Note: This page contains sample records for the topic chaos linking nonlinear from Science.gov.
While these samples are representative of the content of Science.gov,
they are not comprehensive nor are they the most current set.
We encourage you to perform a real-time search of Science.gov
to obtain the most current and comprehensive results.
Last update: November 12, 2013.
1

Chaos in nonlinear optical systems  

NASA Astrophysics Data System (ADS)

We show that coupled Kerr oscillators externally pumped can generate chaotic and hyperchaotic beats. The appearance of chaos within beats depends strongly on the type of interactions between the nonlinear oscillators. To indicate chaotic behavior of the system we make use of the Lyapunov exponents. The structure of chaotic beats can be qualitatively different - the envelope function can be smooth if the system is undamped or can give the impression of noise structure in the presence of strong damping and nonlinear interactions between the individual oscillators. The system considered can be used, in practice, as generators of chaotic beats with chaotically modulated envelopes.

Szlachetka, Przemyslaw

2001-03-01

2

Chaos and transient chaos in an experimental nonlinear pendulum  

Microsoft Academic Search

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

Aline Souza de Paula; Marcelo Amorim Savi; Francisco Heitor Iunes Pereira-Pinto

2006-01-01

3

Detecting nonlinearity and chaos in epidemic data  

SciTech Connect

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

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

1993-08-01

4

Digital Communication Devices Based on Nonlinear Dynamics and Chaos.  

National Technical Information Service (NTIS)

The final report of the ARO MURI 'Digital Communications Based on Chaos and Nonlinear Dynamics' contains research results in the areas of chaos and nonlinear dynamics applied to wireless and optical communications. New modulation and coding approaches wer...

J. Liu L. Larson L. Tsimring W. Dally

2003-01-01

5

Synchronizing Spatiotemporal Chaos in Coupled Nonlinear Oscillators  

Microsoft Academic Search

The synchronization of spatiotemporal chaos of two arrays of coupled nonlinear oscillators is achieved by discrete time coupling of individual cells of the arrays. This synchronization method is based on the knowledge of the local dynamics and can be applied to any type of arrays where the synchronization properties of the cells are known. Furthermore, we discuss possible applications of

Ljupco Kocarev; Ulrich Parlitz

1996-01-01

6

Nonequilibrium chaos of disordered nonlinear waves.  

PubMed

Do nonlinear waves destroy Anderson localization? Computational and experimental studies yield subdiffusive nonequilibrium wave packet spreading. Chaotic dynamics and phase decoherence assumptions are used for explaining the data. We perform a quantitative analysis of the nonequilibrium chaos assumption and compute the time dependence of main chaos indicators-Lyapunov exponents and deviation vector distributions. We find a slowing down of chaotic dynamics, which does not cross over into regular dynamics up to the largest observed time scales, still being fast enough to allow for a thermalization of the spreading wave packet. Strongly localized chaotic spots meander through the system as time evolves. Our findings confirm for the first time that nonequilibrium chaos and phase decoherence persist, fueling the prediction of a complete delocalization. PMID:23971575

Skokos, Ch; Gkolias, I; Flach, S

2013-08-07

7

Nonequilibrium Chaos of Disordered Nonlinear Waves  

NASA Astrophysics Data System (ADS)

Do nonlinear waves destroy Anderson localization? Computational and experimental studies yield subdiffusive nonequilibrium wave packet spreading. Chaotic dynamics and phase decoherence assumptions are used for explaining the data. We perform a quantitative analysis of the nonequilibrium chaos assumption and compute the time dependence of main chaos indicators—Lyapunov exponents and deviation vector distributions. We find a slowing down of chaotic dynamics, which does not cross over into regular dynamics up to the largest observed time scales, still being fast enough to allow for a thermalization of the spreading wave packet. Strongly localized chaotic spots meander through the system as time evolves. Our findings confirm for the first time that nonequilibrium chaos and phase decoherence persist, fueling the prediction of a complete delocalization.

Skokos, Ch.; Gkolias, I.; Flach, S.

2013-08-01

8

Sparse Wiener Chaos approximations of Zakai equation for nonlinear filtering  

Microsoft Academic Search

Sparse Wiener chaos approximations of Zakai equation is considered. The objective is to optimize an approach to nonlinear filtering based on the Cameron-Martin version of Wiener chaos expansion (WCE). The error of the approximation is obtained. The main feature of Wiener chaos expansion is that it allows one to separate the computations involving the observations from those dealing only with

Jian Xu; Jianxun Li

2009-01-01

9

Theory and applications of nonlinear vibration, bifurcation and chaos  

NASA Astrophysics Data System (ADS)

This paper, starting from nonlinear vibration, summarizes the principal achievements in theory and applications of bifurcation and chaos in nonlinear vibration in recent years, and the prospects for them at home and abroad. First, the paper reviews the history of the development in theory of nonlinear vibration, expounds the necessity that the modern theory of bifurcation and chaos is applied to research nonlinear vibrant systems. Moreover, eight important orientations of studying nonlinear vibration are given. In addition, it describes fully the main results and developments of research work at home and abroad in four aspects: analytic methods of nonlinear vibrant systems, theory and analytic methods of local bifurcation of nonlinear vibration systems, global bifurcation and chaos of nonlinear vibration systems, and theory of vibration and bifurcation in nonlinear stochastic systems. Finally, the paper describes the main content in future research of theory of bifurcation and chaos, and its applications in nonlinear vibration.

Chen, Yu S.

1992-09-01

10

Household Chaos--Links with Parenting and Child Behaviour  

ERIC Educational Resources Information Center

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

Coldwell, Joanne; Pike, Alison; Dunn, Judy

2006-01-01

11

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

Microsoft Academic Search

Household chaos has been linked to poorer cognitive, behavioural, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family instability, lack of routine, and television usually on. Chaos was measured at

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

2012-01-01

12

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

Microsoft Academic Search

Household chaos has been linked to poorer cognitive, behavioural, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family instability, lack of routine, and television usually on. Chaos was measured at

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

2011-01-01

13

Household Chaos--Links with Parenting and Child Behaviour  

ERIC Educational Resources Information Center

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

Coldwell, Joanne; Pike, Alison; Dunn, Judy

2006-01-01

14

Short Communication Chaos and transient chaos in an experimental nonlinear pendulum  

Microsoft Academic Search

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

Aline Souza de Paula; Marcelo Amorim Savi

15

Controlling spatiotemporal chaos in coupled nonlinear oscillators  

Microsoft Academic Search

A method for controlling spatiotemporal chaos in coupled ordinary differential equations is presented. It is based on two ideas: stabilization of unstable periodic patterns embedded in spatiotemporal chaos, and perturbation of dynamical variables only at regular time intervals.

Ljupco. Kocarev; Ulrich Parlitz; Toni Stojanovski; Predrag Janjic

1997-01-01

16

Simulation strategies and signatures of chaos in classical nonlinear response.  

PubMed

Algorithms are presented for overcoming the computational challenge of nonlinear response functions which describe the response of a classical system to a sequence of n pulses and depend on nth order multipoint stability matrices containing signatures of chaos. Simulations for the Lorentz gas demonstrate that finite field algorithms can be effectively used for the robust, long time calculation of nonlinear response functions. These offer the possibility to characterize chaos beyond the commonly used Lyapunov exponents and suggest new experimentally accessible measures of chaos. PMID:12689125

Dellago, Christoph; Mukamel, Shaul

2003-03-31

17

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

18

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

19

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

PubMed Central

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

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

2011-01-01

20

Nonlinear system vibration---The appearance of chaos  

SciTech Connect

This paper begins with an examination of the differential equation for a single degree of freedom force excited oscillator and considers the state space behavior of linear, nonlinear, and chaotic single degree of freedom systems. The fundamental characteristics of classical chaos are reviewed: sensitivity to initial conditions, positive Lyapunov exponents, complex Poincare maps, fractal properties of motion in the state space, and broadening of the power spectrum of the system response. Illustrated examples of chaotic behavior include motion in a two well potential -- the chaos beam described in Moon and a hardening base excited Duffing system. Chaos-like phenomenon which occur with nonperiodic forcing are examined in the context of the two well potential and hardening Duffing systems. The paper concludes with some suggestions for detecting and modelling nonlinear or chaotic behavior. 19 refs., 19 figs.

Hunter, N.F. Jr.

1990-01-01

21

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

SciTech Connect

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

22

An application of chaos and bifurcation in nonlinear dynamical power systems  

Microsoft Academic Search

In this article, a nonlinear dynamical phenomena leading to bifurcation and chaos in power systems is explored using a sample power system. After giving an introduction to nonlinear dynamical power systems in section II a basic knowledge to nonlinear dynamics and chaos theory is given. Section III deals with bifurcation theory. In section IV a dynamical power system model has

Leyla Kuru; Ersen Kuru; M. Ali Yalpm

2004-01-01

23

Environmental sustainability, nonlinear dynamics and chaos  

Microsoft Academic Search

Summary.   This paper studies the possibility of nonlinear dynamics in a simple overlapping generations model with the environment –\\u000a the John-Pecchenino (1994) model. We show that if people's concerns towards greener preferences and the maintenance efficiency\\u000a relative to degradation are not sufficiently high, cyclically or chaotically fluctuating equilibria are more likely to exist;\\u000a moreover, under a specific condition, a complicated

Junxi Zhang

1999-01-01

24

Nonlinear Dynamics and Chaos Theory: Concepts and Applications Relevant to Pharmacodynamics  

Microsoft Academic Search

The theory of nonlinear dynamical systems (chaos theory), which deals with deterministic systems that exhibit a complicated, apparently random-looking behavior, has formed an interdisciplinary area of research and has affected almost every field of science in the last 20 years. Life sciences are one of the most applicable areas for the ideas of chaos because of the complexity of biological

Aristides Dokoumetzidis; Athanassios Iliadis; Panos Macheras

2001-01-01

25

Non-intrusive generalized polynomial chaos approach to the stability analysis of uncertain nonlinear dynamic systems  

Microsoft Academic Search

This paper is devoted to the stability analysis of uncertain nonlinear dynamic systems. The generalized polynomial chaos formalism is proposed to deal with this challenging problem treated in most cases by using the prohibitive Monte Carlo based techniques. Two equivalent methods combining the non-intrusive generalized polynomial chaos with the indirect Lyapunov method are presented. Both methods are shown to be

Lyes Nechak; Sebastien Berger; Evelyne Aubry

2011-01-01

26

Chaos  

SciTech Connect

The basic applied mathematical and numerical methods of chaotic dynamics are presented, discussing the wide range of phenomena that can be treated as chaotic processes. The general topics discussed include iterative maps, endogeneous chaos, forced chaos, and the measurement of chaos. Examples of apparently chaotic activity are addressed, including cellular metabolism, cardiac electrophysiology, population biology, electronic oscillators, and laser systems.

Holden, A.V.

1986-01-01

27

Integrability and chaos in nonlinearly coupled optical beams  

SciTech Connect

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

David, D.

1989-01-01

28

Local nature and scaling of chaos in weakly nonlinear disordered chains.  

PubMed

The dynamics of a disordered nonlinear chain can be either regular or chaotic with a certain probability. The chaotic behavior is often associated with the destruction of Anderson localization by the nonlinearity. In the present work it is argued that at weak nonlinearity chaos is nucleated locally on rare resonant segments of the chain. Based on this picture, the probability of chaos is evaluated analytically. The same probability is also evaluated by direct numerical sampling of disorder realizations and quantitative agreement between the two results is found. PMID:23030992

Basko, D M

2012-09-05

29

Nonlinear dynamics and chaos in hydrologic systems: latest developments and a look forward  

Microsoft Academic Search

During the last two decades or so, studies on the applications of the concepts of nonlinear dynamics and chaos to hydrologic\\u000a systems and processes have been on the rise. Earlier studies on this topic focused mainly on the investigation and prediction\\u000a of chaos in rainfall and river flow, and further advances were made during the subsequent years through applications of

Bellie Sivakumar

2009-01-01

30

Pattern selection and low-dimensional chaos in systems of coupled nonlinear oscillators  

SciTech Connect

The longtime behavior of a number of one- and two-dimensional driven, dissipative, dispersive, many-degree-of-freedom systems is studied. It is shown numerically that the attractors are characterized by strong mode-locking into a small number of (nonlinear) modes. On the basis of the observed profiles, estimates of chaotic attractor dimensions, and projections into nonlinear mode bases, it is argued that the same few modes may (in these extended systems) give a unified picture of spatial pattern selection, low-dimensional chaos, and coexisting coherence and chaos. Analytic approaches to this class of problem are summarized.

