butterfly effect, states that a small change in a complex system may cause large changes in the system as time moves forward. This phenomenon was first discovered by Henri Poincare in the 1880's. The computer programs NAMD, VMD (Visual Molecular Dynamics) and Mathematica were used to calculate the movements and graphically analyze the trajectories of the protein ubiquitin. A small change was applied to a single atom's initial position in the x-coordinate to see how it would affect the future dynamics and trajectory of the protein. Our findings indicate an exponential divergence from the controlled trajectory with a Lyapunov exponent = 10.5 [1/ps]. In other words after less than a picosecond (trillionth of a second) the dynamics of a small biophysical system is no longer predictable, even though the underlying Newtonian physical laws are completely deterministic.

Bui, James; Clarage, James

2010-10-01

325

NASA Astrophysics Data System (ADS)

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).

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

2013-04-01

326

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

327

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.

Resnicow, Kenneth; Page, Scott E.

2008-01-01

328

Security of Chaos-Based Communication and Encryption

NASA Astrophysics Data System (ADS)

During the last decade a new approach for secure communication, based on chaotic dynamics attracted the attention of the scientific community. In this chapter we give an overview and describe the research that was done at the Institute for Nonlinear Science (INLS) on this topic. We begin this chapter with a brief introduction to chaos-based encryption schemes. We then describe a new method for public key encryption that we have developed which is based on distributed chaotic dynamics. Next, we lay out a quantitative cryptanalysis approach for symmetric key encryption schemes that are based on active/passive decomposition of chaotic dynamics. We end this chapter with a summary and suggestions for future research.

Tenny, Roy; Tsimring, Lev S.; Abarbanel, Henry D. I.; Larson, Lawrence E.

329

Adaptive chaos control and synchronization in only locally Lipschitz systems

NASA Astrophysics Data System (ADS)

In the existing results on chaos control and synchronization based on the adaptive controlling technique (ACT), a uniform Lipschitz condition on a given dynamical system is always assumed in advance. However, without this uniform Lipschitz condition, the ACT might be failed in both theoretical analysis and in numerical experiment. This Letter shows how to utilize the ACT to get a rigorous control for the system which is not uniformly Lipschitz but only locally Lipschitz, and even for the system which has unbounded trajectories. In fact, the ACT is proved to possess some limitation, which is actually induced by the nonlinear degree of the original system. Consequently, a piecewise ACT is proposed so as to improve the performance of the existing techniques.

Lin, Wei

2008-04-01

330

Implementation of dynamic programming for chaos control in discrete systems

NASA Astrophysics Data System (ADS)

In this paper the control of discrete chaotic systems by designing linear feedback controllers is presented. The linear feedback control problem for nonlinear systems has been formulated under the viewpoint of dynamic programming. For suppressing chaos with minimum control effort, the system is stabilized on its first order unstable fixed point (UFP). The presented method also could be employed to make any desired nth order fixed point of the system, stable. Two different methods for higher order UFPs stabilization are suggested. Afterwards, these methods are applied to two well-known chaotic discrete systems: the Logistic and the Henon Maps. For each of them, the first and second UFPs in their chaotic regions are stabilized and simulation results are provided for the demonstration of performance.

Merat, Kaveh; Salarieh, Hassan; Alasty, Aria

2009-11-01

331

An Anomaly in the Domain Chaos State of Rayleigh-B'enard Convection with Large Aspect Ratio

NASA Astrophysics Data System (ADS)

Rayleigh-B'enard convection-patterns exhibit a type of spatio-temporal chaos known as domain chaos (DC) at the onset of convection when the sample rotates fast enough about the vertical axis. DC is characterized by domains of straight rolls that chaotically change their orientation and size due to the Küppers-Lortz instability.ootnotetextG. Küppers and D. Lortz, J. Fluid Mech. 35, 609 (1969). However, in a large aspect ratio ??r/d=82 cylindrical sample, where r is the radius of the cell and d is the cell thickness, we observed DC in the sample center, surrounded by an annulus of radial rolls populated by occasional defects reminiscent of undulation chaos.ootnotetextK. E. Daniels, B.B. Plapp, and E. Bodenschatz, Phys. Rev. Lett. 84, 5320 (2000). This was unexpected because smaller samples do exhibit domain chaos throughout and the weakly-nonlinear theory that describes the supercritical bifurcation to chaos is expected to be more applicable as ? increases. One possible explanation is that the centrifugal force, which is neglected in the theory, plays an important role.ootnotetextA. Jayaraman and H. Greenside (private communication).

Becker, Nathan

2005-03-01

332

Outer Solar System on the Edge of Chaos

The existence of chaos among the system of Jovian planets (Jupiter, Saturn, Uranus, and Neptune) is not yet firmly established. Although Laskar originally found no chaos in the outer Solar System, his \\

Wayne B. Hayes

2006-01-01

333

Complex Route to Chaos in Velocity Driven Atoms.

National Technical Information Service (NTIS)

The oscillations of linear triatomic molecule with the first atom driven at a constant velocity upsilon are studied numerically. As upsilon increases, we observe a sequence of transitions from quasiperiodicity to chaos, mode locking, chaos, model locking,...

C. T. White D. W. Brenner P. X. Tran

1990-01-01

334

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

335

Chaos, Boltzmann, Shannon and Electroencephalography

NASA Astrophysics Data System (ADS)

Nonlinear dynamics has made possible the development of new tools for the quantitative analysis of electroencephalographic (EEG) signals. Some of the tools used in the initial applications required large quantities of noise-free, stationary data which are usually not available from biological systems. Information theoretic measures calculated using coarsegrained data are more appropriate for the analysis of these data. We review Nonlinear Dynamics and some nonlinear dynamical tools, introduce some Information Theoretic notions and use Mutual Information and Transfer Entropy to probe relationships among data streams in 19-channel scalp EEG recorded during three sleep stages-wakefulness, slow-wave sleep, and REM sleep.

Albano, A. M.; Duckrow, R. B.

2008-06-01

336

Synchronization of chaos in microchip lasers and its communication applications

NASA Astrophysics Data System (ADS)

We overview some experimental and numerical demonstrations on the synchronization of chaos and its communication applications using Nd:YVO 4 microchip solid-state lasers. Synchronization of chaos is achieved with several coupling configurations. Several encoding and decoding schemes for communication applications are also demonstrated by using the synchronization of chaos in microchip lasers. A new approach to secure communications using chaos based on information theoretic security is introduced. To cite this article: A. Uchida, S. Yoshimori, C. R. Physique 5 (2004).

Uchida, Atsushi; Yoshimori, Shigeru

2004-08-01

337

Observation and Control of Hamiltonian Chaos in Wave-particle Interaction

NASA Astrophysics Data System (ADS)

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

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

2010-11-01

338

Chaos in the fractional order Chen system and its control

In this letter, we study the chaotic behaviors in the fractional order Chen system. We found that chaos exists in the fractional order Chen system with order less than 3. The lowest order we found to have chaos in this system is 2.1. Linear feedback control of chaos in this system is also studied.

Chunguang Li; Guanrong Chen

2004-01-01

339

NASA Astrophysics Data System (ADS)

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

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

2012-09-01

340

In this work, we numerically study the dynamics of vertical cavity surface emitting laser (VCSEL) firstly when it is driven by Chua's oscillator, secondly in case where it is driven by a broad frequency spectral bandwidth chaotic oscillator developed by Nana et al. [Commun. Nonlinear Sci. Numer. Simul. 14, 2266 (2009)]. We demonstrated that the VCSEL generated robust chaotic dynamics compared to the ones found in VCSEL subject to a sinusoidally modulated current and therefore it is more suitable for chaos encryption techniques. The synchronization characteristics and the communication performances of unidirectional coupled VCSEL driven by the broad frequency spectral bandwidth chaotic oscillators are investigated numerically. The results show that high-quality synchronization and transmission of messages can be realized for suitable system parameters. Chaos shift keying method is successfully applied to encrypt a message at a high bitrate. PMID:23020447

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

2012-09-01

341

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

NASA Technical Reports Server (NTRS)

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

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

1992-01-01

342

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

343

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

344

Chaos and Related Phenomena in Electrical Circuits.

NASA Astrophysics Data System (ADS)

We will perform demonstrations of chaotic phenomena found in simple electronic circuits. Chaos is produced in a circuit called a diode resonator, which is comprised of a p-n junction diode and an inductor, driven by a sinusoidal source. The circuit follows the period doubling route to chaos and its chaotic attractor will be shown in real time. The control of chaos in this circuit will be demonstrated by using a technique called occasional proportional feedback (OPF). Next we look at the dynamics found of two coupled diode resonators. This circuit shows a Hopf bifurcation followed by the quasiperiodic route to chaos. We will demonstrate OPF control of this circuit to the steady-state, to periodic orbits and to a doubly unstable state. Finally, we hook up a linear array of 32 unidirectionally coupled diode resonators and demonstrate spatiotemporal chaos. We show that stabilizing the first element in particular high- period orbits can stabilize the entire array by creating travelling phase-kink solitons.

Hunt, Earle R.

1996-11-01

345

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?

Abel, David L.

2009-01-01

346

Nonlinear dynamics and chaos in boiling water reactors

There are currently 72 commercial boiling water reactors (BWRs) in operation or under construction in the western world, 37 of them in the United States. Consequently, a great effort has been devoted to the study of BWR systems under a wide range of plant operating conditions. This paper represents a contribution to this ongoing effort; its objective is to study the basic dynamic processes in BWR systems, with special emphasis on the physical interpretation of BWR dynamics. The main thrust in this work is the development of phenomenological BWR models suited for analytical studies performed in conjunction with numerical calculations. This approach leads to a deeper understanding of BWR dynamics and facilitates the interpretation of numerical results given by currently available sophisticated BWR codes. 6 refs., 14 figs., 2 tabs.

March-Leuba, J.

1988-01-01

347

Chaos suppression in NEMs resonators by using nonlinear control design

NASA Astrophysics Data System (ADS)

In this work the chaotic behavior of a micro-mechanical resonator with electrostatic forces on both sides is suppressed. The aim is to control the system in an orbit of the analytical solution obtained by the Method of Multiple Scales. Two control strategies are used for controlling the trajectory of the system, namely: State Dependent Riccati Equation (SDRE) Control and Optimal Linear Feedback Control (OLFC). The controls proved effectiveness in controlling the trajectory of the system. Additionally, the robustness of each strategy is tested considering the presence of parametric errors and measurement noise in control.

Tusset, Angelo Marcelo; Bueno, Atila Madureira; Nascimento, Claudinor Bitencourt; Kaster, Mauricio Dos Santos; Balthazar, José Manoel

2012-11-01

348

NASA Astrophysics Data System (ADS)

The peculiarities of nonlinear dynamics of solid-state bidirectional ring Nd:YAG chip lasers are studied theoretically and experimentally during periodic modulation of mechanical stresses in the active element. It is shown that modulation of mechanical stresses is an effective method for exciting dynamic chaos in a monolithic chip laser.