Bishop, A.

1984-01-01

31

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

32

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

ERIC Educational Resources Information Center

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

Bussolari, Cori J.; Goodell, Judith A.

2009-01-01

33

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

SciTech Connect

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

34

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

ERIC Educational Resources Information Center

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

Bussolari, Cori J.; Goodell, Judith A.

2009-01-01

35

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

36

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

Microsoft Academic Search

An experimental and numerical study of linear and nonlinear wave systems using methods and ideas developed from quantum chaos is presented. We exploit the analogy of the wave equation for the flexural modes of a thin clover-shaped acoustic plate to the stationary solutions of the Schrodinger wave equation for a quantum clover-shaped billiard, a generic system that has regular and

Toni Neicu

2002-01-01

37

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

38

Oscillations and chaos in epidemics: A nonlinear dynamic study of six childhood diseases in Copenhagen, Denmark  

Microsoft Academic Search

Using traditional spectral analysis and recently developed non-linear methods, we analyze the incidence of six childhood diseases in Copenhagen, Denmark. In three cases, measles, mumps, rubella, the dynamics suggest low dimensional chaos. Outbreaks of chicken pox, on the other hand, conform to an annual cycle with noise superimposed. The remaining diseases, pertussis and scarlet fever, remain problematic. The real epidemics

L. F. OLSEN; G. L. TRUTY; W. M. SCHAFFER

1988-01-01

39

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

PubMed

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

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

2012-05-07

40

Chaos Hypertextbook  

NSDL National Science Digital Library

High school teacher Glenn Elert wrote the original edition of the Chaos Hypertextbook for his M.S. degree in secondary science education at Teachers College, Columbia University. After graduation, Elert put the hypertext on the Internet for the benefit of people interested in mathematics, chaos, non-linear dynamics, and fractals. While the hypertext does require some mathematical knowledge, it is geared towards a wide audience. The hypertext addresses a variety of interesting topics including one-dimensional iterated maps; fractal construction; applications and definitions of dimension; and a comparison of non-linear and linear dynamics. The site also offers information about print, software, and Internet resources as well as a fun Eye Candy section. Site visitors can also link to other hypertexts by Elert including The Physics Factbook (an encyclopedia of scientific essays written by high school students), and the Physics Hypertextbook, which is currently under construction.

41

Minimal control synthesis adaptive control of nonlinear systems: utilizing the properties of chaos.  

PubMed

This paper discusses a novel approach to the control of chaos based on the use of the adaptive minimal control synthesis algorithm. The strategies presented are based on the explicit exploitation of different properties of chaotic systems including the boundedness of the chaotic attractors and their topological transitivity (or ergodicity). It is shown that chaos can be exploited to synthesize more efficient control techniques for nonlinear systems. For instance, by using the ergodicity of the chaotic trajectory, we show that a local adaptive control strategy can be used to synthesize a global controller. An application is to the swing-up control of a double inverted pendulum. PMID:16893794

di Bernardo, M; Stoten, D P

2006-09-15

42

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

SciTech Connect

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

43

Nonlinear aeroelastic analysis of airfoils: bifurcation and chaos  

Microsoft Academic Search

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

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

1999-01-01

44

Quantum nonlinear resonance and quantum chaos in Aharonov-Bohm oscillations in mesoscopic semiconductor rings  

SciTech Connect

We consider Aharonov-Bohm oscillations in a mesoscopic semiconductor ring threaded by both a constant magnetic flux and a time-dependent, resonant magnetic field with one or two frequencies. Working in the ballistic regime, we establish that the theory of {open_quotes}quantum nonlinear resonance{close_quotes} applies, and thus that this system represents a possible solid-state realization of {open_quotes}quantum nonlinear resonance{close_quotes} and {open_quotes}quantum chaos.{close_quotes} In particular, we investigate the behavior of the time-averaged electron energy at zero temperature in the regimes of (i) an isolated quantum nonlinear resonance and (ii) the transition to quantum chaos, when two quantum nonlinear resonances overlap. The time-averaged energy exhibits sharp resonant behavior as a function of the applied constant magnetic flux, and has a staircase dependence on the amplitude of the external time-dependent field. In the chaotic regime, the resonant behavior exhibits complex structure as a function of flux and frequency. We compare and contrast the quantum chaos expected in these mesoscopic {open_quotes}solid-state atoms{close_quotes} with that observed in Rydberg atoms in microwave fields, and discuss the prospects for experimental observation of the effects we predict. {copyright} {ital 1997} {ital The American Physical Society}

Berman, G.P. [Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545 (United States); Bulgakov, E.N. [Kirensky Institute of Physics, 660036, Krasnoyarsk (Russia); Campbell, D.K. [Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801-3080 (United States); Krive, I.V. [Institute for Low Temperature Physics and Engineering, Ukrainian Academy of Sciences, 310164, Kharkov (Ukraine)

1997-10-01

45

Chaos in a nonlinear damped Mathieu system, in a nano resonator system and in its fractional order systems  

Microsoft Academic Search

In this paper, the chaotic behaviors of a nonlinear damped Mathieu system and of a nonlinear nano resonator system with integral orders and with fractional orders are studied. By applying numerical analyses such as phase portraits, Poincaré maps and bifurcation diagrams, the periodic and chaotic motions are observed. It is found that chaos exists both in the nonlinear damped Mathieu

Zheng-Ming Ge; Chang-Xian Yi

2007-01-01

46

Nonlinear characteristics (chaos) of high-power microwave (HPM) sources  

NASA Astrophysics Data System (ADS)

Recent advances in the understanding of dynamical systems and chaotic behavior have resulted in the investigation of HPM source design issues. Modern dynamical systems theory can improve our understanding of the dynamics of space charge dominated beams and the RF waveforms generated by them. This paper will review the work done to date using time series analysis techniques to study the state space dynamics of high power microwave sources using simulation (particle-in-cell) code results. Low-dimensional chaos has been observed in simulation results from a variety of HPM sources, including the MILO (Magnetically Insulated Line Oscillator). Additionally, the particle behavior within the diode portion of HPM tubes can have chaotic characteristics. Knowing when these features occur and how they develop are important first steps in our ability to control and/or eliminate them. Central to understanding source behavior is the initial use of joint time frequency analysis to assess whether the dynamics are stationary or not. Subsequently we use delay coordinate embedding techniques to reconstruct an effective state space global dynamics. From this, Poincare sections are examined. Lyapunov exponents are then calculated to determine whether the behavior of the source is noise or deterministic chaos.

Gaudet, John A.; Luginsland, John W.; Wallace, Christopher B.

2000-07-01

47

Facilitating Joint Chaos and Fractal Analysis of Biosignals through Nonlinear Adaptive Filtering  

PubMed Central

Background Chaos and random fractal theories are among the most important for fully characterizing nonlinear dynamics of complicated multiscale biosignals. Chaos analysis requires that signals be relatively noise-free and stationary, while fractal analysis demands signals to be non-rhythmic and scale-free. Methodology/Principal Findings To facilitate joint chaos and fractal analysis of biosignals, we present an adaptive algorithm, which: (1) can readily remove nonstationarities from the signal, (2) can more effectively reduce noise in the signals than linear filters, wavelet denoising, and chaos-based noise reduction techniques; (3) can readily decompose a multiscale biosignal into a series of intrinsically bandlimited functions; and (4) offers a new formulation of fractal and multifractal analysis that is better than existing methods when a biosignal contains a strong oscillatory component. Conclusions The presented approach is a valuable, versatile tool for the analysis of various types of biological signals. Its effectiveness is demonstrated by offering new important insights into brainwave dynamics and the very high accuracy in automatically detecting epileptic seizures from EEG signals.

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

2011-01-01

48

Non-linear protocell models: synchronization and chaos  

NASA Astrophysics Data System (ADS)

We consider generic protocells models allowing linear and non-linear kinetics for the main involved chemical reactions. We are interested in understanding if and how the protocell division and the metabolism do synchronise to give rise to sustainable evolution of the protocell.

Filisetti, A.; Serra, R.; Carletti, T.; Villani, M.; Poli, I.

2010-09-01

49

Chaos in a Nonlinear Driven Oscillator with Exact Solution  

Microsoft Academic Search

A nonlinear oscillator externally driven by an impulsive periodic force is investigated. An exact analytical expression is obtained for the stoboscopic or Poincaré map for all values of parameters. The model displays period-doubling sequences and chaotic behavior. The convergence rate of these cascades is in very good agreement with Feingenbaum theory.

Diego L. Gonzalez; Oreste Piro

1983-01-01

50

Weak chaos in the disordered nonlinear Schroedinger chain: Destruction of Anderson localization by Arnold diffusion  

SciTech Connect

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

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

2011-07-15

51

Nonlinear Dynamics and Chaos in the Sea and Land Breeze  

Microsoft Academic Search

In this work the evolution of the sea and land breeze is studied using a nonlinear model under calm synoptic conditions and diurnal periodic forcing of ground temperature. The breeze is examined as a function of the strength of the heating amplitude of ground temperature theta0. For theta0 6°C, the solution is quasi-periodic with two incommensurate oscillations of 24 and

Yizhak Feliks

2004-01-01

52

Chaos and related nonlinear noise phenomena in Josephson tunnel junctions  

SciTech Connect

The nonlinear dynamics of Josephson tunnel junctions shunted by a resistance with substantial self-inductance have been thoroughly investigated. The current-voltage characteristics of these devices exhibit stable regions of negative differential resistance. Very large increases in the low-frequency voltage noise with equivalent noise temperatures of 10/sup 6/ K or more, observed in the vicinity of these regions, arise from switching, or hopping, between subharmonic modes. Moderate increases in the noise, with temperatures of about 10/sup 3/ K, arise from chaotic behavior. Analog and digital simulations indicate that under somewhat rarer circumstances the same junction system can sustain a purely deterministic hopping between two unstable subharmonic modes, accompanied by excess low-frequency noise. Unlike the noise-induced case, this chaotic process occurs over a much narrower range in bias current and is destroyed by the addition of thermal noise. The differential equation describing the junction system can be reduced to a one-dimensional mapping in the vicinity of one of the unstable modes. A general analytical calculation of switching processes for a class of mappings yields the frequency dependence of the noise spectrum in terms of the parameters of the mapping. Finally, the concepts of noise-induced hopping near bifurcation thresholds are applied to the problem of the three-photon Josephson parametric amplifier. Analog simulations indicate that the noise rise observed in experimental devices arises from occasional hopping between a mode at the pump frequency ..omega../sub p/ and a mode at the half harmonic ..omega../sub p//2. The hopping is induced by thermal noise associated with the shunt resistance. 71 references.

Miracky, R.F.

1984-07-01

53

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

54

Chaos induced by breakup of waves in a spatial epidemic model with nonlinear incidence rate  

NASA Astrophysics Data System (ADS)

Spatial epidemiology is the study of spatial variation in disease risk or incidence, including the spatial patterns of the population. The spread of diseases in human populations can exhibit large scale patterns, underlining the need for spatially explicit approaches. In this paper, the spatiotemporal complexity of a spatial epidemic model with nonlinear incidence rate, which includes the behavioral changes and crowding effect of the infective individuals, is investigated. Based on both theoretical analysis and computer simulations, we find out when, under the parameters which can guarantee a stable limit cycle in the non-spatial model, spiral and target waves can emerge. Moreover, two different kinds of breakup of waves are shown. Specifically, the breakup of spiral waves is from the core and the breakup of target waves is from the far-field, and both kinds of waves become irregular patterns at last. Our results reveal that the spatiotemporal chaos is induced by the breakup of waves. The results obtained confirm that diffusion can form spiral waves, target waves or spatial chaos of high population density, which enrich the findings of spatiotemporal dynamics in the epidemic model.

Sun, Gui-Quan; Jin, Zhen; Liu, Quan-Xing; Li, Li

2008-08-01

55

Chaos and simple determinism in reversed field pinch plasmas: Nonlinear analysis of numerical simulation and experimental data  

SciTech Connect

In this dissertation the possibility that chaos and simple determinism are governing the dynamics of reversed field pinch (RFP) plasmas is investigated. To properly assess this possibility, data from both numerical simulations and experiment are analyzed. A large repertoire of nonlinear analysis techniques is used to identify low dimensional chaos in the data. These tools include phase portraits and Poincare 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 date 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 low 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.A.

1993-09-01

56

Chaos Rules  

NSDL National Science Digital Library

This Physics Central feature provides historical background for chaos theory. It also describes three recent investigations in this field--weather patterns, population dynamics, and the dripping faucet. On the right side of the page, visitors will also find a link to further online resources to help educators teach about chaos.

2008-06-11

57

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

58

Chaos prediction and control of Goodwin’s nonlinear accelerator model  

Microsoft Academic Search

Chaos prediction and its control of the Goodwin model under the deterministic or stochastic excitation are studied theoretically and numerically. Applying the Melnikov technique, the threshold conditions for the occurrence of chaos are obtained theoretically. The stable and unstable manifolds of saddle are computed to verify the effectiveness of the analytical prediction in the deterministic case. Also, the safe basins

Shuang Li; Qian Li; Jiaorui Li; Jinqian Feng

2011-01-01

59

Impact of Noise and Seasonality on the Detection and Nonlinear Prediction of Chaos From Finite River-Flow Time Series  

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

60

Chirped elliptically polarised cnoidal waves and polarisation 'chaos' in an isotropic medium with spatial dispersion of cubic nonlinearity  

NASA Astrophysics Data System (ADS)

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.

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

2012-12-01

61

Chaos at Maryland  

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.

62

Adaptive nonlinear boundary control of a flexible link robot arm  

Microsoft Academic Search

We consider the problem of designing a boundary controller for a flexible link robot arm with a payload mass at the link's free-end. Specifically, we utilize a nonlinear, hybrid dynamic system model (the model is hybrid in the sense that it comprises a distributed parameter, dynamic field equation coupled to discrete, dynamic boundary equations) to design a model-based control law

M. S. de Queiroz; D. M. Dawson; M. Agarwal; F. Zhang

1999-01-01

63

Measuring Chaos  

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

64

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

Microsoft Academic Search

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

65

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

NASA Astrophysics Data System (ADS)

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.

Sugihara, George; May, Robert M.

1990-04-01

66

Routes to chaos and multiple time scale dynamics in broadband bandpass nonlinear delay electro-optic oscillators.  

PubMed

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

2009-02-09

67

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.

Chua, Leon O., 1936-

2007-07-24

68

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

69

Solitons and Chaos in Plasma.  

National Technical Information Service (NTIS)

Plasma exhibits a full variety of nonlinear phenomena. Active research in nonlinear plasma physics contributed to explore the concepts of soliton and chaos. Structure of the soliton equations and the dynamics of low dimensional Hamiltonian systems are dis...

Y. H. Ichikawa

1991-01-01

70

An Introduction to Chaos  

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

71

Decreased nonlinear complexity and chaos during sleep in first episode schizophrenia: a preliminary report  

Microsoft Academic Search

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

72

Closer Look at a Fibonacci-Like Iterated Nonlinear Map: More Chaos and Order.  

National Technical Information Service (NTIS)

The continuation of a study of a Fibonacci like analog of the well known iterated nonlinear map x(sub n+1) = lambda x(sub n)(1- x(sub n)) is presented. This second order variant contains two parameters: one which corresponds to lambda, and a second one de...

P. R. J. Asveld

1991-01-01

73

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

74

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

Microsoft Academic Search

The nonlinear vibration isolation system (NVIS) works in a chaotic state when its parameters are in chaotic range. Under single-frequency harmonic excitation, the system exhibits chaotic behavior with broad band frequency. This idea can be used to control the line spectra water-born noise of the underwater vehicle, and to improve its capability of concealment. In order to ensure that the

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

2008-01-01

75

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

Microsoft Academic Search

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

76

Nonlinear time series modeling and prediction using functional networks. Extracting information masked by chaos  

Microsoft Academic Search

Functional networks are a recently introduced extension of neural networks which deal with general functional models instead of sigmoidal-like ones. In this paper we show that functional network architectures provide simple and efficient techniques to model nonlinear time series. To this aim, the neural functions are approximated by finite combinations of known functions from a given family (polynomials, Fourier expansions,

E. Castillo; J. M. Gutiérrez

1998-01-01

77

A strategy to control chaos in nonlinear driven oscillators with least prior knowledge  

Microsoft Academic Search

A strategy to control a class of nonlinear driven oscillators is studied. The class of oscillators includes externally and parametrically excited oscillators, such as the Duffing oscillator and the externally excited pendulum. By assuming that the exact model of the system is not known and that position is the only state available for feedback, the controller comprises a linearizing-like feedback

Ricardo Femat; José Alvarez-Ramírez; Jesús González

1997-01-01

78

Critical bifurcations and chaos in a delayed nonlinear model for the immune response  

Microsoft Academic Search

In this work, we consider the dynamical behaviour associated with the interaction of the immune system with a target population. We consider a model with delayed responses, which consists in a set of two coupled nonlinear differential equations. We show that the stationary solution becomes unstable above a critical delay time of the immune response. In the delay induced oscillatory

Elder de Souza; Marcelo Lyra; Iram Gleria

2009-01-01

79

Nonlinear dynamics and chaos in a pseudoelastic two-bar truss  

NASA Astrophysics Data System (ADS)

Stability aspects of structures are usually treated by archetypal models that provide global comprehension of the system behavior. The two-bar truss is an example of this kind of model that presents snap-through behavior. This paper deals with the dynamical response of a pseudoelastic two-bar truss, representing an archetypal model of a structural system that exhibits both geometrical and constitutive nonlinearities. Adaptive trusses with shape memory alloy actuators are examples of dynamical systems that may behave like the structure considered in this paper. A constitutive model is employed in order to describe the SMA behavior, presenting close agreement with experimental data. An iterative numerical procedure based on the operator split technique, the orthogonal projection algorithm and the classical fourth order Runge-Kutta method is developed to deal with nonlinearities in the formulation. Numerical investigation is carried out considering free and forced responses of the pseudoelastic two-bar truss showing complex behaviors.

Savi, Marcelo A.; Nogueira, Jefferson B.

2010-11-01

80

Nonlinear instability and chaos in plasma wave-wave interactions, I., Introduction  

SciTech Connect

Conventional linear stability analyses may fail for fluid systems with an indefinite free energy functional. When such a system is linearly stable, it is said to possess negative energy modes. Instability may then occur either via dissipation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, leading to explosive growth. In the dissipationless case, it is conjectured that intrinsic chaotic behavior may allow initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper [submitted to Physics of Plasmas], this phenomenon is demonstrated for a simple equilibrium involving cold counterstreaming ions. The system is described in the fluid approximation by a Hamiltonian functional and associated noncanonical Poisson bracket. By Fourier decomposition and appropriate coordinate transformations, the Hamiltonian for the perturbed energy is expressed in action-angle form. The normal modes correspond to Doppler-shifted ion-acoustic waves of positive and negative energy. Nonlinear coupling leads to decay instability via two-wave interactions, and to either decay or explosive instability via three-wave interactions. These instabilities are described for various (integrable) systems of waves interacting via single nonlinear terms. This discussion provides the foundation for the treatment of nonintegrable systems in the companion paper.

Kueny, C.S.; Morrison, P.J.

1994-11-01

81

The geometry of chaos: Dynamics of a nonlinear second-order difference equation  

Microsoft Academic Search

The nonlinear second-order difference equationx\\u000a n+1=axn(1-xn?1), where 0?x\\u000a nX?1 anda ?1, is examined from varying points of view, analytical, numerical and geometrical. An analytic expression is obtained for\\u000a an invariant attracting curveC\\u000a ? (a) in phase space, which becomes the central object of study. This basic curve, which replaces the simple parabolic shape typical\\u000a of many analogous first-order models, may

J. R. Pounder; Thomas D. Rogers

1980-01-01

82

Stabilization of chaos systems described by nonlinear fractional-order polytopic differential inclusion.  

PubMed

In this paper, sliding mode control is utilized for stabilization of a particular class of nonlinear polytopic differential inclusion systems with fractional-order-0?

Balochian, Saeed; Sedigh, Ali Khaki

2012-03-01

83

Periodic solutions and chaos in a non-linear model for the delayed cellular immune response  

NASA Astrophysics Data System (ADS)

We model the cellular immune response using a set of non-linear delayed differential equations. We observe that the stationary solution becomes unstable above a critical immune response time. The exponents characterizing the approach to this bifurcation point as well as the critical slow dynamics are obtained. In the periodic regime, the minimum virus load is substantially reduced with respect to the stationary solution. Further increasing the delay time, the dynamics display a series of bifurcations evolving to a chaotic regime characterized by a set of 2D portraits.

Canabarro, A. A.; Gléria, I. M.; Lyra, M. L.

2004-10-01

84

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

PubMed

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

Ugulava, A; Chotorlishvili, L; Nickoladze, K

2004-08-30

85

Chaos in Computing the Environmental Interface Temperature: Nonlinear Dynamic and Complexity Analysis of Solutions  

NASA Astrophysics Data System (ADS)

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

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

2013-10-01

86

Nonlinear time series modeling and prediction using functional networks. Extracting information masked by chaos  

NASA Astrophysics Data System (ADS)

Functional networks are a recently introduced extension of neural networks which deal with general functional models instead of sigmoidal-like ones. In this paper we show that functional network architectures provide simple and efficient techniques to model nonlinear time series. To this aim, the neural functions are approximated by finite combinations of known functions from a given family (polynomials, Fourier expansions, etc.) and the associated coefficients are estimated from data. In this paper we present two architectures from the same functional networks family, introducing efficient learning algorithms leading to error functions with a single global minimum that need not to be learned by an iterative process. We demonstrate the effectiveness of these models by applying them to several examples, including data from the Hénon, Holmes, Lozi and Burgers maps. Finally, we show that these models can also be used to extract information masked in chaotic time series.

Castillo, E.; Gutiérrez, J. M.

1998-07-01

87

Simultaneous nonlinearity and dispersion compensation into an embedded link: Experimental demonstration  

Microsoft Academic Search

We experimentally demonstrate for the first time, simultaneous compensation of nonlinearity and dispersion into an embedded link with strongly asymmetrical power profiles. Two configurations satisfying the mid-nonlinearity-temporal-inversion principle are tested.

P. Minzioni; I. Cristiani; V. Degiorgio; L. Marazzi; M. Martinelli; C. Langrock; M. M. Fejer

2006-01-01

88

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

SciTech Connect

In Part I of this work [Phys. Plasmas {bold 2}, 1926 (1995)], the behavior of linearly stable, integrable systems of waves in a simple plasma model was described using a Hamiltonian formulation. Explosive instability arose from nonlinear coupling between positive and negative energy modes, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. The time evolution is modeled with an explicit symplectic integrator derived using Lie algebraic methods. For amplitudes large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region in phase space. Diffusive growth then leads to explosive instability, effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, slow growth via Arnold diffusion might still lead to instability; however, this was not observed in numerical experiments. The diffusion rate is probably underestimated in this simple model. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

Kueny, C.S.; Morrison, P.J. [Department of Physics and Institute for Fusion Studies, The University of Texas at Austin, Austin, Texas 78712 (United States)

1995-11-01

89

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

NASA Astrophysics Data System (ADS)

In Part 1 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 coupling between modes of positive and negative energy, with well-defined threshold amplitudes depending on the physical parameters. In this concluding paper, the nonintegrable case is treated numerically. Several sets of waves are considered, comprising systems of two and three degrees of freedom. The time evolution is modelled with an explicit symplectic integration algorithm derived using Lie algebraic methods. When initial wave amplitudes are large enough to support two-wave decay interactions, strongly chaotic motion destroys the separatrix bounding the stable region for explosive triplets. Phase space orbits then experience diffusive growth to amplitudes that are sufficient for explosive instability, thus effectively reducing the threshold amplitude. For initial amplitudes too small to drive decay instability, small perturbations might still grow to arbitrary size via Arnold diffusion. Numerical experiments do not show diffusion in this case, although the actual diffusion rate is probably underestimated due to the simplicity of the model.