Kravtsov, Nikolai V.; Sidorov, S. S.; Pashinin, Pavel P.; Firsov, V. V.; Chekina, S. N.

2004-04-01

349

Chaos in orbits due to disk crossings.

We study orbits of halo stars in simple models of galaxies with disks and halos to see if the cumulative effects of the sudden changes in acceleration that occur at disk crossings can induce chaos. We find that they can, although not in all orbits and not in all potentials. Most of the orbits that become chaotic stay relatively close to the disk and range widely in the radial direction. Heavier disks and increased halo flattening both enhance the extent of the chaos. A limited range of experiments with a three-component model of the Milky Way with an added central bulge finds that many chaotic disk-crossing orbits can be expected in the central regions, and that prolateness of the halo is much more effective than oblateness in generating chaos. PMID:15980309

Hunter, C

2005-06-01

350

A novel chaos danger model immune algorithm

NASA Astrophysics Data System (ADS)

Making use of ergodicity and randomness of chaos, a novel chaos danger model immune algorithm (CDMIA) is presented by combining the benefits of chaos and danger model immune algorithm (DMIA). To maintain the diversity of antibodies and ensure the performances of the algorithm, two chaotic operators are proposed. Chaotic disturbance is used for updating the danger antibody to exploit local solution space, and the chaotic regeneration is referred to the safe antibody for exploring the entire solution space. In addition, the performances of the algorithm are examined based upon several benchmark problems. The experimental results indicate that the diversity of the population is improved noticeably, and the CDMIA exhibits a higher efficiency than the danger model immune algorithm and other optimization algorithms.

Xu, Qingyang; Wang, Song; Zhang, Li; Liang, Ying

2013-11-01

351

Chaos, dynamical structure, and climate variability

Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. Techniques for identifying deterministic chaos from observed data, without recourse to mathematical models, are being developed. Powerful methods exist for reconstructing multidimensional phase space from an observed time series of a single scalar variable; these methods are invaluable when only a single scalar record of the dynamics is available. However in some applications multiple concurrent time series may be available for consideration as phase space coordinates. Here we propose some basic analytical tools for such multichannel time series data, and illustrate them by applications to a simple synthetic model of chaos, to a low-order model of atmospheric circulation, and to two high-resolution paleoclimate proxy data series. {copyright} {ital 1996 American Institute of Physics.}

Stewart, H.B. [Department of Applied Science, Brookhaven National Laboratory, Upton, New York 11973 (United States)

1996-06-01

352

Towards CHAOS-5 - How can Swarm contribute?

NASA Astrophysics Data System (ADS)

The launch of ESA's satellite trio Swarm in November 2013 opens an exciting new chapter in the observation and monitoring of Earth's magnetic field from space. We report preliminary results from an extension of the CHAOS series of geomagnetic field models to include both scalar and vector field observations from the three Swarm satellites, along with the most recent quasi-definitive ground observatory data. The fit of this new update CHAOS field model to the Swarm observations will be presented in detail providing useful insight the initial Swarm data. Enhancements of the CHAOS modelling scheme include a 1 minute time resolution for the RC index and anisotropic weighting of vector field data depending on quasi-dipole latitude. We shall also report on the perspective given by the initial Swarm data on rapid field changes currently taking place in the Atlantic sector.

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

2014-05-01

353

Experimental realization of chaos control by thresholding.

We report the experimental verification of thresholding as a versatile tool for efficient and flexible chaos control. The strategy here simply involves monitoring a single state variable and resetting it when it exceeds a threshold. We demonstrate the success of the technique in rapidly controlling different chaotic electrical circuits, including a hyperchaotic circuit, onto stable fixed points and limit cycles of different periods, by thresholding just one variable. The simplicity of this controller entailing no run-time computation, and the ease and rapidity of switching between different targets it offers, suggests a potent tool for chaos based applications. PMID:12935228

Murali, K; Sinha, Sudeshna

2003-07-01

354

Chaos für die Schule!: Nichtlinearität und Strukturbildung

NASA Astrophysics Data System (ADS)

Modellsysteme können Schülern die Grundlagen der nichtlinearen Physik anschaulich vermitteln. Sie schlagen so einen Bogen von der Schulphysik zur aktuellen Forschung. Ein solches Modellsystem ist das chaotische Wasserrad, das Lehrer auf einfache Weise für den Schulunterricht nachbauen können. Im Wesentlichen steuert der Zufluss des Wassers das Verhalten des Wasserrads. Wächst er, so durchläuft das Rad von der geordneten, gleichförmigen Drehung bis zum Chaos verschiedene Phasen von Bewegungsfiguren. Das Experiment kann grundlegende Modelle und Begriffe der Chaostheorie demonstrieren: lokale und globale Bifurkationen und verschiedene Übergänge ins Chaos.

Nordmeier, Volkhard; Schlichting, Hans Joachim

2003-01-01

355

On chaos synchronization and secure communication.

Chaos synchronization, in particular isochronal synchronization of two chaotic trajectories to each other, may be used to build a means of secure communication over a public channel. In this paper, we give an overview of coupling schemes of Bernoulli units deduced from chaotic laser systems, different ways to transmit information by chaos synchronization and the advantage of bidirectional over unidirectional coupling with respect to secure communication. We present the protocol for using dynamical private commutative filters for tap-proof transmission of information that maps the task of a passive attacker to the class of non-deterministic polynomial time-complete problems. PMID:20008407

Kinzel, W; Englert, A; Kanter, I

2010-01-28

356

Parametrization of nonlinear and chaotic oscillations in driven beam-plasma diodes

NASA Astrophysics Data System (ADS)

Nonlinear phenomena in a driven plasma diode are studied using a fluid code and the particle-in-cell simulation code xpdp1. When a uniform electron beam is injected to a bounded diode filled with uniform ion background, the beam is destabilized by the Pierce instability and a perturbation grows to exhibit nonlinear oscillations including chaos. Two standard routes to chaos, period doubling and quasiperiodicity, are observed. Mode lockings of various winding numbers are observed in an ac driven system. A new diagnostic quantity is used to parametrize various nonlinear oscillations.

Hur, Min Sup; Lee, Hae June; Lee, Jae Koo

1998-07-01

357

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

358

A Teaching and Learning Sequence about the Interplay of Chance and Determinism in Nonlinear Systems

ERIC Educational Resources Information Center

A teaching and learning sequence aimed at introducing upper secondary school students to the interplay between chance and determinism in nonlinear systems is presented. Three experiments concerning nonlinear systems (deterministic chaos, self-organization and fractals) and one experiment concerning linear systems are introduced. Thirty upper…

Stavrou, D.; Duit, R.; Komorek, M.

2008-01-01

359

Universal learning network and its application to chaos control.

Universal Learning Networks (ULNs) are proposed and their application to chaos control is discussed. ULNs provide a generalized framework to model and control complex systems. They consist of a number of inter-connected nodes where the nodes may have any continuously differentiable nonlinear functions in them and each pair of nodes can be connected by multiple branches with arbitrary time delays. Therefore, physical systems, which can be described by differential or difference equations and also their controllers, can be modeled in a unified way, and so ULNs may form a super set of neural networks and fuzzy neural networks. In order to optimize the ULNs, a generalized learning algorithm is derived, in which both the first order derivatives (gradients) and the higher order derivatives are incorporated. The derivatives are calculated by using forward or backward propagation schemes. These algorithms for calculating the derivatives are extended versions of Back Propagation Through Time (BPTT) and Real Time Recurrent Learning (RTRL) of Williams in the sense that generalized node functions, generalized network connections with multi-branch of arbitrary time delays, generalized criterion functions and higher order derivatives can be deal with. As an application of ULNs, a chaos control method using maximum Lyapunov exponent of ULNs is proposed. Maximum Lyapunov exponent of ULNs can be formulated by using higher order derivatives of ULNs, and the parameters of ULNs can be adjusted so that the maximum Lyapunov exponent approaches the target value. From the simulation results, it has been shown that a fully connected ULN with three nodes is able to display chaotic behaviors. PMID:10935763

Hirasawa, K; Wang, X; Murata, J; Hu, J; Jin, C

2000-03-01

360

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.

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

2011-01-01

361

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. PMID:21915254

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

2011-01-01

362

Prospects for chaos control of machine tool chatter

The authors analyze the nonlinear tool-part dynamics during turning of stainless steel in the nonchatter and chatter regimes, toward the ultimate objective of chatter control. Their previous work analyzed tool acceleration in three dimensions at four spindle speeds. In the present work, the authors analyze the machining power and obtain nonlinear measures of this power. They also calculate the cycle-to-cycle energy for the turning process. Return maps for power cycle times do not reveal fixed points or (un)stable manifolds. Energy return maps do display stable and unstable directions (manifolds) to and from an unstable period-1 orbit, which is the dominant periodicity. Both nonchatter and chatter dynamics have the unusual feature of arriving at the unstable period-1 fixed point and departing from that fixed point of the energy return map in a single step. This unusual feature makes chaos maintenance, based on the well-known Ott-Grebogi-Yorke scheme, a very difficult option for chatter suppression. Alternative control schemes, such as synchronization of the tool-part motion to prerecorded nonchatter dynamics or dynamically damping the period-1 motion, are briefly discussed.

Hively, L.M.; Protopopescu, V.A.; Clapp, N.E.; Daw, C.S.

1998-06-01

363

Reexamination of measurement-induced chaos in entanglement-purification protocols

NASA Astrophysics Data System (ADS)

Entanglement-purification protocols, developed for the sake of high-fidelity communication through noisy quantum channels, are highly nonlinear quantum operations and can offer a very useful context to studies of nonlinear complex maps. Recently it was demonstrated that the feedback mechanism used in a typical purification protocol can cause the evolution dynamics of qubits to exhibit chaos [Kiss , Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.107.100501 107, 100501 (2011)]. In this work we extend the investigation by considering the natural time evolution of qubits during a purification process, leading to a number of interesting findings that reflect the competition between the natural unitary evolution of qubits and nonlinear purification operations. As a result, the overall evolution dynamics of entanglement can be much richer. Possible applications are also proposed.

Guan, Yilun; Nguyen, Duy Quang; Xu, Jingwei; Gong, Jiangbin

2013-05-01

364

Control mechanisms for a nonlinear model of international relations

Some issues of control in complex dynamical systems are considered. The authors discuss two control mechanisms, namely: a short range, reactive control based on the chaos control idea and a long-term strategic control based on an optimal control algorithm. They apply these control ideas to simple examples in a discrete nonlinear model of a multi-nation arms race.

Pentek, A.; Kadtke, J. [Univ. of California, San Diego, La Jolla, CA (United States). Inst. for Pure and Applied Physical Sciences; Lenhart, S. [Univ. of Tennessee, Knoxville, TN (United States). Mathematics Dept.; Protopopescu, V. [Oak Ridge National Lab., TN (United States). Computer Science and Mathematics Div.