Kueny, C. S.; Morrison, P. J.

1995-05-01

90

Filtering nonlinear spatio-temporal chaos with autoregressive linear stochastic models  

NASA Astrophysics Data System (ADS)

Fundamental barriers in practical filtering of nonlinear spatio-temporal chaotic systems are model errors attributed to the stiffness in resolving multiscale features. Recently, reduced stochastic filters based on linear stochastic models have been introduced to overcome such stiffness; one of them is the Mean Stochastic Model (MSM) based on a diagonal Ornstein-Uhlenbeck process in Fourier space. Despite model errors, the MSM shows very encouraging filtering skill, especially when the hidden signal of interest is strongly chaotic. In this regime, the dynamical system statistical properties resemble to those of the energy-conserving equilibrium statistical mechanics with Gaussian invariant measure; therefore, the Ornstein-Uhlenbeck process with appropriate parameters is sufficient to produce reasonable statistical estimates for the filter model.In this paper, we consider a generalization of the MSM with a diagonal autoregressive linear stochastic model in Fourier space as a filter model for chaotic signals with long memory depth. With this generalization, the filter prior model becomes slightly more expensive than the MSM, but it is still less expensive relative to integrating the perfect model which is typically unknown in real problems. Furthermore, the associated Kalman filter on each Fourier mode is computationally as cheap as inverting a matrix of size D, where D is the number of observed variables on each Fourier mode (in our numerical example, D=1). Using the Lorenz 96 (L-96) model as a testbed, we show that the non-Markovian nature of this autoregressive model is an important feature in capturing the highly oscillatory modes with long memory depth. Second, we show that the filtering skill with autoregressive models supersedes that with MSM in weakly chaotic regime where the memory depth is longer. In strongly chaotic regime, the performance of the AR(p) filter is still better or at least comparable to that of the MSM. Most importantly, we find that this reduced filtering strategy is not as sensitive as standard ensemble filtering strategies to additional intrinsic model errors that are often encountered when model parameters are incorrectly specified.

Kang, Emily L.; Harlim, John

2012-06-01

91

Coherence and chaos in condensed matter  

SciTech Connect

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

Bishop, A.R.

1989-01-01

92

Duffing Chaos Model  

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 - x²) = 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

93

Fire!, Probability, and Chaos  

NSDL National Science Digital Library

This lesson is designed to introduce students to the concept of chaos and how it relates to probability. The lesson briefly delves into the ideas of mean and variance as well. This lesson provides links to discussions and activities related to chaos as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one. Note, reading level is not indicated because the lesson does not include student reading material.

2010-01-01

94

Chaos Rules  

NSDL National Science Digital Library

This Physics Central feature provides historical background for chaos theory. It also describes three recent investigations in this field--weather patterns, population dynamics, and the dripping faucet.

2006-06-30

95

A Prime Case of Chaos  

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

96

Chaos Theory.  

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

97

Prime Case of Chaos  

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

98

Efficient nonlinearity cancellation through optical phase conjugation into an embedded link with asymmetrical power profiles  

Microsoft Academic Search

We experimentally demonstrate, for the first time, that nonlinearity compensation into an embedded link with strongly asymmetrical power profiles can be obtained using a properly modified phase conjugation setup

P. Minzioni; I. Cristiani; V. Degiorgio; L. Marazzi; A. Colciago; M. Martinelli; C. Langrock; M. M. Fejer

2006-01-01

99

Quantum Correlations, Chaos and Information  

NASA Astrophysics Data System (ADS)

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

Madhok, Vaibhav

100

Long and short delay feedback on one-link nonlinear forearm with coactivation  

Microsoft Academic Search

Control strategies for a one-link model of the human forearm system are presented. Three attributes of the human forearm are implemented in the second order nonlinear model: neural transmission delays in the feedback paths, nonlinear behavior of the spindle reflex, and stiffness regulation through coactivation. Three feedback loops are present in the model: intrinsic feedback (undelayed) from the actuators, spindle

John H. Gossett; Bradley D. Clymer; Hooshang Hemami

1994-01-01

101

Chaos Theory and the Problem of Change in Family Systems  

Microsoft Academic Search

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

102

Experimental demonstration of nonlinearity and dispersion compensation in an embedded link by optical phase conjugation  

Microsoft Academic Search

We report in this letter, the experimental demonstration of simultaneous dispersion and nonlinearity compensation in an embedded link characterized by strongly asymmetrical power profiles. This result is obtained by using a highly efficient optical phase conjugator based on a periodically poled lithium-niobate waveguide, combined with two small dispersion-compensating elements properly inserted in the link.

Paolo Minzioni; Ilaria Cristiani; Vittorio Degiorgio; Lucia Marazzi; Mario Martinelli; Carsten Langrock; M. M. Fejer

2006-01-01

103

Chaos in laser-matter interactions  

Microsoft Academic Search

There is much interest in deterministic chaos which can appear in nonlinear dynamical systems. Various nonlinear systems in quantum optics have been investigated and found to admit chaotic behavior with well-defined routes to chaos. For instance, the well-known Maxwell-Bloch equations for a Doppler-broadened, unidirectional ring laser have been found to have chaotic behavior for parameters in the region of the

M. L. Shih

1985-01-01

104

Application of Chaos Theory to the Modeling of Compressed Video  

Microsoft Academic Search

We apply nonlinear chaos theory in modeling and forecasting variable-bit-rate (VBR) video sequences. Nonlinear chaos modeling offers an alternative approach to stochastic (typically, linear) approaches, with the advantages of lower dimensionality and more determinism. However, the goodness of its predictions strongly depends on the accuracy with which the dimensionality of a chaotic model is estimated from empirical data. The contributions

Ahmad Alkhatib; Marwan Krunz

2000-01-01

105

The Chaos Theory of Careers.  

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

106

Non-Linear vibrations and chaos in harmonically excited rectangular plates with one-to-one internal resonance  

Microsoft Academic Search

Nonlinear flexural vibrations of a rectangular plate with uniform stretching are studied for the case when it is harmonically excited with forces acting normal to the midplane of the plate. The physical phenomena of interest here arise when the plate has two distinct linear modes of vibration with nearly the same natural frequency. It is shown that, depending on the

S. I. Chang; A. K. Bajaj; C. M. Krousgrill

1993-01-01

107

Fractals, Chaos  

NSDL National Science Digital Library

Paul Bourke of the Astrophysics and Supercomputing department at Swinburne University of Technology is the author of this massive resource on fractals and chaos. He gives examples of many different kinds and classes of fractals, including the Mandelbrot set and various attractors; and brief explanations accompany each one. A substantial introduction to fractals covers the underlying principles and connection to chaos theory. Many stunning, high resolution fractal image galleries show elaborate patterns and colors. Examples of C and PovRay code used to create the remarkable images are provided. Bourke's homepage has many other sections of tutorials, papers, and notes on a diverse range of subjects.

2003-01-01

108

Annotated bibliography of chaos for occupational therapy.  

PubMed

Given the level of complexity at which the practice of occupational therapy operates, chaos may be the key to fresh insight into the nature of occupation. This article, through an innovative scholarly format-the annotation-presents essential concepts of chaos theory which are relevant for occupational therapy. A rationale for the importance of chaos theory and complexity science is presented and the limited extent to which chaos theory has been addressed in the occupational therapy literature is identified. Occupational therapy links to chaos and complexity are delineated and explained based upon a review of fourteen articles appearing in peer reviewed journals over a five year period (1993-1998), which are presented in three categories: (a) interdisciplinary applications, (b) mental health and creativity applications, and (c) educational and research applications. Conclusions about the relevance of chaos theory to occupational therapy are presented in the last section of the paper. PMID:23952063

Royeen, Charlotte Brasic; Luebben, Aimee J

2002-01-01

109

Chaos and microbial systems  

SciTech Connect

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 forded double-Monod equations, a model for a predator and a prey in a chemostat with periodic variation of inflowing substrate, suggested that simple microbial systems might provide the perfect framework for determining the efficacy and relevance of the new nonlinear dynamics in dealing with complex population dynamics. Progress in two areas of research, 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 also judge the usefulness of various new techniques of nonlinear dynamics to the study of populations) is reported.

Kot, M.

1991-01-01

110

Nonlinearity Compensation in a Fiber-Optic Link by Optical Phase Conjugation  

Microsoft Academic Search

This article is intended as a guide to the techniques for nonlinearity compensation in a fiber-optic communication link based on optical phase conjugation. In the first part, the basics of the phase conjugation process are illustrated from both a mathematical and physical point of view. Then, the more commonly used devices for optical phase conjugation are described, with particular attention

Paolo Minzioni

2009-01-01

111

Chaos & Fractals  

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

112

Dolphin Chaos  

NSDL National Science Digital Library

Dolphins have an uncanny sense of sonar, based partly on their ability to figure out exactly what type of sound signal to use to analyze their surroundings. This radio broadcast reports on research using chaos theory to analyze how the dolphin does this. The clip is 2 minutes in length.

113

Physicalism, Chaos and Reductionism  

NASA Astrophysics Data System (ADS)

In addition to ignoring the severe practical problems posed by decoherence phenomena, quantum mind hypotheses are motivated by a misunderstanding of the nature of classical (i. e. nonquantum) dynamics. As presently understood, nonlinear dynamical systems — of which the brain is clearly one — exhibit the twin phenomena of chaos and emergence. The first of these impedes reductionist formulations as does quantum theory, and the second leads to hierarchical structures in biological organisms and cognitive systems, which are difficult to analyze reductively. Thus a quantum mind theory must rest on empirical evidence rather than philosophical speculation.

Scott, Alwyn

114

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

115

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

116

Major Depression with Ischemic Heart Disease: Effects of Paroxetine and Nortriptyline on Measures of Nonlinearity and Chaos of Heart Rate  

Microsoft Academic Search

Depression is associated with increased cardiovascular mortality in patients with preexisting cardiac illness. A decrease in cardiac vagal function as suggested by a decrease in heart rate variability (HRV) or heart period variability has been linked to sudden death in patients with cardiac disease as well as in normal controls. Recent studies have shown decreased vagal function in cardiac patients

Vikram K. Yeragani; Steven Roose; Mallika Mallavarapu; R. K. A. Radhakrishna; Vanessa Pesce

2002-01-01

117

Chaos-Induced Diffusion in a Nonlinear Dissipative Mathieu Equation for a Charged Fine Particle in an AC Trap  

NASA Astrophysics Data System (ADS)

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

Ishizaki, Ryuji; Hata, Hiroki; Shoji, Tatsuo

2011-04-01

118

Inversion-based nonlinear control of robot arms with flexible links  

Microsoft Academic Search

The design of inversion-bas ed nonlinear control laws solving the problem of accurate trajectory tracking for robot arms having flexible links is considered. It is shown that smooth joint trajectories can always be exactly reproduced preserving internal stability of the closed-loop system. The interaction between the Lagrangian\\/as- sumed modes modeling approach and the complexity of the resulting inversion control laws

Alessandro De Luca; Bruno Sicilianot

1993-01-01

119

Adaptively combined FIR and functional link artificial neural network equalizer for nonlinear communication channel.  