1997-07-15

365

Nonlinear adaptive synchronization of a class of chaotic systems

In this Letter, a new control approach to synchronize a class of chaotic systems using the drive-response concept is presented. The proposed technique exploits adaptive observer design and Lyapunov stability theory. A remarkable feature of this approach is that, nonlinear terms are required to achieve chaos synchronization. An application to secure chaotic communication is also proposed. Computer simulation on the

F. M. Moukam Kakmeni; Samuel Bowong; Clement Tchawoua

2006-01-01

366

Creativity on the edge of chaos.

The health care environment is chaotic, with many threats and problems. Despite nursing's resulting discomfort, being able to see the opportunities and the potential within such complexity is freeing. The author illustrates the use of creative thinking in formulating deliberate responses to the unpredictability of chaos. With such innovative actions, the essential nature of professional nursing can be reaffirmed. PMID:10788957

Forrest, S

1999-09-01

367

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

368

Controlling Chaos Using Modified Lyapunov Exponents

NASA Astrophysics Data System (ADS)

We suggested a method using a small perturbation to modify Lyapunov exponents of the unstable periodic orbit for controlling chaos. The benefit of this control scheme is studied and the effect of noise is discussed. Based on these studies, a more practical control method is recommended, and some experiments can be better understanded.

Tan, Yi; He, Xiantu; X. T., He; Chen, Shigang; S. G., Chen

1993-06-01

369

Chaos in a computer-animated pendulum

A classroom demonstration based on computer animation illustrates chaotic motion in a driven pendulum. Generated by a 76 line BASIC program that runs on PC-compatible computers, the animation shows four simultaneous displays, including the pendulum and its trajectory in state space. The program can be used to illustrate periodic attractors, symmetry breaking, period doubling, and chaos.

R. L. Kautz

1993-01-01

370

Chaos-based cryptography: a brief overview

Over the past decade, there has been tremendous interest in studying the behavior of chaotic systems. They are characterized by sensitive dependence on initial conditions, similarity to random behavior, and continuous broad-band power spectrum. Chaos has potential applications in several functional blocks of a digital communication system: compression, encryption and modulation. The possibility for self-synchronization of chaotic oscillations has sparked

Ljupco Kocarev

2001-01-01

371

Still Another Approach to Administration: Chaos Theory.

ERIC Educational Resources Information Center

Uses chaos systems concepts to analyze a case study of rapid growth and conflict in a southwestern school district. Difficulties arising from the need for very precise initial measurements, data forms adaptable to pattern modeling, and precise meanings for chaotic systems concepts limit chaotic theory's application to educational administration…

Griffiths, Daniel E.; And Others

1991-01-01

372

Waveguide experiment related to field chaos

An experiment is described in which a waveguide configuration is employed to test for field chaos. The analysis is based on the identical structures of the equation for the component of electric field of TM modes parallel to the guide axis in a metal waveguide and the Schrödinger equation for a particle confined to an equivalent 2-d quantum billiard. It

Gregory E Dionne; Richard L Liboff

1995-01-01

373

ADDENDUM: Chaos in Bohmian quantum mechanics

In our recently published paper 'Chaos in Bohmian quantum mechanics' we criticized a paper by Parmenter and Valentine (1995 Phys. Lett. A 201 1), because the authors made an incorrect calculation of the Lyapunov exponent in the case of Bohmian orbits in a quantum system of two uncoupled harmonic oscillators. After our paper was published, we became aware of an

C. Efthymiopoulos; G. Contopoulos

2006-01-01

374

Neural control: Chaos control sets the pace

NASA Astrophysics Data System (ADS)

Even simple creatures, such as cockroaches, are capable of complex responses to changes in their environment. But robots usually require complicated dedicated control circuits to perform just a single action. Chaos control theory could allow simpler control strategies to realize more complex behaviour.

Schöll, Eckehard

2010-03-01

375

Global sensitivity analysis using polynomial chaos expansions

Global sensitivity analysis (SA) aims at quantifying the respective effects of input random variables (or combinations thereof) onto the variance of the response of a physical or mathematical model. Among the abundant literature on sensitivity measures, the Sobol’ indices have received much attention since they provide accurate information for most models. The paper introduces generalized polynomial chaos expansions (PCE) to

Bruno Sudret

2008-01-01

376

Chaos Theory in the Arts and Design.

ERIC Educational Resources Information Center

This paper explores questions associated with chaos theory as it relates to problems in the arts. It reviews the work of several scholars including Minai, Eckersley, Pickover, the Kirsches, and the Molnars. The document directs special attention toward three basic areas in art and design education, which are: (1) the integration of the computer…

McWhinnie, Harold J.

377

Topological chaos in spatially periodic mixers

Topologically chaotic fluid advection is examined in two-dimensional flows with either or both directions spatially periodic. Topological chaos is created by driving flow with moving stirrers whose trajectories are chosen to form various braids. For spatially periodic flows, in addition to the usual stirrer-exchange braiding motions, there are additional topologically nontrivial motions corresponding to stirrers traversing the periodic directions. This

Matthew D. Finn; Jean-Luc Thiffeault; Emmanuelle Gouillart

2006-01-01

378

Topological chaos in spatially periodic mixers

In many industrial fluid stirring processes it is desirable to produce a high stretching rate of material lines. In two-dimensional flows this stretching rate is given by the topological entropy of the flow. Topological Chaos offers a way of constructing flows that have a rigorous topological entropy lower bound that is robust against changes in fluid properties and the exact

Matthew D. Finn; Emmanuelle Gouillart

2005-01-01

379

Improved particle swarm optimization combined with chaos

As a novel optimization technique, chaos has gained much attention and some applications during the past decade. For a given energy or cost function, by following chaotic ergodic orbits, a chaotic dynamic system may eventually reach the global optimum or its good approximation with high probability. To enhance the performance of particle swarm optimization (PSO), which is an evolutionary computation

Bo Liu; Ling Wang; Yi-Hui Jin; Fang Tang; De-Xian Huang

2005-01-01

380

How to Generate Chaos at Home.

ERIC Educational Resources Information Center

Describes an electronic circuit that can function as a prototype for chaotic systems. Specific applied voltages produce chaotic signals that can be viewed with an oscilloscope or be made audible with a home stereo system. Provides directions for assembly with typical costs, mathematical basis of chaos theory, and experimental extensions. (JJK)

Smith, Douglas

1992-01-01

381

AnRCop amp chaos generator is presented with experimental results showing the practicality and convenience of the system. The circuit is achieved by inserting dynamics on a nondynamic semistate variable of a second-order bent hysteresis Lienard system, the idea stemming from observations of Shinriki et al.

R. Newcomb; S. Sathyan

1983-01-01

382

We consider a simple nonautonomous dissipative nonlinear electronic circuit consisting of Chua's diode as the only nonlinear element, which exhibit a typical period doubling bifurcation route to chaotic oscillations. In this paper, we show that the effect of additional periodic pulses in this Murali-Lakshmanan-Chua (MLC) circuit results in novel multiple-period-doubling bifurcation behavior, prior to the onset of chaos, by using both numerical and some experimental simulations. In the chaotic regime, this circuit exhibits a rich variety of dynamical behavior including enlarged periodic windows, attractor crises, distinctly modified bifurcation structures, and so on. For certain types of periodic pulses, this circuit also admits transcritical bifurcations preceding the onset of multiple-period-doubling bifurcations. We have characterized our numerical simulation results by using Lyapunov exponents, correlation dimension, and power spectrum, which are found to be in good agreement with the experimental observations. Further controlling and synchronization of chaos in this periodically pulsed MLC circuit have been achieved by using suitable methods. We have also shown that the chaotic attractor becomes more complicated and their corresponding return maps are no longer simple for large n-periodic pulses. The above study also indicates that one can generate any desired n-period-doubling bifurcation behavior by applying n-periodic pulses to a chaotic system. PMID:18163784

Parthasarathy, S; Manikandakumar, K

2007-12-01

383

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

384

Nonlinear Dynamics of Forced Catalytic Systems

Period-doubling oscillations and chaos in the course of CO oxidation on Pt crystallites under UHV conditions and on Pt\\/?-Al2O3 catalyst under atmosferic pressure were observed experimentally many years ago (1,2). Interpretation of observed nonlinear dynamics was not possible at that time as proper non-stationary kinetic relations were not available. The most common reactor, where the oxidation of CO and hydrocarbons

M. Marek; P. Ko?ía; I. Schreiber; M. Schejbal; M. Kubí?ek

385

On the evidence of deterministic chaos in ECG: Surrogate and predictability analysis

NASA Astrophysics Data System (ADS)

The question whether the human cardiac system is chaotic or not has been an open one. Recent results in chaos theory have shown that the usual methods, such as saturation of correlation dimension D2 or the existence of positive Lyapunov exponent, alone do not provide sufficient evidence to confirm the presence of deterministic chaos in an experimental system. The results of surrogate data analysis together with the short-term prediction analysis can be used to check whether a given time series is consistent with the hypothesis of deterministic chaos. In this work nonlinear dynamical tools such as surrogate data analysis, short-term prediction, saturation of D2 and positive Lyapunov exponent have been applied to measured ECG data for several normal and pathological cases. The pathology presently studied are PVC (Premature Ventricular Contraction), VTA (Ventricular Tachy Arrhythmia), AV (Atrio-Ventricular) block and VF (Ventricular Fibrillation). While these results do not prove that ECG time series is definitely chaotic, they are found to be consistent with the hypothesis of chaotic dynamics.

Govindan, R. B.; Narayanan, K.; Gopinathan, M. S.

1998-06-01

386

Simulation of stochastic systems via polynomial chaos expansions and convex optimization

NASA Astrophysics Data System (ADS)

Polynomial chaos expansions represent a powerful tool to simulate stochastic models of dynamical systems. Yet, deriving the expansion's coefficients for complex systems might require a significant and nontrivial manipulation of the model, or the computation of large numbers of simulation runs, rendering the approach too time consuming and impracticable for applications with more than a handful of random variables. We introduce a computationally tractable technique for computing the coefficients of polynomial chaos expansions. The approach exploits a regularization technique with a particular choice of weighting matrices, which allows to take into account the specific features of polynomial chaos expansions. The method, completely based on convex optimization, can be applied to problems with a large number of random variables and uses a modest number of Monte Carlo simulations, while avoiding model manipulations. Additional information on the stochastic process, when available, can be also incorporated in the approach by means of convex constraints. We show the effectiveness of the proposed technique in three applications in diverse fields, including the analysis of a nonlinear electric circuit, a chaotic model of organizational behavior, and finally a chemical oscillator.

Fagiano, Lorenzo; Khammash, Mustafa

2012-09-01

387

Chaos Threshold and Failure of Chirikov's Criteria in Mean Field Bose-Hubbard Model

NASA Astrophysics Data System (ADS)

We calculate the threshold for chaos in the one-dimensional mean-field Bose-Hubbard model. The threshold is found to depend on two parameters, the nonlinear coupling strength and total energy per particle, both of which survive in the thermodynamic limit [A.C. Cassidy, D. Mason, V. Dunjko, M. Olshanii, Phys. Rev. Lett. 102, 025302 (2009)]. The dependence on these parameters contradicts the predictions obtained by Chirkov's criterion of overlapping resonances. We study the influence of the conserved quantities of the nearby, fully integrable model of Ablowitz and Ladik.

Cassidy, Amy; Dunjko, Vanja; Olshanii, Maxim

2009-05-01

388

Chaos control and synchronization, with input saturation, via recurrent neural networks.

This paper deals with the adaptive tracking problem of non-linear systems in presence of unknown parameters, unmodelled dynamics and input saturation. A high order recurrent neural network is used in order to identify the unknown system and a learning law is obtained using the Lyapunov methodology. Then a stabilizing control law for the reference tracking error dynamics is developed using the Lyapunov methodology and the Sontag control law. Tracking error boundedness is established as a function of a design parameter. The new approach is illustrated by examples of complex dynamical systems: chaos control and synchronization. PMID:12850026

Sanchez, Edgar N; Ricalde, Luis J

2003-01-01

389

Dynamical behavior, chaos control and synchronization of a memristor-based ADVP circuit

NASA Astrophysics Data System (ADS)

This paper is devoted to study the dynamical behavior of a modified Autonomous Van der Pol-Duffing (ADVP) circuit when its nonlinear element is replaced by a flux controlled memristor. The bifurcation diagrams, Lyapunov exponents, and phase portraits of the state variables are presented. Then, the chaos which appears at certain values of the system's parameters is controlled using linear feedback control. Finally, the synchronization between two chaotic modified ADVP circuits is achieved in the case of fully unknown parameters of the system using adaptive synchronization.

El-Sayed, A. M. A.; Elsaid, A.; Nour, H. M.; Elsonbaty, A.

2013-01-01

390

NASA Astrophysics Data System (ADS)

Weak chaos in high-dimensional conservative systems can be characterized through sticky effect induced by invariant structures on chaotic trajectories. Suitable quantities for this characterization are the higher cummulants of the finite time Lyapunov exponents (FTLEs) distribution. They gather the whole phase space relevant dynamics in one quantity and give information about ordered and random states. This is analyzed here for discrete Hamiltonian systems with local and global couplings. It is also shown that FTLEs plotted versus initial condition (IC) and the nonlinear parameter are essential to understand the fundamental role of ICs in the dynamics of weakly chaotic Hamiltonian systems.

Manchein, C.; Beims, M. W.; Rost, J. M.

2014-04-01

391

Novel photonic applications of nonlinear semiconductor laser dynamics

With a proper perturbation, even a single-mode semiconductor laser can exhibit highly complex dynamical characteristics ranging\\u000a from stable, narrow-linewidth oscillation to broadband chaos. In recent years, three approaches to invoke complex nonlinear\\u000a dynamical states in a single-mode semiconductor laser have been thoroughly studied: optical injection, optical feedback, and\\u000a optoelectronic feedback. In each case, the nonlinear dynamics of the semiconductor laser

Sze-Chun Chan; Rosemary Diaz; Jia-Ming Liu

2008-01-01

392

Scenarios Leading to Chaos in a Forced Lotka-Volterra Model

A predator-prey ecosystem is proposed to investigate roads to chaos in a differential system. In this model, Malthusian rate of prey is driven by a periodic external force. Feigenbaum scenarios and a torus to chaos with frequency locking as 1->torus->5->chaos->4->chaos->3->chaos->5- >chaos->4->2 are observed numerically and their scaling properties and multi-basins are investigated.

Masayoshi Inoue; Hiroshi Kamifukumoto

1984-01-01

393

NASA Astrophysics Data System (ADS)

In this thesis, we present a comprehensive study of chaos and thermalization of the one-dimensional Bose-Hubbard Model (BHM) within the classical field approximation. Two quantitative measures are compared: the ensemble-averaged Finite-time Maximal Lyapunov exponent, a measures of chaos and the normalized spectral entropy, a measure of the distance between the numerical time-averaged momentum distribution and the one predicted by thermodynamics. A threshold for chaos is found, which depends on two parameters, the nonlinearity and the total energy-per-particle. Below the threshold, the dynamics are regular, while far above the threshold, complete thermalization is observed, as measured by the normalized spectral entropy. We study individual resonances in the Bose-Hubbard model to determine the criterion for chaos. The criterion based on Chirikov's method of overlapping resonances diverges in the thermodynamic limit, in contrast to the criterion parameters inferred from numerical calculations, signifying the failure of the standard Chirikov's approach. The Ablowitz-Ladik lattice is one of several integrable models that are close to the BHM. We outline the method of Inverse Scattering Transform and generate the integrals of motion of the Ablowitz-Ladik lattice. Furthermore, we discuss the possible role of these quantities in the relaxation dynamics of the BHM.

Cassidy, Amy C.

2010-03-01

394

Chaos theory: a new paradigm for psychotherapy?

Thomas Kuhn's concept of paradigm as central to the functioning of a mature science is linked with Johnson-Abercrombie's recognition that perception itself is shaped by the schemata available to the subject. The rapidly advancing field of non-linear mathematics, in offering conceptual forms to represent complex events, may provide a useful framework in which to place various psychodynamic formulations about the development of the personality, and suggests the possibility of a new approach to research concerning the efficacy of psychotherapy. Dan Stern's latest concept of "moments" as the basic unit in structuring the personality, leading to the complex representational patterns and feed-back loops he terms "RIGS" may be viewed in this context. The paradigm may be extended to include such concepts as Peterfreund's linkage of psychodynamic theorising with aspects of information theory generated by the study of computers, and with Sullivan's concepts of repetitive patterns of behaviour recognisable, and changing, throughout the course of a therapy. PMID:1793425

Lonie, I

1991-12-01

395

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

Elmar Bittner; Harald Markum; Rainer Pullirsch

2001-01-01

396

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, Eckenrode, & Marcynyszyn, 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 cross-lagged 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

Kamp Dush, Claire M; Schmeer, Kammi K; Taylor, Miles

2013-10-01

397

Photo-induced chaos in the Briggs-Rauscher reaction

NASA Astrophysics Data System (ADS)

Discovery of the photo-induced chaos in the Briggs-Rauscher system is reported. The chaotic oscillations were observed between the large- and the small-amplitude simple oscillatory states existent in low and high light intensity regions, respectively. Period-doubling sequence from the large-amplitude oscillations to the chaos was observed. Deterministic nature of the chaos was confirmed by the next-amplitude return map. The stretching and folding mechanism of the trajectories was revealed through the three-dimensional attractor reconstructed via the singular value decomposition method. The chemical origin of the photoinduced chaos is discussed based on the photoautocatalysis of HIO2.

Okazaki, Noriaki; Hanazaki, Ichiro

1998-07-01

398

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

399

Chaos synchronization using a continuous chaos control method was studied in two identical chaotic laser systems consisting of semiconductor lasers and optical feedback from an external mirror. Numerical calculations for rate equations indicate that the stability of chaos synchronization depends significantly on the external mirror position. We performed a linear stability analysis for the rate equations. Our results show that the stability of the synchronization is much influenced by the mode interaction between the relaxation oscillation frequency of the semiconductor laser and the external cavity frequency. Due to this interaction, an intensive mode competition between the two frequencies destroys the synchronization, but stable synchronization can be achieved when the mode competition is very weak. PMID:11415202

Murakami, A; Ohtsubo, J

2001-06-01

400

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

401

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

402

Guiding an adaptive system through chaos

We study the parametric controls of self-adjusting systems with numerical models. We investigate the situation where the target dynamics changes slowly and passes through a chaotic region. We find that feedback destabilizes controls if the target is chaotic. If the control is unstable the system migrates to the closest non-chaotic target, i.e. it adapts to the edge of chaos. For

Alfred W. Hübler; Kirstin C. Phelps

403

Optimal chaos control through reinforcement learning.

A general purpose chaos control algorithm based on reinforcement learning is introduced and applied to the stabilization of unstable periodic orbits in various chaotic systems and to the targeting problem. The algorithm does not require any information about the dynamical system nor about the location of periodic orbits. Numerical tests demonstrate good and fast performance under noisy and nonstationary conditions. (c) 1999 American Institute of Physics. PMID:12779873

Gadaleta, Sabino; Dangelmayr, Gerhard

1999-09-01

404

The CHAOS-4 geomagnetic field model

NASA Astrophysics Data System (ADS)

We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly determined. More than 14 yr of data from the satellites Ørsted, CHAMP and SAC-C, augmented with magnetic observatory monthly mean values have been used for this model. Maximum spherical harmonic degree of the static (lithospheric) field is n = 100. The core field is expressed by spherical harmonic expansion coefficients up to n = 20; its time-evolution is described by order six splines, with 6-month knot spacing, spanning the time interval 1997.0-2013.5. The third time derivative of the squared radial magnetic field component is regularized at the core-mantle boundary. No spatial regularization is applied to the core field, but the high-degree lithospheric field is regularized for n > 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its high-degree lithospheric field part is solely determined from low-altitude CHAMP satellite observations taken during the last 2 yr (2008 September-2010 September) of the mission. We obtain a good agreement with other recent lithospheric field models like MF7 for degrees up to n = 85, confirming that lithospheric field structures down to a horizontal wavelength of 500 km are currently robustly determined.

Olsen, Nils; Lühr, Hermann; Finlay, Christopher C.; Sabaka, Terence J.; Michaelis, Ingo; Rauberg, Jan; Tøffner-Clausen, Lars

2014-05-01

405

Nonadiabatic quantum chaos in atom optics

NASA Astrophysics Data System (ADS)

Coherent dynamics of atomic matter waves in a standing-wave laser field is studied. In the dressed-state picture, wave packets of ballistic two-level atoms propagate simultaneously in two optical potentials. The probability to make a transition from one potential to another one is maximal when centroids of wave packets cross the field nodes and is given by a simple formula with the single exponent, the Landau-Zener parameter ?. If ? ? 1, the motion is essentially adiabatic. If ? ? 1, it is (almost) resonant and periodic. If ? ? 1, atom makes nonadiabatic transitions with a splitting of its wave packet at each node and strong complexification of the wave function as compared to the two other cases. This effect is referred as nonadiabatic quantum chaos. Proliferation of wave packets at ? ? 1 is shown to be connected closely with chaotic center-of-mass motion in the semiclassical theory of point-like atoms with positive values of the maximal Lyapunov exponent. The quantum-classical correspondence established is justified by the fact that the Landau-Zener parameter ? specifies the regime of the semiclassical dynamical chaos in the map simulating chaotic center-of-mass motion. Manifestations of nonadiabatic quantum chaos are found in the behavior of the momentum and position probabilities.