PubMed

This paper proposes a novel computational efficient adaptive nonlinear equalizer based on combination of finite impulse response (FIR) filter and functional link artificial neural network (CFFLANN) to compensate linear and nonlinear distortions in nonlinear communication channel. This convex nonlinear combination results in improving the speed while retaining the lower steady-state error. In addition, since the CFFLANN needs not the hidden layers, which exist in conventional neural-network-based equalizers, it exhibits a simpler structure than the traditional neural networks (NNs) and can require less computational burden during the training mode. Moreover, appropriate adaptation algorithm for the proposed equalizer is derived by the modified least mean square (MLMS). Results obtained from the simulations clearly show that the proposed equalizer using the MLMS algorithm can availably eliminate various intensity linear and nonlinear distortions, and be provided with better anti-jamming performance. Furthermore, comparisons of the mean squared error (MSE), the bit error rate (BER), and the effect of eigenvalue ratio (EVR) of input correlation matrix are presented. PMID:19244019

Zhao, Haiquan; Zhang, Jiashu

2009-02-24

120

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

SciTech Connect

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

121

Monitoring chaos of cardiac rhythms  

SciTech Connect

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

122

Chaos in Atomic Physics  

NASA Astrophysics Data System (ADS)

Preface; 1. Introduction; 2. Chaos: tools and concepts; 3. Chaos in classical mechanics; 4. Chaos in quantum mechanics; 5. The kicked rotor: paradigm of chaos; 6. Microwave-driven surface state electrons; 7. The hydrogen atom in a strong magnetic field; 8. The kicked hydrogen atom; 9. Chaotic scattering with CsI molecules; 10. The helium atom; 11. Chaos in atomic physics: state of the art and research directions; References; Index.

Blümel, R.; Reinhardt, W. P.

2005-08-01

123

Control of Chaos in Thin Films at Ferromagnetic Resonance  

Microsoft Academic Search

Recent results of controlling chaos in many experimental systems have yielded interesting results in nonlinear dynamics and suggest possible applications. Since thin magnetic films at ferromagnetic resonance (FMR) have long been known to display chaotic behavior, this would appear to be a promising system in which to control chaos. Through small control perturbations to the static field applied to magnetic

Derrick William Peterman

1996-01-01

124

Chaos/Complexity Science and Second Language Acquisition.  

ERIC Educational Resources Information Center

|Discusses the similarities between the science of chaos/complexity and second language acquisition (SLA). Notes that chaos/complexity scientists focus on how disorder yields to order and on how complexity arises in nature. Points out that the study of dynamic, complex nonlinear systems is meaningful in SLA as well. (78 references) (Author/CK)|

Larsen-Freeman, Diane

1997-01-01

125

Applying Chaos Theory to Lesson Planning and Delivery  

ERIC Educational Resources Information Center

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

Cvetek, Slavko

2008-01-01

126

Dynamical symmetry breaking and chaos in Duffing's equation  

SciTech Connect

In certain frequency ranges a nonlinear damped and driven oscillator will respond asymmetri-cally even though the potential energy is a single symmetric well. This dynamical symmetry breaking heralds the onset of a period doubling transition to chaos.

Olson, C.L.; Olsson, M.G. (Department of Physics, University of Wisconsin, Madison, Wisconsin (USA))

1991-10-01

127

Chaos and microbial systems  

SciTech Connect

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

128

Embrace the Chaos  

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…

Huwe, Terence K.

2009-01-01

129

Chaos, External Noise and Fredholm Theory  

NASA Astrophysics Data System (ADS)

The Fredholm theory of integral equations is applied to the Perron-Frobenius equation which determines the invariant measure of nonlinear difference equations. The resultant Fredholm determinant D is identical to 1/?. where ? is the Artine-Mazure-Ruelle ?-function. From the investigation of D we get the observable condition of the invariant measure of chaos, its stability against external noise, etc.

Oono, Y.; Takahashi, Y.

1980-05-01

130

Coherence and chaos in extended dynamical systems  

SciTech Connect

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

131

Optical link upgrade by dispersion and nonlinearity management technique realized by compensating optical cable coiled around of fiber optic closure  

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

132

Chaos in plasma simulation and experiment  

SciTech Connect

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

133

Reflection-antisymmetric spatiotemporal chaos under field-translational invariance  

NASA Astrophysics Data System (ADS)

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 ?x2u?x3u is important to make a nontrivial dynamics, and show that the nonlinear dynamical equation having this term produces a turbulent dynamics.

Matsuo, Miki Y.; Sano, Masaki

2012-03-01

134

Chaos and irregularity in karst percolation  

NASA Astrophysics Data System (ADS)

This paper focuses on analyzing chaos in cave percolation water drip rates, which has implications for flow routing in fractured media and on the use of speleothems for paleoclimate reconstructions. It has been shown that the physics of dripping faucets involve a set of non-linear equations leading to chaotic drip rate, meaning that, for a given drip rate, the interval between individual drops can vary greatly. It can be expected that drip waters supplying stalagmites show similar properties, and consequently the dependency between water flux and stalagmite growth rate or geochemistry could be more complicated than usually assumed. We used high-frequency monitoring of two contrasting drips in a cave in Australia, and identified chaos in cave drip rate. Our findings also indicate that the occurrence of chaos can give insights into flow routing in fractured media.

Mariethoz, Gregoire; Baker, Andy; Sivakumar, Bellie; Hartland, Adam; Graham, Peter

2012-12-01

135

Role of grains and weak links in the nonlinear magnetic response of Y-Ba-Cu-O  

SciTech Connect

We present a study of the field dependence of the remanent nonlinear magnetic response induced in sintered Y-Ba-Cu-O samples by momentary application of a dc magnetic field {ital H}. The results show that, contrary to theoretical predictions, the remanent nonlinear response depends strongly on {ital H}. We attribute this behavior to weak links subjected to internal fields induced by flux trapped within the grains. To support this view, we present an extensive comparison between ac and dc data in the same samples. This comparison clarifies the role of grains and of weak links in various field regimes, and demonstrates the relationship between the remanent nonlinear response and the trapped flux.

Shaulov, A. (Department of Physics, Bar-Ilan University, 52 100 Ramat-Gan, Israel (IL) Philips Laboratories, North American Philips Corporation, Briarcliff-Manor, New York 10510 (USA)); Yeshurun, Y.; Shatz, S.; Hareuveni, R.; Wolfus, Y. (Department of Physics, Bar-Ilan University, 52 100 Ramat-Gan (Israel)); Reich, S. (Department of Materials Research, Weizmann Institute, Rehovot (Israel))

1991-02-01

136

100G upgrade over legacy submarine dispersion-managed fiber link using fiber nonlinearity compensation and maximum likelihood sequence estimation  

Microsoft Academic Search

The maximum transmission reach of 127 Gb\\/s DP-QPSK over legacy DMF link is extended to 4,800 km with 7.4 dB Q-factor using hybrid nonlinearity compensation and maximum likelihood sequence estimation, amounting to ?37% distance increase.

Shaoliang Zhang; Eduardo Mateo; Lei Xu; Ming-Fang Huang; Fatih Yaman; Yin Shao; Ting Wang; Yoshihisa Inada; Takanori Inoue; Takaaki Ogata; Yasuhiro Aoki

2012-01-01

137

Replication of chaos  

NASA Astrophysics Data System (ADS)

We propose a rigorous method for replication of chaos from a prior one to systems with large dimensions. Extension of the formal properties and features of a complex motion can be observed such that ingredients of chaos united as known types of chaos, Devaney's, Li-Yorke and obtained through period-doubling cascade. This is true for other appearances of chaos: intermittency, structure of the chaotic attractor, its fractal dimension, form of the bifurcation diagram, the spectra of Lyapunov exponents, etc. That is why we identify the extension of chaos through the replication as morphogenesis. To provide rigorous study of the subject, we introduce new definitions such as chaotic sets of functions, the generator and replicator of chaos, and precise description of ingredients for Devaney and Li-Yorke chaos in continuous dynamics. Appropriate simulations which illustrate the chaos replication phenomenon are provided. Moreover, in discussion form we consider inheritance of intermittency, replication of Shil'nikov orbits and quasiperiodical motions as a possible skeleton of a chaotic attractor. Chaos extension in an open chain of Chua circuits is also demonstrated.

Akhmet, M. U.; Fen, M. O.

2013-10-01

138

Detecting chaos in heavy-noise environments  

NASA Astrophysics Data System (ADS)

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.

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

2011-04-01

139

Parabolic Resonance: A Route to Hamiltonian Spatiotemporal Chaos  

SciTech Connect

We show that initial data near an unperturbed stable plane wave can evolve into a regime of spatiotemporal chaos in the slightly forced conservative periodic one-dimensional nonlinear Schroedinger equation. Statistical measures are employed to demonstrate that this spatiotemporal chaos is intermittent: there are windows in time for which the solution gains spatial coherence. The parameters and initial profiles that lead to such intermittency are predicted by utilizing a novel geometrical description of the integrable unforced equation.

Shlizerman, Eli; Rom-Kedar, Vered [Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Post Office Box 26, Rehovot 76100 (Israel)

2009-01-23

140

The chaos paradigm: developments and applications in engineering and science  

SciTech Connect

These proceedings are a compilation of technical topics presented at the Office of Naval Research (ONR)/Naval Undersea Warfare Center (NUWS) Technical Conference on Nonlinear Dynamics and Full-spectrum processing. The topics discussed consisted of synchronization and control of chaos, mechanical sources of chaos, turbulences, and advanced signal processing methods. There were eighteen papers presented at the conference and none is abstracted for the Energy Science and Technology database. (AIP)

Katz, R.A. (ed.) (Naval Undersea Warfare Center, New London, Connecticut (United States))

1994-01-01

141

THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT  

SciTech Connect

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

142

Nonlinear Dynamics in Semiconductor Lasers and VCSELs  

Microsoft Academic Search

The studies of dynamics properties for these lasers are important not only from a fundamental physical aspect of nonlinear dynamics and chaos but also applications. Both edge-emitting semiconductor lasers with external perturbations and VCSELs with and without external perturbations are excellent models for chaos systems, since a rich variety of nonlinear dynamics can be observed. Also these chaotic lasers are

Junji Ohtsubo

2007-01-01

143

"Chaos Rules" Revisited  

ERIC Educational Resources Information Center

|About 20 years ago, while lost in the midst of his PhD research, the author mused over proposed titles for his thesis. He was pretty pleased with himself when he came up with "Chaos Rules" (the implied double meaning was deliberate), or more completely, "Chaos Rules: An Exploration of the Work of Instructional Designers in Distance Education." He…

Murphy, David

2011-01-01

144

Teaching as Chaos  

ERIC Educational Resources Information Center

|In this article, the authors advance a metaphor born of chaos theory that views the college classroom as a complex dynamical system. The authors reason further that "teaching as chaos" provides a more accurate representation of the teaching-learning process than the existing linear scientific metaphors on which traditional learning assessments…

Moseley, Bryan; Dustin, Daniel

2008-01-01

145

Chaos, Complexity and Deterrence.  

National Technical Information Service (NTIS)

Chaos theory in the West (considerable work on chaos was also conducted in the Soviet Union) developed from the 1960s work of meteorologist Edward Lorenz. Lorenz developed a simple meteorological model based on differential equations. When he ran his mode...

V. Valle

2000-01-01

146

Teaching as Chaos  

ERIC Educational Resources Information Center

In this article, the authors advance a metaphor born of chaos theory that views the college classroom as a complex dynamical system. The authors reason further that "teaching as chaos" provides a more accurate representation of the teaching-learning process than the existing linear scientific metaphors on which traditional learning assessments are…

Moseley, Bryan; Dustin, Daniel

2008-01-01

147

Cyberterrorism: Postmodern State of Chaos  

Microsoft Academic Search

This paper examines cyberterrorism and its potential to create a postmodern state of chaos. In general, chaos refers to a state of extreme confusion and disorder. This analysis breaks new ground in that it describes chaos theory as a foundation for better understanding cyberterrorism and explains how chaos theory and game theory are tightly coupled. The author also contrasts modern,

Jonathan Matusitz

2008-01-01

148

Cyberterrorism: Postmodern State of Chaos  

Microsoft Academic Search

This paper examines cyberterrorism and its potential to create a postmodern state of chaos. In general, chaos refers to a state of extreme confusion and disorder. This analysis breaks new ground in that it describes chaos theory as a foundation for better understanding cyberterrorism and explains how chaos theory and game theory are tightly coupled. The author also contrasts modern,

Jonathan Matusitz

2010-01-01

149

Chaos and spectral analyses of heart rate variability during head-up tilting in essential hypertension  

Microsoft Academic Search

To investigate nonlinear and linear components of heart rate variability (HRV) in essential hypertension (EHT), we analyzed HRV by chaos and spectral analyses in patients with EHT (n=18) and normotensives (n=10) during head-up tilting. We used the correlation dimension (CD) and Lyapunov exponents as the parameters of chaos. The CD, an index of complexity, was lower at rest in EHT

Shuntaro Kagiyama; Akira Tsukashima; Isao Abe; Shinichiro Fujishima; Susumu Ohmori; Uran Onaka; Yusuke Ohya; Koji Fujii; Takuya Tsuchihashi; Masatoshi Fujishima

1999-01-01

150

Solitons in the midst of chaos  

SciTech Connect

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

Seghete, Vlad; Menyuk, Curtis R.; Marks, Brian S. [Department of Computer Science and Electrical Engineering, University of Maryland Baltimore County, 1000 Hilltop Circle, Baltimore, Maryland 21250 (United States); Department of Statistics and Department of Psychological and Brain Sciences, 1101 East 10th Street, PY 190A, Bloomington, Indiana 47405 (United States)

2007-10-15

151

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

152

Hierarchical interpretation of nonlinear relationships linking yellowfin tuna (Thunnus albacares) distribution to the environment in the  

Microsoft Academic Search

Using generalized additive models, we show evidence for nonlinear relationships between various hydrologi- cal factors and age-structured catch per unit effort of Atlantic yellowfin tuna ( Thunnus albacares) for two fishing fleets. Catchability effects are distinguished from tuna environmental preference effects in the catch per unit effort variability. With respect to catchability, an important nonlinear effect of local fishing effort

Atlantic Ocean; Olivier Maury; Didier Gascuel; Francis Marsac; Alain Fonteneau; Anne-Laure De Rosa

2001-01-01

153

Chaos and Galaxy Evolution  

NASA Astrophysics Data System (ADS)

This talk summarises a combined theoretical and numerical investigation of the role of chaos and transient chaos in time-dependent Hamiltonian systems which aim to model elliptical galaxies. The existence of large amounts of chaos in near-equilibrium configurations is of potential importance because configurations incorporating large numbers of chaotic orbits appear to be substantially more susceptible than nearly integrable systems to various irregularities associated with, e.g., internal substructures, satellite galaxies, and/or the effects of a high density environment. Alternatively, transient chaos, reflecting exponential sensitivity over comparatively short time intervals, can prove important by significantly increasing the overall efficiency of violent relaxation so as to facilitate a more rapid evolution towards a `well-mixed' equilibrium. Completely conclusive `smoking gun' evidence for chaos and chaotic mixing has not yet been obtained, although evidence for the presence of chaos can in principle be extracted from such data sets as provided by the Sloan Digital Sky Survey. Interestingly, however, arguments completely analogous to those applied to self-gravitating systems also suggest the presence of chaos in charged particle beams, a setting which is amenable to controlled experiments.

Kandrup, H. E.

2002-09-01

154

Hydroclimate variability and its statistical links to the large-scale climate indices for the Upper Chao Phraya River Basin, Thailand  

NASA Astrophysics Data System (ADS)

The local hydroclimates get impacts from the large-scale atmospheric variables via atmospheric circulation. The developing of their relationships could enhance the understanding of hydroclimate variability. This study focuses on the Upper Chao Phraya River Basin in Thailand in which rainfall is influenced by the Indian Ocean and tropical Pacific Ocean atmospheric circulation. The Southwest monsoon from the Indian Ocean to Thailand is strengthened by the temperature gradient between land and ocean. Thus, the anomalous sea surface temperature (SST) is systematically correlated with the monthly rainfall and identified as the best predictor based on the significant relationships revealed by cross-correlation analysis. It is found that rainfall, especially during the monsoon season in the different zones of study basin, corresponds to the different SST indices. This suggests that the region over the ocean which develops the temperature gradient plays a role in strengthening the monsoon. The enhanced gradient with the SST over the South China Sea is related to rainfall in High Rainfall Zone (HRZ); however, the anomalous SST over the Indian Ocean and the equatorial Pacific Ocean are associated with rainfall in Normal and Low Rainfall Zone (NRZ and LRZ) in the study area. Moreover, the identified predictors are related to the rainfall with lead periods of 1-4 months for the pre-monsoon rainfall and 6-12 months for the monsoon and dry season rainfall. The study results are very useful in developing rainfall forecasting models and consequently in the management of water resources and extreme events.

Singhrattna, N.; Babel, M. S.; Perret, S. R.

2009-10-01

155

Chaos and order in models of black hole pairs  

SciTech Connect

Chaos in the orbits of black hole pairs has by now been confirmed by several independent groups. While the chaotic behavior of binary black hole orbits is no longer argued, it remains difficult to quantify the importance of chaos to the evolutionary dynamics of a pair of comparable mass black holes. None of our existing approximations are robust enough to offer convincing quantitative conclusions in the most highly nonlinear regime. It is intriguing to note that, in three different approximations to a black hole pair built of a spinning black hole and a nonspinning companion, two approximations exhibit chaos and one approximation does not. The fully relativistic scenario of a spinning test mass around a Schwarzschild black hole shows chaos, as does the post-Newtonian Lagrangian approximation. However, the approximately equivalent post-Newtonian Hamiltonian approximation does not show chaos when only one body spins. It is well known in dynamical systems theory that one system can be regular while an approximately related system is chaotic, so there is no formal conflict. However, the physical question remains: Is there chaos for comparable mass binaries when only one object spins? We are unable to answer this question given the poor convergence of the post-Newtonian approximation to the fully relativistic system. A resolution awaits better approximations that can be trusted in the highly nonlinear regime.

Levin, Janna [Department of Physics and Astronomy, Barnard College, Columbia University, 3009 Broadway, New York, New York 10027 (United States)

2006-12-15

156

Preface: ``Nonlinear dynamics and acceleration mechanisms''  

NASA Astrophysics Data System (ADS)

The JIFT workshop on ``Nonlinear dynamics and acceleration mechanisms'' covered the following subjects: i) Stochastic properties of low dimensional nonlinear dynamical systems, ii) Nonlinear plasma phenomena and nonlinear dynamical system: a) Motion of charged particles in the tail of the geomagnetic sphere and magnetic field reconnection, b) Magnetic dynamo and chaos, c) Particle acceleration by coherent electromagnetic wave, and d) Chaos in free electron laser; iii) Chaos in chemical reactions, and iv) Stability of particle orbits in accelerators and toroidal magnetic fields in fusion devices. The plasma confinement by magnetic fields is also discussed. (AIP)

Ichikawa, Y. H.; Tajima, T.

1991-06-01

157

Quantum chaos in Aharonov-Bohm oscillations  

SciTech Connect

Aharonov-Bohm oscillations in a mesoscopic ballistic ring are considered under the influence of a resonant magnetic field with one and two frequencies. The authors investigate the oscillations of the time-averaged electron energy at zero temperature in the regime of an isolated quantum nonlinear resonance and at the transition to quantum chaos, when two quantum nonlinear resonances overlap. It is shown that the time-averaged energy exhibits resonant behavior as a function of the magnetic flux, and has a ``staircase`` dependence on the amplitude of the external field. The delocalization of the quasi-energy eigenfunctions is analyzed.

Berman, G.P. [Los Alamos National Lab., NM (United States). Theoretical Div.; Campbell, D.K. [Univ. of Illinois, Urbana, IL (United States). Dept. of Physics; Bulgakov, E.N. [Kirensky Inst. of Physics, Krasnoyarsk (Russian Federation); Krive, I.V. [Ukrainian Academy of Sciences, Kharkov (Ukraine). Inst. for Low Temperature Physics and Engineering

1995-10-01

158

Half-Lives and Chaos  

NASA Astrophysics Data System (ADS)

The statistical nature of quantum mechanical transitions has often led to a comparison of half-lives of, say, nuclear transitions with the predictions of actuarial tables---although impossible to predict when an individual will transform, statistically one can obtain precise population predictions. For complex biological systems this is quite believable, but in ``simple" nuclear systems, the analogy is more questionable. Another way of looking at this is through feedback in non-linear systems. In many chaos games, e.g., varied, unpredictable starting points will always arrive at one or a few end points, but they take widely varying numbers of moves and routes to reach such end positions---this is the essence of chaotic attractors. Using the Uncertainty Principle to justify slightly varying initial states, one can play similar chaos games with quantum mechanical systems, and it is possible to arrive at the final destination(s) with predictable half-lives. Some simple examples of such transitions, as relating to nuclear transitions, will be presented.

McHarris, Wm. C.

1999-10-01

159

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

160

Chaos and Economics  

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

161

Chaos and fractals  

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

162

Chaos: Chto Delat  

SciTech Connect

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

163

Chaos in a Water Drop.  

NASA Astrophysics Data System (ADS)

Nature is chaotic. It appears to be more disorderly and random than orderly and regular. The path of a leaf in a rocky stream can appear as complex as the smoke from a cigarette or the outline of a cloud. In trying to model the path of a leaf in a rocky stream, the dynamical equations become rapidly complicated. A branch of scientific analysis know as Chaos has sprung up in the last few decades with techniques that can be applied to most of the physical sciences in an attempt to describe or categorize the various non-linear phenomena found in Nature. The aim of this paper is to provide an introduction to the study of chaotic behavior, with an emphasis on the potential teaching possibilities contained in some of the analysis. An appropriate beginning would be motion that is regular and "easy" to understand--stable motion. Along the way, various graphical representations will be developed that enable a clear viewing of the motion of the system under study. Next, the Logistic model will be used to gain an understanding of the nature of chaos; it is very comprehensive in representing the characteristics of chaos that will be studied in other systems. Another system studied is the three-dimensional Rossler model. In the study of the "dripping faucet", a time series of the periods between drips of water is recorded. Various techniques (collected from the introductory systems) are applied in an attempt to model the mechanism behind the water drops, or at least to characterize the graphical "animals" that we find. The water drop "attractor" is found to be chaotic, exhibiting many of the chaotic characteristics seen in other models. It is hoped that this work can be used as a primer for those students beginning a journey into Chaos, or as a reference tool for those already familiar with the topics enclosed. Many areas in this work were touched lightly; there is a rich un-tapped complexity still waiting future study. The waters here have only begun to be charted.

Schneider, Scott Dudley

164

Construction of classes of circuit-independent chaotic oscillators using passive-only nonlinear devices  

Microsoft Academic Search

Two generic classes of chaotic oscillators comprising four different configurations are constructed. The proposed structures are based on the simplest possible abstract models of generic second-order RC sinusoidal oscillators that satisfy the basic condition for oscillation and the frequency of oscillation formulas. By linking these sinusoidal oscillator engines to simple passive first-order or second-order nonlinear composites, chaos is generated and

Ahmed S. Elwakil; Michael Peter Kennedy

2001-01-01

165

The Chinese chaos game  

Microsoft Academic Search

The yuan-dollar returns prior to the 2005 revaluation show a Sierpinski triangle in an iterated function system clumpiness test. Yet the fractal vanishes after the revaluation. The Sierpinski commonly emerges in the chaos game, where randomness coexists with deterministic rules (M.F. Barnsley, Fractals Everywhere, Academic Press, San Diego, 1988; H.O. Peitgen, H. Jurgens, D. Saupe, Chaos and Fractals: New Frontiers

Raul Matsushita; Iram Gleria; Annibal Figueiredo; Sergio Da Silva

2007-01-01

166

Fractal Patterns and Chaos Games  

ERIC Educational Resources Information Center

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

Devaney, Robert L.

2004-01-01

167

Fractal Patterns and Chaos Games  

ERIC Educational Resources Information Center

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

Devaney, Robert L.