Prants, S. V.

2012-07-01

406

Detecting chaos in irregularly sampled time series.

Recently, Wiebe and Virgin [Chaos 22, 013136 (2012)] developed an algorithm which detects chaos by analyzing a time series' power spectrum which is computed using the Discrete Fourier Transform (DFT). Their algorithm, like other time series characterization algorithms, requires that the time series be regularly sampled. Real-world data, however, are often irregularly sampled, thus, making the detection of chaotic behavior difficult or impossible with those methods. In this paper, a characterization algorithm is presented, which effectively detects chaos in irregularly sampled time series. The work presented here is a modification of Wiebe and Virgin's algorithm and uses the Lomb-Scargle Periodogram (LSP) to compute a series' power spectrum instead of the DFT. The DFT is not appropriate for irregularly sampled time series. However, the LSP is capable of computing the frequency content of irregularly sampled data. Furthermore, a new method of analyzing the power spectrum is developed, which can be useful for differentiating between chaotic and non-chaotic behavior. The new characterization algorithm is successfully applied to irregularly sampled data generated by a model as well as data consisting of observations of variable stars. PMID:24089946

Kulp, C W

2013-09-01

407

Diffusion and relaxation in Hamiltonian chaos

NASA Astrophysics Data System (ADS)

Chaos in Hamiltonian systems have great importance in fundamental physics as a basis of classical statistical mechanics, as well as in application to plasma physics and solid state physics. Some results are introduced on the properties of global diffusion for Hamiltonian systems with many degrees of freedom, through numerical studies on coupled map lattices. Many important facts were revealed for the chaos in area preserving mappings. The phase space of area preserved mapping is filled with self-similar structure of islands and cantori, which are related to dynamical properties such as anomalous diffusion and flicker noise. Such delicate structures are expected to smear out when the number of degrees of freedom increases. The main topic is whether making the system size large enhances the chaos and diffusion. The models are (1) standard map and (2) symplectic version of the coupled map lattices. The anomalous diffusion is observed both for area preserving mappings and for systems with many degrees of freedom, reflecting the self similar structures of phase spaces. In both cases, however, they are transients appearing only for a finite time. Crossover from anomalous to normal diffusion has its origin in array-like arrangement of equivalent hierarchies of island chains in phase space, and are common to low dimensional and high dimensional systems.

Konishi, Tetsuro

1991-04-01

408

Stabilization of stochastic cycles and control of noise-induced chaos

NASA Astrophysics Data System (ADS)

We consider a nonlinear control system forced by stochastic disturbances. The problem addressed is a design of the feedback regulator which stabilizes a limit cycle of the closed-loop deterministic system and synthesizes a required dispersion of random states of the forced cycle for the corresponding stochastic system. To solve this problem, we develop a method based on the stochastic sensitivity function technique. The problem of a synthesis of the required stochastic sensitivity for cycles by feedback regulators is reduced to the solution of the linear algebraic equation for the gain matrix of the regulator. For this matrix, in the general n-dimensional case, a full parametric representation is found. An attractive case of nonlinear 3D systems which exhibit both regular and chaotic regimes is studied in detail. To construct a regulator, we use a new technique based on a singular decomposition of the assigned stochastic sensitivity matrix. Explicit formulas for parameters of this regulator synthesizing the required stochastic sensitivity for 3D-cycle are obtained. The constructiveness of the developed theory is shown on the example of the stabilization of the cycle for stochastic Lorenz model which exhibits a noise-induced transition to chaos. Using our technique for this model we provide a required small sensitivity for stochastically forced cycle and suppress chaos successfully.

Bashkirtseva, Irina

2014-04-01

409

Investigating chaos in river stage and discharge time series

NASA Astrophysics Data System (ADS)

SummaryThe existence of chaotic behaviour in the river stage and discharge time series observed at the Sogutluhan hydrometric station, Turkey, is investigated. Five nonlinear dynamic methods are employed: (1) phase space reconstruction; (2) False Nearest Neighbour (FNN) algorithm; (3) correlation dimension method; (4) Lyapunov exponent method; and (5) local approximation method. These methods have their bases on data embedding, nearest neighbour search, dimensionality analysis, system divergence/convergence, and local approximation and have varying levels of sophistication in conceptualisation and implementation. They provide either direct identification of chaotic behaviour or at least facilitate identification through system reconstruction, complexity determination (especially in terms of dimensionality), and prediction (including predictability horizon). As the discharge data used in this study are produced by rating directly gauged stage time series, it becomes feasible to investigate any interference triggered by chaotic signals with the rating. The results indicate the existence of low-dimensional chaos in the two time series. They also suggest that the rating of the stage time series to obtain the discharge time series amplifies significantly the fluctuations in the latter in the presence of chaotic signals.

Khatibi, Rahman; Sivakumar, Bellie; Ghorbani, Mohammad Ali; Kisi, Ozgur; Koçak, Kasim; Farsadi Zadeh, Davod

2012-01-01

410

Endogenous rhythms and chaos in crassulacean acid metabolism.

Endogenous free-running regular circadian oscillations of net CO2 exchange in the crassulacean-acidmetabolism (CAM) plant Kalanchoë daigremontiana Hamet et Perrier de la Bâthie under constant external conditions in continuous light have been shown to change to irregular non-predictable (chaotic) time behaviour as irradiance or temperature are raised above a critical level. A model of CAM has been constructed with pools of major metabolites of varying concentrations, flows of metabolites leading to exchange between pools, metabolite transformations determined by chemical reactions, and feedback regulations. The model is described by a system of coupled non-linear differential equations. It shows stable rhythmicity in normal dark-light cycles and in continuous light and, like the K. daigremontiana leaves in the experiments, a change to chaos as irradiance is increased. The maintenance of endogenous oscillations in the model is brought about by a hysteresis switch or beat oscillator between two stable oscillation modes. In CAM these stable modes are vacuolar malate accumulation and remobilization. The model shows that the physical nature of the beat oscillator in the leaves can be explained by the balance between active and passive transport at the tonoplast. PMID:24178196

Lüttge, U; Beck, F

1992-08-01

411

Behavior of a nonlinear resonator driven at subharmonic frequencies

NASA Astrophysics Data System (ADS)

We have experimentally investigated the behavior of a driven nonlinear electrical resonator over a large region of its control parameter space. If one regards the various responses of the resonator as different ``phases'' and constructs a ``phase diagram'' in the system control parameter space, many intriguing regularities become apparent. At drive frequencies far below the system's resonant frequency, there exists a series of regions which are bounded by contours that mark the successive bifurcations in a period-doubling route to chaos. There are geometrical regularities in the size and location of these regions, and we suggest empirical scaling laws to describe these features. The appearance of period doubling and chaos in nonlinear systems that are driven far below resonance can have considerable practical significance and, in the empirical observations that are given in this paper, are a step in understanding the global parameter-space behavior of nonlinear systems.

Baxter, Jeffrey H.; Bocko, Mark F.; Douglass, David H.

1990-01-01

412

[Dynamic paradigm in psychopathology: "chaos theory", from physics to psychiatry].

For the last thirty years, progress in the field of physics, known as "Chaos theory"--or more precisely: non-linear dynamical systems theory--has increased our understanding of complex systems dynamics. This framework's formalism is general enough to be applied in other domains, such as biology or psychology, where complex systems are the rule rather than the exception. Our goal is to show here that this framework can become a valuable tool in scientific fields such as neuroscience and psychiatry where objects possess natural time dependency (i.e. dynamical properties) and non-linear characteristics. The application of non-linear dynamics concepts on these topics is more precise than a loose metaphor and can throw a new light on mental functioning and dysfunctioning. A class of neural networks (recurrent neural networks) constitutes an example of the implementation of the dynamical system concept and provides models of cognitive processes (15). The state of activity of the network is represented in its state space and the time evolution of this state is a trajectory in this space. After a period of time those networks settle on an equilibrium (a kind of attractor). The strength of connections between neurons define the number and relations between those attractors. The attractors of the network are usually interpreted as "mental representations". When an initial condition is imposed to the network, the evolution towards an attractor is considered as a model of information processing (27). This information processing is not defined in a symbolic manner but is a result of the interaction between distributed elements. Several properties of dynamical models can be used to define a way where the symbolic properties emerge from physical and dynamical properties (28) and thus they can be candidates for the definition of the emergence of mental properties on the basis of neuronal dynamics (42). Nevertheless, mental properties can also be considered as the result of an underlying dynamics without explicit mention of the neuronal one (47). In that case, dynamical tools can be used to elucidate the Freudian psychodynamics (34, 35). Recurrent neuronal networks have been used to propose interpretation of several mental dysfunctions (12). For example in the case of schizophrenia, it has been proposed that troubles in the cortical pruning during development (13) may cause a decrease in neural network storage ability and lead to the creation of spurious attractors. Those attractors do not correspond to stored memories and attract a large amount of initial conditions: they were thus associated to reality distorsion observed in schizophrenia (14). Nevertheless, the behavior of these models are too simple to be directly compared with real physiological data. In fact, equilibrium attractors are hardly met in biological dynamics. More complex behaviors (such as oscillations or chaos) should thus to be taken into account. The study of chaotic behavior have lead to the development of numerical methods devoted to the analysis of complex time series (17). These methods may be used to characterise the dynamical processes at the time-scales of both the cerebral dynamics and the clinical symptoms variations. The application of these methods to physiological signals have shown that complex behaviors are related to healthy states whereas simple dynamics are related to pathology (8). These studies have thus confirmed the notion of "dynamical disease" (20, 21) which denotes pathological conditions characterised by changes in physiological rhythms. Depression has been studied within this framework (25, 32) in order to define possible changes in brain electrical rhythms related to this trouble and its evolution. It has been shown that controls' brain dynamics is more complex than depressive one and that the recovery of a complex brain activity depends on the number of previous episodes. In the case of the symptoms time evolution, several studies have demonstrated that non-linear dynamical process may be involved in the recur

Pezard, L; Nandrino, J L

2001-01-01

413

NASA Astrophysics Data System (ADS)

We consider the nonlinear dynamics of multiwavelength laser cavities with saturable transmitter and saturating homogeneous gain using a simple and general discrete model. Saturable transmitter is an intensity dependent loss in which the transmittance decreases when the incident optical power increases. We determine the condition under which the saturable transmitter will generate behaviors such as stable steady-state lasing states, periodic lasing states, and chaotic lasing states. Indeed, for sufficiently large power, steady-state operation is first destabilized through a Hopf bifurcation which generates periodic lasing solutions. This is followed by a sequence of period doubling bifurcations to chaotic lasing. The bifurcation structure leading to chaos is characterized by three key methods of dynamical systems: a Feigenbaum series, the calculation of Lyapunov exponents and the computation of the correlation dimension of the system. We found that even single wavelength operation can exhibit complex nonlinear dynamics if the loss element is a saturable transmitter.

Li, Feng; Kutz, J. Nathan; Wai, P. K. A.