2004-01-01

168

Three-Wave Interactions and Spatiotemporal Chaos  

NASA Astrophysics Data System (ADS)

Three-wave interactions form the basis of our understanding of many pattern-forming systems because they encapsulate the most basic nonlinear interactions. In problems with two comparable length scales, it is possible for two waves of the shorter wavelength to interact with one wave of the longer, as well as for two waves of the longer wavelength to interact with one wave of the shorter. Consideration of both types of three-wave interactions can generically explain the presence of complex patterns and spatiotemporal chaos. Two length scales arise naturally in the Faraday wave experiment, and our results enable some previously unexplained experimental observations of spatiotemporal chaos to be interpreted in a new light. Our predictions are illustrated with numerical simulations of a model partial differential equation.

Rucklidge, A. M.; Silber, M.; Skeldon, A. C.

2012-02-01

169

Nonlinear regulation, with internal stability, of a two link flexible robot arm  

Microsoft Academic Search

The problem of endpoint asymptotic tracking, with internal stability, of a two-link flexible robot arm is discussed. First the problem of exact tracking with bounded internal evolution is reviewed, and an approach for finding bounded solutions of the inverse dynamics is given. Then the linear regulator problem with internal stability is solved for the one-link case and extended to the

P. Lucibello

1989-01-01

170

Chaos in a three-species food chain  

Microsoft Academic Search

A continuous time model of a food chain incorporating nonlinear functional (and numerical) responses exhibits chaotic dynamics in long-term behavior when biologically reasonable parameter values are chosen. The appearance of chaos in this model suggests the chaotic dynamics may be common in natural food webs. One approach to the study of an ecological community begins with an important object: its

A. Hastings; T. Powell

1991-01-01

171

Hopf bifurcation and chaos in synchronous reluctance motor drives  

Microsoft Academic Search

This paper first presents the occurrence of Hopf bifurcation and chaos in a practical synchronous reluctance motor drive system. Based on the derived nonlinear system equation, the bifurcation analysis shows that the system loses stability via Hopf bifurcation when the d-axis component of its three-phase motor voltages loses its control. Moreover, the corresponding Lyapunov exponent calculation further proves the existence

Y. Gao; K. T. Chau

2004-01-01

172

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…

Sinn, Robb

2007-01-01

173

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

174

A Bayesian Approach for Nonlinear Structural Equation Models With Dichotomous Variables Using Logit and Probit Links  

Microsoft Academic Search

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 WinBUGS and R2WinBUGS to obtain Bayesian estimates of the unknown parameters, estimates of

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

2010-01-01

175

Stochastic chaos: An analog of quantum chaos.  

National Technical Information Service (NTIS)

Some intriguing connections between the properties of nonlinear, noise driven systems and the nonlinear dynamics of a particular set of Hamilton's equation are discussed. A large class of Fokker-Planck Equations, like the Schroedinger equation, can exhibi...

M. M. Millonas

1993-01-01

176

Chaos and noise  

NASA Astrophysics Data System (ADS)

Simple dynamical systems--with a small number of degrees of freedom--can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model.

He, Temple; Habib, Salman

2013-09-01

177

Chaos and noise.  

PubMed

Simple dynamical systems-with a small number of degrees of freedom-can behave in a complex manner due to the presence of chaos. Such systems are most often (idealized) limiting cases of more realistic situations. Isolating a small number of dynamical degrees of freedom in a realistically coupled system generically yields reduced equations with terms that can have a stochastic interpretation. In situations where both noise and chaos can potentially exist, it is not immediately obvious how Lyapunov exponents, key to characterizing chaos, should be properly defined. In this paper, we show how to do this in a class of well-defined noise-driven dynamical systems, derived from an underlying Hamiltonian model. PMID:24089959

He, Temple; Habib, Salman

2013-09-01

178

Time-dependent regimes of a tourism-based social–ecological system: Period-doubling route to chaos  

Microsoft Academic Search

The period-doubling route to chaos has occupied a prominent position and it is still object of great interest among the different complex phenomena observed in nonlinear dynamical systems. The reason of such interest is that such route to chaos has been observed in many physical, chemical and ecological models when they change over from simple periodic to complex aperiodic motion.

D. Lacitignola; I. Petrosillo; G. Zurlini

2010-01-01

179

Relation of Home Chaos to Cognitive Performance and Behavioral Adjustment of Pakistani Primary School Children  

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

180

Relation of Home Chaos to Cognitive Performance and Behavioral Adjustment of Pakistani Primary School Children  

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

181

Organized Chaos at Europa?  

NASA Astrophysics Data System (ADS)

Historically one of the most studied and yet least constrained of Europa’s terrains, chaos regions are likely indicators of a geologically active ice shell. Chaos terrain is generally characterized by broken ice “raft” relicts of the former surface embayed by a dark, hummocky matrix rich in non-ice material. Chaos features, though they bear resemblance to broken-up terrestrial sea-ice, are generally topographically higher than the surrounding plains. Interior to these features topographic variation can also be found. From a geophysical perspective, chaos terrain may offer the possibility to test models for Europa’s ice shell thickness, its rheological properties, and its dynamics, since they occur ubiquitously across the surface. The existence of chaos terrain has, in the past, been used to suggest that either the shell is thin, and thus large-scale melt-through events have taken place to create chaos, or that the shell is actively convecting, and thus that the chaos terrain is formed by diapirism associated with rising plumes. Partial melt and the movement of warm ice have also been suggested to contribute to the formation of chaos. While these formation models are strongly tied to an ice thickness assumption, it is agreed that the break-up of ice and the subsequent motion of the blocks is suggestive of a material that has been free to flow at some point; the nature of the “fluidization” has not been discovered. In terrestrial marine ice sheets, brine infiltration is known to occur in porous layers called firn that are formed by annual accretion of snow. At the seaward edge of the sheet, or through tidally-formed basal cracks, sea water can percolate inward through the porous layer and travel kilometers from the source. In the McMurdo Ice shelf, brine extends radially through the ice to 10’s of km from the source at the shelf edge. In the Larsen ice shelf, a brine-laden layer of ice exists that does not reach the seaward edge, arguing that infiltration has instead occurred from basal cracks. Brine infiltration occurs even at many degrees below the freezing point of the embaying brine. We have undertaken a study of how brine infiltration may operate on Europa and contribute to the formation of chaos terrain. Rising plumes within the shell may not be sufficient to melt or break the ice, however pressure melt driven by rising ice may promote the collection of enriched brines at the heads of plumes. If such activity can cause small scale cracks to form in the brittle lithospheric layer of Europa’s ice shell overlying large plumes, brines may percolate into the multiply fractured and porous upper ice. The fluid can then both break up existing, denser blocks and destroy more brittle regions, allowing for the formation of a matrix enhanced in non-ice materials while preserving blocks and allowing them to move. Such a process may explain the height of, as well as topographic variability within, chaos terrain. Our goal is to establish how orbital lidar and radar sounding observations of chaos terrain may be used to evaluate hypothesized ice shell properties and ice-ocean exchange processes.

Schmidt, B. E.; Blankenship, D. D.

2010-12-01

182

Chaos and The Changing Nature of Science and Medicine. Proceedings  

SciTech Connect

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

183

Decoherence, determinism and chaos.  

National Technical Information Service (NTIS)

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. elec...

H. P. Noyes

1994-01-01

184

A new chaos detector  

Microsoft Academic Search

This paper proposes a new detector for chaos. It is simpler and numerically less intensive than previous methods. It is more robust than previous methods. It works well even with short data sets (200 time scalar points), in the presence of noise (as low as 4 dB signal to noise ratio in stationary additive white Gaussian noise), and with severe

Paul V. Mcdonough; Joseph P. Noonan; G. R. Hall

1995-01-01

185

Design of robust controllers and a nonlinear observer for the control of a single-link flexible robotic manipulator  

NASA Astrophysics Data System (ADS)

Two robust nonlinear controllers along with a nonlinear observer have been developed in this study to control the rigid and flexible motions of a single-link robotic manipulator. The controllers and the observer have been designed based on a simplified model of the arm, which only accounts for the first elastic mode of the beam. The controllers consist of a conventional sliding mode controller (CSMC) and a fuzzy-sliding mode controller (FSMC). Moreover, the robust nonlinear observer has been designed based on the sliding mode methodology. The dynamic model, used in assessing the performances of the controllers and the observer, considers the first two elastic modes of the beam. The inclusion of the second elastic mode has been done to investigate the effects of unstructured uncertainties on the overall performance of the closed-loop system. The digital simulations have demonstrated the capability of the observer in yielding accurate estimates of the state variables in the presence of modeling uncertainties. Moreover, they served to prove the viability of using the observer to provide on-line estimates of the state variables for the computation of the control signals. The results have illustrated robust performances of the controllers and the observer in controlling the rigid and flexible motions of the manipulator in the presence of both structured and unstructured uncertainties. This was achieved irrespective of the differences in the initial conditions between the plant and the observer. Furthermore, the structural deformations, incurred by the beam at the onset of its movement, have been shown to be significantly reduced by fuzzy-tuning the ?-control parameter. The results have demonstrated the superiority of the FSMC over the CSMC in producing less oscillatory and more accurate response of the angular displacement at the base joint, in damping out the unwanted vibrations of the beam, and in requiring significantly smaller control torques.

Chalhoub, N. G.; Kfoury, G. A.; Bazzi, B. A.

2006-03-01

186

Microwave induced nonlinearity in low frequency biased YBCO superconducting weak link rings (abstract)  

Microsoft Academic Search

We fabricated weak link rings using YBCO thin films deposited on the single crystal MgO substrate by laser ablation. The dimensions of the microbridges in the rings were between 0.5–1 ? in length and 500 A?–0.5 ? in width which were made by focused ion beam milling. We biased the ring by Faraday induction voltage while monitoring the voltage across

Y. Huang; A. Widom; C. Vittoria

1993-01-01

187

Optical wavelet de-noising applied in multi-span nonlinear fiber links  

Microsoft Academic Search

In this work, optical wavelet de-noising with several different types of wavelets such as db4, coif4 and dmey wavelet was applied at the end of the 40Gbit\\/s multi-span intensity-modulated fiber communication systems. The results of numerical simulations carried out in different fiber links demonstrated that the optical wavelet de-noising method could remove the random amplitude fluctuation induced by the interaction

Qunfeng Shao; Xiaoping Zhang; Xiaoqiong Qi; Hu Li; Lian Xiang

2010-01-01

188

Chaos in neurons and its application: Perspective of chaos engineering  

NASA Astrophysics Data System (ADS)

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

Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki

2012-12-01

189

Speculations on Nonlinear Speculative Bubbles  

Microsoft Academic Search

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

190

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

PubMed

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

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

2008-09-29

191

Predicting chaos for infinite dimensional dynamical systems: the Kuramoto-Sivashinsky equation, a case study.  

PubMed

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. PMID:11607246

Smyrlis, Y S; Papageorgiou, D T

1991-12-15

192

Predicting chaos for infinite dimensional dynamical systems: the Kuramoto-Sivashinsky equation, a case study.  

PubMed Central

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

193

A Current-Sampling-Mode CMOS Arbitrary Chaos Generator Circuit Using Pulse Modulation Approach  

NASA Astrophysics Data System (ADS)

This paper proposes a new chaos generator circuit with a current sampling scheme. This circuit generates an arbitrary nonlinear function corresponding to the time-domain current waveform supplied from an external source by using a pulse phase modulation approach. The measurement results of a fabricated chip with TSMC 0.25 µm process technology demonstrate that the proposed circuit can generate chaos signals even if D/A conversion is used for nonlinear waveform generation, because a current integral by sampling with a short pulse smooths the quantized nonlinear function.

Atuti, Daisuke; Morie, Takashi; Aihara, Kazuyuki

194

Chaos in the brain: a short review alluding to epilepsy, depression, exercise and lateralization  

Microsoft Academic Search

Electroencephalograms (EEGs) reflect the electrical activity of the brain. Even when they are analyzed from healthy individuals, they manifest chaos in the nervous system. EEGs are likely to be produced by a nonlinear system, since a nonlinear system with at least 3 degrees of freedom (or state variables) may exhibit chaotic behavior. Furthermore, such systems can have multiple stable states

S. N. Sarbadhikari; K. Chakrabarty

2001-01-01

195

Weak-chaos ratchet accelerator  

NASA Astrophysics Data System (ADS)

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

Dana, Itzhack; Roitberg, Vladislav B.