2012-04-01

414

The partial dynamics equations (PDE) of space manipulator with flexible-joint and flexible-link are modelled using the second Lagrange method. Then, the unstable quality of the conventional numerical integration methods under Lagrange system are appropriately proved through energy analysis; therefore, the precise integration method (PIM) under Hamilton system is adopted to solve the strictly stiff PDE owing to rigidness\\/flexibility coupling matter.

Jia Qing-xuan; Chu Ming; Sun Han-xu

2009-01-01

415

Chaos and order in non-integrable model field theories

We illustrate the presence of chaos and order in non-integrable, classical field theories, which we view as many-degree-of-freedom Hamiltonian nonlinear dynamical systems. For definiteness, we focus on the {chi}{sup 4} theory and compare and contrast it with the celebrated integrable sine-Gordon equation. We introduce and investigate two specific problems: the interactions of solitary kink''-like waves in non-integrable theories; and the existence of stable breather'' solutions -- spatially-localized, time-periodic nonlinear waves -- in the {chi}{sup 4} theory. For the former problem we review the rather well developed understanding, based on a combination of computational simulations and heuristic analytic models, of the presence of a sequence of resonances in the kink-antikink interactions as a function of the relative velocity of the interaction. For the latter problem we discuss first the case of the continuum {chi}{sup 4} theory. We discuss the multiple-scale asymptotic perturbation theory arguments which first suggested the existence of {chi}{sup 4} breathers, then the subsequent discovery of terms beyond-all-orders'' in the perturbation expansion which destroy the putative breather, and finally, the recent rigorous proofs of the non-existence of breathers in the continuum theory. We then present some very recent numerical results on the existence of breathers in discrete {chi}{sup 4} theories which show an intricate interweaving of stable and unstable breather solutions on finite discrete lattices. We develop a heuristic theoretical explanation of the regions of stability and instability.

Campbell, D.K.; Peyrard, M.

1989-01-01

416

The chaos in synthetic circuit experiment for vacuum circuit breaker

The chaos characteristic of vacuum circuit breaker (VCB) under different interruption conditions in synthetic circuit experiment is researched. Using four parameter and two parameter method, comparing the influence of the metal vapor arc model, the variations of voltage and current for different VCBs are obtained. And the chaos in synthetic circuit experiment for the demonstrated VCBs based on the Lyapunov

Xiaoming Liu; Xue Leng; Yundong Cao; Jinhui Wang; Peng Sun

2010-01-01

417

Chaos and cryptography: block encryption ciphers based on chaotic maps

This paper is devoted to the analysis of the impact of chaos-based techniques on block encryption ciphers. We present several chaos based ciphers. Using the well-known principles in the cryptanalysis we show that these ciphers do not behave worse than the standard ones, opening in this way a novel approach to the design of block encryption ciphers

Goce Jakimoski; Ljupco Kocarev

2001-01-01

418

Dependent switched capacitor chaos generator and its synchronization

This paper discusses a circuit family including a dependent switched capacitor (DSC). The DSC function is instantaneously short of one capacitor at the moment when its voltage reaches a threshold. The chaos generation can be guaranteed theoretically. We also consider a master-slave system. If there does not exist a homoclinic orbit in the master chaos attractor, it exhibits either in-phase

Kunihiko Mitsubori; Toshimichi Saito

1997-01-01

419

Bifurcations and chaos control in discrete small-world networks

NASA Astrophysics Data System (ADS)

An impulsive delayed feedback control strategy to control period-doubling bifurcations and chaos is proposed. The control method is then applied to a discrete small-world network model. Qualitative analyses and simulations show that under a generic condition, the bifurcations and the chaos can be delayed or eliminated completely. In addition, the periodic orbits embedded in the chaotic attractor can be stabilized.

Li, Ning; Sun, Hai-Yi; Zhang, Qing-Ling

2012-01-01

420

Adaptive Chaos Synchronization of FitzHugh-Nagumo Neurons

NASA Astrophysics Data System (ADS)

The remarkable system of FitzHugh-Nagumo (FHN) neurons in external electrical stimulation is studied from the view of chaos synchronization in this paper. An effective adaptive sliding mode controller is derived to achieve chaos synchronization even when the parameters of the drive and response FHN neurons are fully unknown. An illustrative example is presented for the purpose of verification and illustration.

Lai, Tsung-Wen; Lin, Jui-Sheng; Liao, Teh-Lu; Yan, Jun-Juh

421

Home Chaos: Sociodemographic, Parenting, Interactional, and Child Correlates

ERIC Educational Resources Information Center

We conducted 2 studies to (a) establish the usefulness of the construct of home chaos, (b) investigate its correlates, and (c) determine the validity of the Confusion, Hubbub, and Order Scale (CHAOS) used to measure the construct in each study. Study 1 relied on a sample of European American preschoolers and their mothers and Study 2 on a sample…

Dumas, Jean E.; Nissley, Jenelle; Nordstrom, Alicia; Smith, Emilie Phillips; Prinz, Ronald J.; Levine, Douglas W.

2005-01-01

422

Optical image encryption using improper Hartley transforms and chaos

We propose a new method for image encryption using improper Hartley transform and chaos theory. Improper Hartley transform is a Hartley transform in which the phase between the two Fourier transforms is a fractional multiple of ?\\/2. This fractional order is called fractional parameter and serves as a key in the image encryption and decryption process. Four types of chaos

Narendra Singh; Aloka Sinha

2010-01-01

423

Secure communication using a chaos based signal encryption scheme

The large-scale proliferation of wireless communications both inside and outside the home-office environment has led to an increased demand for effective and cheap encryption schemes. Now a new chaos based signal encryption scheme is proposed to transmit digital information signals by using the conventional synchronization of chaos and digital encryption approaches. In this scheme, either a chaotic or hyperchaotic system

K. Murali; Haiyang Yu; Vinay Varadan; Henry Leung

2001-01-01

424

A multiple access technique for differential chaos shift keying

Various chaos-based digital communications techniques have been proposed recently. Among them, differential chaos shift keying (DCSK) allows the receiving end to decode the signal using noncoherent detection. This paper proposes and analyses a multiple access scheme for DCSK. A simple I-dimensional iterative map has been used to generate the chaotic signals for all users. Bit error probabilities have been derived

Francis Chi-moon Lau; M. M. Yip; C. K. Tse; S. F. Hau

2001-01-01

425

Quantum Chaos Fundamental Problems an Application to Material Science

We investigate quantum mechanics of nonintegrable and chaotic systems. Two realistic examples of quantum chaos in magnetic phenomena are given: (1) Quantum billiard in a magnetic field; (2) quantum dynamics of a pulsed spin system. In these examples, we discuss salient aspects of irregular energy spectra and complicated quantum diffusion. Then, fundamental problems of quantum chaos are examined from a

Katsuhiro Nakamura

1989-01-01

426

Early systems theory was a precursor of complexity theory, a global theory that suggests that the universe is an open system interacting on many dimensions. Chaos theory, a subset of complexity theory, states that in seeming chaos there is an underlying order. Between chaos and order lies emergence, from which healthy growth and change occur. Twenty years ago, chaos theory

Lynne Bradford Drinkard

1995-01-01

427

Chaos and routes to chaos in coupled Duffing oscillators with multiple degrees of freedom

New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of

D. E. Musielak; Z. E. Musielak; J. W. Benner

2005-01-01

428

Chaos formation by sublimation of volatile-rich substrate: Evidence from Galaxias Chaos, Mars

NASA Astrophysics Data System (ADS)

Galaxias Chaos deviates significantly from other chaotic regions due to the lack of associated outflow channels, lack of big elevation differences between the chaos and the surrounding terrain and due to gradual trough formation. A sequence of troughs in different stages is observed, and examples of closed troughs within blocks suggest that the trough formation is governed by a local stress field rather than a regional stress field. Moreover, geomorphic evidence suggests that Galaxias Chaos is capped by Elysium lavas, which superpose an unstable subsurface layer that causes chaotic tilting of blocks and trough formation. Based on regional mapping we suggest a formation model, where Vastitas Borealis Formation embedded between Elysium lavas is the unstable subsurface material, because gradual volatile loss causes shrinkage and differential substrate movement. This process undermines the lava cap, depressions form and gradually troughs develop producing a jigsaw puzzle of blocks due to trough coalescence. Observations of chaos west of Elysium Rise indicate that this process might have been widespread along the contact between Vastitas Borealis Formation and Elysium lavas. However, the chaotic regions have probably been superposed by Elysium/Utopia flows to the NW of Elysium Rise, and partly submerged with younger lavas to the west.

Pedersen, G. B. M.; Head, J. W.

2011-01-01

429

Multifractals and Chaos, Predictability and Prediction Skills in Geophysics

NASA Astrophysics Data System (ADS)

The question of prediction - from short to very long term - and its intrinsic limits is a fundamental question in Geophysics; it cross-cuts traditional discipline boundaries. The chaos revolution emphasized the fact that nonlinearity is at the core of this question. This was widely popularized as the 'butterfly effect' with the help of the celebrated Lorenz model, which was introduced as a highly simplliefied mathematical model of convection and has the lowest possible dimensionality, i.e. three, for chaotic differential systems. Unfortunately, this success may have lead to an awkward tendency to reduce complex systems to their low dimensional caricatures including the corresponding predictibility limits. This tendency may have been reinforced by the apparent success of the rather straightforward correlation dimension algorithm to estimate the dimensionality for various complex systems. As a consequence - in spite of observed discrepancies - the existence of characteristic predictability time and a corresponding exponential fall-off of predictability were considered as the universal long-time asymptotic laws. However, for rather well known reasons, the low dimension estimates of geophysical systems turn out to be spurious. It is now rather clear that the chaos of these spatially extended systems, requires approaches dealing with very large number of degrees of freedom and that certain asymptotic behaviors correspond instead to the infinite limit. The modelling of this high number of degreees of freedom liimit can be obtained by an original blending of stochastics and scaling dynamics, e.g. multiplicative cascade processes, more generally with the help of multifractal processes. The latter do not yield characteristic times of predictability: a limited uncertainty on initial and/or boundary conditions on a given range of time and space scales rapidly grows across the scales and yields scaling (i.e. power-law) decays of the predictability, therefore we should be able to predict on the average much better and longer than previously thought. However, intermittency plays a crucial role, as it will be illustrated with the help of multifractal simulations. Decay of predictability is not homogeneous, but occurs by bursts. Some non trivial questions about multifractal prediction are related to it: it is not sufficient, although an improvement in respect to usual methods, to forecast a field with a lower and lower resolution for larger and larger time lag. Indeed, one need to take into account the interactions between the rather predictable large scales with the hihgly impredictible smaller scales. This is particularly indispensable to forecast the extreme events.

Schertzer, D. J.; Lovejoy, S.

2003-12-01

430

Dynamic modeling of chaos and turbulence

The series, Diophantus: Introduction to Mathematical Philosophy, Kalikasan, Manila, 1993; Nonlinear Anal. 30 (8) (1997) 5021–5032; Nonlinear Stud. 5 (2) (1998) 227–254; Nonlinear Anal., 35 (8) (1999) 259–285; Proc. Second Int. Conf. Tool. Math. Model., St. Petersburg, 4 (1999) 74–89; Proceedings of Third International Conference on Differential Equations, St. Petersburg, 2000 pp. 71–86; Probl. Nonlinear Anal. Eng. Syst. 7 (1)

Edgar E. Escultura

2005-01-01

431

NASA Astrophysics Data System (ADS)

Investigating the biological function of proteins is a key aspect of protein studies. Bioinformatic methods become important for studying the biological function of proteins. In this paper, we first give the chaos game representation (CGR) of randomly-linked functional protein sequences, then propose the use of the recurrent iterated function systems (RIFS) in fractal theory to simulate the measure based on their chaos game representations. This method helps to extract some features of functional protein sequences, and furthermore the biological functions of these proteins. Then multifractal analysis of the measures based on the CGRs of randomly-linked functional protein sequences are performed. We find that the CGRs have clear fractal patterns. The numerical results show that the RIFS can simulate the measure based on the CGR very well. The relative standard error and the estimated probability matrix in the RIFS do not depend on the order to link the functional protein sequences. The estimated probability matrices in the RIFS with different biological functions are evidently different. Hence the estimated probability matrices in the RIFS can be used to characterise the difference among linked functional protein sequences with different biological functions. From the values of the Dq curves, one sees that these functional protein sequences are not completely random. The Dq of all linked functional proteins studied are multifractal-like and sufficiently smooth for the Cq (analogous to specific heat) curves to be meaningful. Furthermore, the Dq curves of the measure ? based on their CGRs for different orders to link the functional protein sequences are almost identical if q >= 0. Finally, the Cq curves of all linked functional proteins resemble a classical phase transition at a critical point.

Yu, Zu-Guo; Xiao, Qian-Jun; Shi, Long; Yu, Jun-Wu; Vo, Anh

2010-06-01

432

The CHAOS-4 Geomagnetic Field Model

NASA Astrophysics Data System (ADS)

We present CHAOS-4, a new version in the CHAOS model series, which aims at describing the Earth's magnetic field with high spatial resolution (terms up to spherical degree n=90 for the crustal field, and up to n=16 for the time-varying core field are robustly determined) and high temporal resolution (allowing for investigations of sub-annual core field changes). More than 14 years of data from the satellites Ørsted (March 1999 to June 2013), CHAMP (July 2000 to September 2010) and SAC-C (2000 to 2004), augmented with ground observatory revised monthly mean values (1997 to 2013) have been used for this model. Maximum spherical harmonic degree of the static (crustal) field is n=100. The core field time changes are expressed by spherical harmonic expansion coefficients up to n=20, described by order 6 splines (with 6-month knot spacing) spanning the time interval 1997.0 to 2013.5. The third time derivative of the squared magnetic field intensity is regularized at the core-mantle boundary. No spatial regularization is applied for the core field, but the high-degree crustal field is regularized for n>85. As part of the modeling effort we co-estimate a model of the large-scale magnetospheric field (with expansions in the GSM and SM coordinate system up to degree n = 2 and parameterization of the time dependence using the decomposition of Dst into external (Est) and induced (Ist) parts) and perform an in-flight alignment of the vector data (co-estimation of the Euler describing the rotation between the coordinate systems of the vector magnetometer and of the star sensor providing attitude information). The final CHAOS-4 model is derived by merging two sub-models: its low-degree part has been obtained using similar model parameterization and data sets as used for previous CHAOS models (but of course including newer satellite observations), while its high-degree crustal field part is solely determined from low-altitude CHAMP satellite observations between January 2009 and September 2010.

Olsen, N.; Finlay, C. C.; Luhr, H.; Sabaka, T. J.; Michaelis, I.; Rauberg, J.; Tøffner-clausen, L.

2013-12-01

433

Chaos game representation of gene structure.

This paper presents a new method for representing DNA sequences. It permits the representation and investigation of patterns in sequences, visually revealing previously unknown structures. Based on a technique from chaotic dynamics, the method produces a picture of a gene sequence which displays both local and global patterns. The pictures have a complex structure which varies depending on the sequence. The method is termed Chaos Game Representation (CGR). CGR raises a new set of questions about the structure of DNA sequences, and is a new tool for investigating gene structure.

Jeffrey, H J

1990-01-01

434

Geometry in the large and hyperbolic chaos

This is the final report of a three-year, Laboratory Directed Research and Development (LDRD) project at the Los Alamos National Laboratory (LANL). The authors calculated observables in strongly chaotic systems. This is difficult to do because of a lack of a workable orbit classification for such systems. This is due to global geometrical information from the original dynamical system being entangled in an unknown way throughout the orbit sequence. They used geometrical methods from modern mathematics and recent connections between global geometry and modern quantum field theory to study the natural geometrical objects belonging to hard chaos-hyperbolic manifolds.

Hasslacher, B.; Mainieri, R.

1998-11-01

435

Feigenbaum graphs at the onset of chaos

NASA Astrophysics Data System (ADS)

We analyze the properties of networks obtained from the trajectories of unimodal maps at the transition to chaos via the horizontal visibility (HV) algorithm. We find that the network degrees fluctuate at all scales with amplitude that increases as the size of the network grows, and can be described by a spectrum of graph-theoretical generalized Lyapunov exponents. We further define an entropy growth rate that describes the amount of information created along paths in network space, and find that such entropy growth rate coincides with the spectrum of generalized graph-theoretical exponents, constituting a set of Pesin-like identities for the network.

Luque, Bartolo; Lacasa, Lucas; Robledo, Alberto

2012-11-01

436

A New Approach for Controlling Chaos in Lorenz System

NASA Astrophysics Data System (ADS)

Is there a need for chaos? In order to answer to this important question, first, we should answer to ``what chaos is?'' Does ``chaos'' mean anarchy and confusion, or it means ``randomness''? In order to answer to the second question, one may briefly consider that ``chaos'' means ``far from the equilibrium.'' It is true that in a random behavior, we have ``far from the equilibrium'' phenomenon, but in the chaotic behavior, however, the trajectory goes far from the equilibrium, but it moves in a bounded basin. Therefore, chaos differs from randomness. In order to answer to the first question, we distinguish two states from each other. Chaos could be dangerous in many states, e.g. for an aircraft in the sky. Therefore, we should control it and return the system from the chaotic mood. But, in some states it is useful. Suppose that we have a periode-2 behavior system. If we intend to change its period, what should we do? One of the best techniques in order to change a system behavior is reaching the system into the chaotic mood for a short time, and then, by controlling chaos which is based on the feedback law, we could return the system into the desired period. Further, the control of chaos is also a way to manipulate the natural systems that are already chaotic. In this paper, we can imagine each mentioned states for chaos. Our goal is the control of a very famous system in the chaotic mood, in order to stabilize it and change its behavior into the desired behavior. We will achieved to this goal using OGY method which is based on the discrete dynamical system concept, and find the stabilized state by a new approach which is based on the generalized Routh-Hurwitz criterion.

Sanayei, Ali

2009-09-01

437

NASA Astrophysics Data System (ADS)

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 brief survey of the fundamental ideas and terminology underlying these types of investigations, covering such concepts as strange attractors, fractal dimensions and self-organized criticality. Their application in many areas of geomorphological research is subsequently reviewed, in river network modeling and in surface analysis amongst others, followed by more detailed descriptions of the use of chaos theory, fractals and self-organization in coastal geomorphology in particular. These include self-organized behavior of beach morphology, the fractal nature of ocean surface gravity waves, the self-organization of beach cusps and simulation models of ripples and dune patterns. This paper further presents a substantial extension of existing dune landscape simulation models by incorporating vegetation in the algorithm, enabling more realistic investigations into the self-organization of coastal dune systems. Interactions between vegetation and the sand transport process in the model—such as the modification of erosion and deposition rules and the growth response of vegetation to burial and erosion—introduce additional nonlinear feedback mechanisms that affect the course of self-organization of the simulated landscape. Exploratory modeling efforts show tantalizing results of how vegetation dynamics have a decisive impact on the emerging morphology and—conversely—how the developing landscape affects vegetation patterns. Extended interpretation of the modeling results in terms of attractors is hampered, however, by want of suitable state variables for characterizing vegetated landscapes, with respect to both morphology and vegetation patterns.

Baas, Andreas C. W.

2002-11-01

438

A linearized dual parallel Mach-Zehnder modulator (DPMZM) based on electro-optic (EO) polymer was both fabricated, and experimentally used to suppress the third-order intermodulation distortion (IMD3) in a coherent analog fiber optic link. This optical transmitter design was based on a new EO chromophore called B10, which was synthesized for applications dealing with the fiber-optic communication systems. The chromophore was mixed with amorphous polycarbonate (APC) to form the waveguide's core material. The DPMZM was configured with two MZMs, of different lengths in parallel, with unbalanced input and output couplers and a phase shifter in one arm. In this configuration each of the MZMs carried a different optical power, and imposed a different depth of optical modulation. When the two optical beams from the MZMs were combined to generate the transmitted signal it was possible to set the IMD3 produced by each modulator to be equal in amplitude but 180° out of phase from the other. Therefore, the resulting IMD3 of the DPMZM transmitter was effectively canceled out during two-tone experiments. A reduction of the IMD3 below the noise floor was observed while leaving fifth-order distortion (IMD5) as the dominant IMD product. This configuration has the capability of broadband operation and shot-noise limited operation simultaneously. PMID:21503098

Kim, Seong-Ku; Liu, Wei; Pei, Qibing; Dalton, Larry R; Fetterman, Harold R

2011-04-11

439

Chaos and structure of level densities

The energy region of the first few MeV above the ground state shows interesting features of the nucleus. Beyond an ordered energy region just above the ground-state the dynamics changes, and chaotic features are observed in the neutron resonance region. The statistical properties of energies and wave-functions are common to all chaotic nuclei. However, if instead a global property, like the local level-density function is studied, strong structure effects emerge. In this contribution we discuss these two different facets of warm nuclei. In section 2 the onset of chaos with increasing excitation energy is discussed, with both experimental observations and proposed theoretical mechanisms as starting points. The structure of level densities in the same excitation energy region based on the two different starting points, is treated in section 3, where we give a short presentation of a newly developed combinatorial level-density modell. Some results from the model are presented and discussed. Two coexisting facets of warm nuclei, quantum chaos and structure of the level density, are considered. A newly developed combinatorial level-density model is presented, and the role of collective enhancements discussed. An example of extreme parity enhancement is shown.

Moller, Peter [Los Alamos National Laboratory; Aberg, Sven [LUND SWEDEN; Uhrenholt, Henrik [LUND SWEDEN; Ickhikawa, Takatoshi [RIKEN

2008-01-01

440

Transient chaos in two coupled, dissipatively perturbed Hamiltonian Duffing oscillators

NASA Astrophysics Data System (ADS)

The dynamics of two coupled, dissipatively perturbed, near-integrable Hamiltonian, double-well Duffing oscillators has been studied. We give numerical and experimental (circuit implementation) evidence that in the case of small positive or negative damping there exist two different types of transient chaos. After the decay of the transient chaos in the neighborhood of chaotic saddle we observe the transient chaos in the neighborhood of unstable tori. We argue that our results are robust and they exist in the wide range of system parameters.

Sabarathinam, S.; Thamilmaran, K.; Borkowski, L.; Perlikowski, P.; Brzeski, P.; Stefanski, A.; Kapitaniak, T.

2013-11-01

441

Chaos control: The problem of a bouncing ball revisited

NASA Astrophysics Data System (ADS)

The problem of a body bouncing on a periodically oscillating surface is revisited to demonstrate chaos control. When the bouncing body is magnetic, it is possible to modify its behavior by adding a magnetic driving force. The mechanism of chaos control may be understood by means of a mechanical analysis which shows that the main result of applying the driving force is to shift the bifurcation diagram in such a way that chaotic behavior is replaced by periodic behavior and vice versa. A simple experiment is presented, along with a numerical simulation, that provides insight into chaos control.

Vargas, M. Cristina; Huerta, D. A.; Sosa, Victor

2009-09-01

442

Nonlinear Control of Heart Rate Variability in Human Infants

NASA Astrophysics Data System (ADS)

Nonlinear analyses of infant heart rhythms reveal a marked rise in the complexity of the electrocardiogram with maturation. We find that normal mature infants (gestation >= 35 weeks) have complex and distinctly nonlinear heart rhythms (consistent with recent reports for healthy adults) but that such nonlinearity is lacking in preterm infants (gestation <= 27 weeks) where parasympathetic-sympathetic interaction and function are presumed to be less well developed. Our study further shows that infants with clinical brain death and those treated with atropine exhibit a similar lack of nonlinear feedback control. These three lines of evidence support the hypothesis championed by Goldberger et al. [Goldberger, A. L., Rigney, D. R. & West, B. J. (1990) Sci. Am. 262, 43-49] that autonomic nervous system control underlies the nonlinearity and possible chaos of normal heart rhythms. This report demonstrates the acquisition of nonlinear heart rate dynamics and possible chaos in developing human infants and its loss in brain death and with the administration of atropine. It parallels earlier work documenting changes in the variability of heart rhythms in each of these cases and suggests that nonlinearity may provide additional power in characterizing physiological states.

Sugihara, George; Allan, Walter; Sobel, Daniel; Allan, Kenneth D.

1996-03-01

443

Mode interaction in horses, tea, and other nonlinear oscillators: The universal role of symmetry

NASA Astrophysics Data System (ADS)

This paper is about mode interaction in systems of coupled nonlinear oscillators. The main ideas are demonstrated by means of a model consisting of two coupled, parametrically driven pendulums. On the basis of this we also discuss mode interaction in the Faraday experiment (as observed by Ciliberto and Gollub) and in running animals. In all these systems the interaction between two modes is seen to take place via a third mode: This interaction mode is a common daughter, born by means of a symmetry breaking bifurcation, of the two interacting modes. Thus, not just any two modes can interact with each other, but only those that are linked (in the system's group-theoretical hierarchy) by a common daughter mode. This is the quintessence of mode interaction. In many cases of interest, the interaction mode is seen to undergo further bifurcations, and this can eventually lead to chaos. These stages correspond to lower and lower levels of symmetry, and the constraints imposed by group theory become less and less restrictive. Indeed, the precise sequence of events during these later stages is determined not so much by group-theoretical stipulations as by the accidental values of the nonlinear terms in the equations of motion.

van der Weele, Jacobus P.; Banning, Erik J.

2001-09-01

444

NASA Astrophysics Data System (ADS)

A mathematical modeling technique is proposed for oscillation chaotization in an essentially nonlinear dissipative Duffing oscillator with two-frequency excitation on an invariant torus in ?2. The technique is based on the joint application of the parameter continuation method, Floquet stability criteria, bifurcation theory, and the Everhart high-accuracy numerical integration method. This approach is used for the numerical construction of subharmonic solutions in the case when the oscillator passes to chaos through a sequence of period-multiplying bifurcations. The value of a universal constant obtained earlier by the author while investigating oscillation chaotization in dissipative oscillators with single-frequency periodic excitation is confirmed.

Zavrazhina, T. V.

2007-10-01

445

Detecting and disentangling nonlinear structure from solar flux time series

NASA Technical Reports Server (NTRS)

Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.

Ashrafi, S.; Roszman, L.

1992-01-01

446

Chaos-order transition in Bianchi type I non-Abelian Born-Infeld cosmology

We investigate the Bianchi I cosmology with the homogeneous SU(2) Yang-Mills field governed by the non-Abelian Born-Infeld action. A similar system with the standard Einstein-Yang-Mills (EYM) action is known to exhibit chaotic behavior induced by the Yang-Mills field. When the action is replaced by the Born-Infeld-type non-Abelian action (NBI), the chaos-order transition is observed in the high-energy region. This is interpreted as a smothering effect due to (nonperturbative in {alpha}{sup '}) string corrections to the classical EYM action. We give numerical evidence for the chaos-order transition and present an analytical proof of regularity of color oscillations in the limit of strong Born-Infeld nonlinearity. We also perform a general analysis of the Bianchi I NBI cosmology and derive an exact solution in the case of only the U(1) component excited. Our new exact solution generalizes the Rosen solution of the Bianchi I Einstein-Maxwell cosmology to the U(1) Einstein-Born-Infeld theory.

Dyadichev, Vladimir V.; Gal'tsov, Dmitri V.; Moniz, Paulo Vargas [Department of Theoretical Physics, Moscow State University, 119899, Moscow (Russian Federation); Astronomy Unit, School of Mathematical Sciences, University of London, Mile End Road, London E1 4NS (United Kingdom)

2005-10-15

447

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

448

Temporal modulation instability, transition to chaos in non-feedback biased photorefractive media

NASA Astrophysics Data System (ADS)

This paper surveys the theoretical dynamic model of chaotic regime in optical delayed feedback system; chaotic control parameters of optical input intensity and externally applied bias electric field are investigated. It is also shown that quasi-periodic state identified as temporal modulation instability can be deeply considered as a route to chaos through the evolution equation. Numerical solution of nonlinear Schrödinger equation as the universal model of modulation instability approves such claim. Pre-experiment based on optical delayed feedback system confirms theoretical model results and clarifies the crucial role of critical frequency as the competition point between optical bistability and the chaotic regime. Then, the simple experiment of non-feedback chaos control in Lithium Niobate photorefractive medium without delay indicates that quasi-periodic state -implies on temporal modulation instability- is also attainable and thus chaotic control can be achieved. The causal explanation of such behavior in slow response time Lithium Niobate photorefractive medium is analytically discussed as the generation of the internal feedback inside the medium.

Sharif, Morteza A.; Borjkhani, Mehdi; Ghafary, Bijan

2014-05-01

449

Theory for the experimental observation of chaos in a rotating waterwheel

NASA Astrophysics Data System (ADS)

We study the chaos for a set of coupled, nonlinear partial-differential equations that originate from the equation of motion and the Fourier transform of the mass-conservation equation for the Malkus waterwheel. Dissipation for this system is produced by an adjustable brake. The braking force, proportional to the angular velocity of the wheel, is responsible for the appearance of chaos. The variation of the moment of inertia with time is taken into account. In the large-time limit, the moment of inertia of the composite system, consisting of the wheel and water, tends to a constant, and the three controlling equations of the set of coupled limit equations reduce to a special case of the Lorenz equations, in which the Rayleigh number ? (here characterizing the distribution of water inflow along the perimeter of the wheel) can also assume negative values. Chaotic attractors of the higher harmonics of the water density have been investigated. Boundaries between various regimes of the wheel's limit behavior (uniform rotation, periodic reversals of spin, chaotic reversals) in the Lorenz parameter space have been found. The Lorenz parameter space has thus been explored in considerably more detail than by previous authors.

Kolá, Miroslav; Gumbs, Godfrey

1992-01-01

450

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

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

R.M.Wheat, Jr.

2003-04-01

451

Experimental evidence for deterministic chaos in thermal pulse combustion.

National Technical Information Service (NTIS)

Given the existence of chaotic oscillations in reacting chemical systems, it is reasonable to ask whether or not similar phenomena can occur in combustion. In this paper, the authors present experimental evidence that kinetically driven chaos occurs in a ...

C. S. Daw J. F. Thomas G. A. Richards L. L. Narayanaswami

1994-01-01

452

Digital key for chaos communication performing time delay concealment.

We introduce a scheme that integrates a digital key in a phase-chaos electro-optical delay system for optical chaos communications. A pseudorandom binary sequence (PRBS) is mixed within the chaotic dynamics in a way that a mutual concealment is performed; e.g., the time delay is hidden by the binary sequence, and the PRBS is also masked by the chaos. In addition to bridging the gap between algorithmic symmetric key cryptography and chaos-based analog encoding, the proposed approach is intended to benefit from the complex algebra mixing between a (pseudorandom) Boolean variable, and another continuous time (chaotic) variable. The scheme also provides a large flexibility allowing for easy reconfigurations to communicate securely at a high bit rate between different systems. PMID:21838363

Nguimdo, Romain Modeste; Colet, Pere; Larger, Laurent; Pesquera, Luís

2011-07-15

453

Numerical and experimental exploration of phase control of chaos.

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. PMID:16599742

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

2006-03-01

454

Filtering with Marked Point Process Observations via Poisson Chaos Expansion

We study a general filtering problem with marked point process observations. The motivation comes from modeling financial ultra-high frequency data. First, we rigorously derive the unnormalized filtering equation with marked point process observations under mild assumptions, especially relaxing the bounded condition of stochastic intensity. Then, we derive the Poisson chaos expansion for the unnormalized filter. Based on the chaos expansion, we establish the uniqueness of solutions of the unnormalized filtering equation. Moreover, we derive the Poisson chaos expansion for the unnormalized filter density under additional conditions. To explore the computational advantage, we further construct a new consistent recursive numerical scheme based on the truncation of the chaos density expansion for a simple case. The new algorithm divides the computations into those containing solely system coefficients and those including the observations, and assign the former off-line.

Sun Wei, E-mail: wsun@mathstat.concordia.ca [Concordia University, Department of Mathematics and Statistics (Canada); Zeng Yong, E-mail: zengy@umkc.edu [University of Missouri at Kansas City, Department of Mathematics and Statistics (United States); Zhang Shu, E-mail: zhangshuisme@hotmail.com [Concordia University, Department of Mathematics and Statistics (Canada)

2013-06-15