2011-06-01

196

Nonlinear optical collagen cross-linking and mechanical stiffening: a possible photodynamic therapeutic approach to treating corneal ectasia  

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

197

Evolution of periodic states and chaos in two types of neuronal models  

NASA Astrophysics Data System (ADS)

Studies on how chaos theory may be applied to neural disorders is a very challenging theoretical problem. But, to determine the applications of chaos theory cellular functions, it is best to study the genesis of chaos and its characteristics using a minimal model of cellular excitability. In this paper we present two neuronal models which gives rise to interesting types of bursting and chaos. The first model is based on the model of Chay, in which the bursting of neuronal cells is caused by voltage- and time-dependent inactivation of calcium channels. The second model is based on Chay's work in which the bursting is caused by the conformational transformation of the calcium channels that is induced by binding of Ca2+ ion to the receptor site. With these two models, we elucidate how the periodic states and chaos can be evolved when the properties of two types of inward current change. Our bifurcation diagram reveals new types of bifurcations and chaos which were not seen in the other non-linear dynamic models. The predicted chaos from the models closely resembles that observed experimentally in neuronal cells. An implication of our finding is that chaos theory may be used to understand and improve the treatment of certain irregular activities in the brain.

Chay, Teresa R.; Fan, Yinshui

1993-11-01

198

Modeling physical uncertainties in dynamic stall induced fluid–structure interaction of turbine blades using arbitrary polynomial chaos  

Microsoft Academic Search

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

199

Wireless communication with chaos.  

PubMed

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

2013-04-29

200

The Chinese chaos game  

NASA Astrophysics Data System (ADS)

The yuan-dollar returns prior to the 2005 revaluation show a Sierpinski triangle in an iterated function system clumpiness test. Yet the fractal vanishes after the revaluation. The Sierpinski commonly emerges in the chaos game, where randomness coexists with deterministic rules (M.F. Barnsley, Fractals Everywhere, Academic Press, San Diego, 1988; H.O. Peitgen, H. Jurgens, D. Saupe, Chaos and Fractals: New Frontiers of Science, Springer, New York, 1992). Here, it is explained by the yuan's pegs to the US dollar, which made more than half of the data points close to zero. Extra data from the Brazilian and Argentine experiences do confirm that the fractal emerges whenever exchange rate pegs are kept for too long.

Matsushita, Raul; Gleria, Iram; Figueiredo, Annibal; da Silva, Sergio

2007-05-01

201

A chaos model of meandering rivers  

SciTech Connect

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

202

Nonlinear dynamics of magnetic vortices in single-crystal and ion-damaged NbSe2  

NASA Astrophysics Data System (ADS)

Nonlinear dynamics of magnetic flux lines in superconducting NbSe2 are studied using the vibrating-reed technique and a resonance-line-shape analysis. A yield point for plastic deformation of the flux-line lattice is linked to the onset of a dissipation anomaly previously associated with a flux-line lattice melting transition. The resonance (10 kHz range) of radiation-damaged samples bifurcates into patterned sidebands at high drives, with additional nonlinear response emerging above 200 kHz, which may signal the onset of chaos.

Zhang, J.; de Long, L. E.; Majidi, V.; Budhani, R. C.

1996-04-01

203

Counseling Chaos: Techniques for Practitioners  

ERIC Educational Resources Information Center

|The chaos theory of careers draws together a number of themes in current theory and research. This article applies some of these themes to career counseling. The chaos theory of careers is outlined, and a conceptual framework for understanding assessment and counseling issues that focuses on convergent and emergent qualities is presented. Three…

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

2006-01-01

204

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

205

Investigating Chaos in Ocean Acoustics.  

National Technical Information Service (NTIS)

Chaos is a term assigned to a class of motions in deterministic systems whose time history has a sensitive dependence on initial conditions. Such phenomenon has previously been shown to exhibit in ocean acoustics ray tracing, and called ray chaos by the o...

K. K. Yen J. Yan

1997-01-01

206

Counseling Chaos: Techniques for Practitioners  

ERIC Educational Resources Information Center

The chaos theory of careers draws together a number of themes in current theory and research. This article applies some of these themes to career counseling. The chaos theory of careers is outlined, and a conceptual framework for understanding assessment and counseling issues that focuses on convergent and emergent qualities is presented. Three…

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

2006-01-01

207

Quantitative indicator for semiquantum chaos  

NASA Astrophysics Data System (ADS)

By generalizing to a mixed-state environment the treatment recently given to a model advanced by Cooper et al. [Phys. Rev. Lett. 72, 1337 (1994)], we show that some characteristics of the so-called semiquantum chaos can be described by recourse to a special motion invariant of the problem, that thus becomes a chaos indicator.

Kowalski, A. M.; Martin, M. T.; Nuñez, J.; Plastino, A.; Proto, A. N.

1998-09-01

208

Applied Nonlinear Dynamics and Stochastic Systems Near The Millenium. Proceedings  

Microsoft Academic Search

These proceedings represent papers presented at the Applied Nonlinear Dynamics and Stochastic Systems conference held in San Diego, California in July 1997. The conference emphasized the applications of nonlinear dynamical systems theory in fields as diverse as neuroscience and biomedical engineering, fluid dynamics, chaos control, nonlinear signal\\/image processing, stochastic resonance, devices and nonlinear dynamics in socio-economic systems. There were 56

J. B. Kadtke; A. Bulsara

1997-01-01

209

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

210

Chaos from switched-capacitor circuits - Discrete maps  

Microsoft Academic Search

A special-purpose analog computer made of switched-capacitor circuits is presented for analyzing chaos and bifurcation phenomena in nonlinear discrete dynamical systems modeled by discrete maps. The performance of these circuit realization techniques is illustrated with experimental results taken from four switched-capacitor circuits designed for implementing four well-known discrete maps: the one-dimensional parabolic map, the one-dimensional piecewise linear map, the two-dimensional

Angel Rodriguez-Vazquez; Jose L. Huertas; Adoracion Rueda; Belen Perez-Verdu; Leon O. Chua

1987-01-01

211

Chaos from switched-capacitor circuits - Discrete maps  

NASA Astrophysics Data System (ADS)

A special-purpose analog computer made of switched-capacitor circuits is presented for analyzing chaos and bifurcation phenomena in nonlinear discrete dynamical systems modeled by discrete maps. The performance of these circuit realization techniques is illustrated with experimental results taken from four switched-capacitor circuits designed for implementing four well-known discrete maps: the one-dimensional parabolic map, the one-dimensional piecewise linear map, the two-dimensional Henon map, and the two-dimensional Lozi map.

Rodriguez-Vazquez, Angel; Huertas, Jose L.; Rueda, Adoracion; Perez-Verdu, Belen; Chua, Leon O.

1987-08-01

212

Nonlinear aspects of shock response in isolated accelerometers  

SciTech Connect

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

213

[Chaos, complexity and cardiology].  

PubMed

Science is an ever-changing discipline. Modern medical knowledge is based on science. Current medical paradigm is both linear and reductionist. There is a new general theory validated by computer's calculations named chaos and complexity theory. This new paradigm will probably have an impact on medical practice. Cardiovascular physiology may display fractal and/ or chaotic behavior. Computerized heart rhythm analyses enhanced our understanding of complex diseases otherwise not explainable by current linear-reductionist paradigms. Cases in point are diverse dysautonomia including orthostatic intolerance, cardiac X syndrome and fibromyalgia. Derived from this, new knowledge is a different diagnostic and therapeutic stance: scientific holism. PMID:22452867

Martínez-Lavín, Manuel

214

Cryptography with cycling chaos  

NASA Astrophysics Data System (ADS)

Periodic switching of cryptographic keys is commonly employed as a mechanism to enhance the security of encryption methods. In this Letter, cycling chaos, in which orbits of certain coupled iterated maps make periodic excursions between chaotic sets, is proposed as a new encryption approach that combines chaotic behavior with periodic switching of keys. The actual encryption process is similar to the one used by Baptista [Phys. Lett. A (1998) 50], except that now different chaotic attractors, and consequently different keys, are periodically switched to encrypt each character of a message. Advantages and disadvantages of this approach are also discussed.

Palacios, A.; Juarez, H.

2002-10-01

215

Between order and chaos  

NASA Astrophysics Data System (ADS)

What is a pattern? How do we come to recognize patterns never seen before? Quantifying the notion of pattern and formalizing the process of pattern discovery go right to the heart of physical science. Over the past few decades physics' view of nature's lack of structure--its unpredictability--underwent a major renovation with the discovery of deterministic chaos, overthrowing two centuries of Laplace's strict determinism in classical physics. Behind the veil of apparent randomness, though, many processes are highly ordered, following simple rules. Tools adapted from the theories of information and computation have brought physical science to the brink of automatically discovering hidden patterns and quantifying their structural complexity.

Crutchfield, James P.

2012-01-01

216

A STUDY OF PHAGOCYTOSIS IN THE AMEBA CHAOS CHAOS  

PubMed Central

The process of phagocytosis was investigated by observing the interactions between the ameba Chaos chaos and its prey (Paramecium aurelia), by studying food cup formation in the living cell, and by studying the fine structure of the newly formed cup using electron microscopy of serial sections. The cytoplasm surrounding the food cup was found to contain structures not seen elsewhere in the ameba. The results are discussed in relation to the mechanisms which operate during food cup formation.

Christiansen, Richard G.; Marshall, John M.

1965-01-01

217

Transition to spatiotemporal chaos via stationary branching shocks and holes  

NASA Astrophysics Data System (ADS)

Spatiotemporal chaos in the complex Ginzburg-Landau equation is known to be associated with a rapid increase in the density of defects, which are isolated points at which the solution amplitude is zero and the phase is undefined. Recently there have been significant advances in understanding the details and interactions of defects and other coherent structures, and in the theory of convective and absolute stability. In this paper, the authors exploit both of these advances to update and clarify the onset of spatiotemporal chaos in the particular case of the complex Ginzburg-Landau equation with zero linear dispersion. They show that very slow increases in the coefficient of nonlinear dispersion cause a shock-hole (defect) pair to develop in the midst of a uniform expanse of plane wave. This is followed by a cascade of splittings of holes into shock-hole-shock triplets, culminating in spatiotemporal chaos at a parameter value that matches the change in absolute stability of the plane wave. The authors demonstrate a close correspondence between the splitting events and theoretical predictions, based on the theory of absolute stability. They also use measures based on power spectra and spatial correlations to show that when the plane wave is convectively unstable, chaos is restricted to localised regions, whereas it is extensive when the plane wave is absolutely unstable.

Sherratt, Jonathan A.; Smith, Matthew J.

2012-10-01

218

Modeling of nonlinear metamaterials  

NASA Astrophysics Data System (ADS)

We report the results of a study to model the behavior of nonlinear metamaterials in the microwave frequency range composed of arrays of split-ring resonators combined with nonlinear circuit elements. The overall model consists of an array of coupled damped oscillators whose inter-element coupling is a function of signal amplitude, similar to that which exists in the Fermi-Pasta-Ulam system. [8] We note the potential occurrence of classical nonlinear effects including parametric coupling, FPU recurrence and chaos. These effects lead to nonlinear waves on the array which are a type of soliton particular to the form of nonlinearity that has been incorporated. We have studied, in particular, the nonlinear effects that arise from tunnel diodes embedded in the resonant circuits. We carry out simulations of the resulting circuit frequency response.

Colestock, P. L.; Reiten, M.; O'Hara, J.

2011-09-01

219

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

220

A Chaos Conveyor Belt  

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

221

Chaos Manager 2.23  

NSDL National Science Digital Library

As any physicist will tell you, managing chaos is difficult, if not impossible. Fortunately, this type of Âchaos refers primarily to the chaotic nature of maintaining an orderly and logical desktop calendar on oneÂs 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

222

On the chaos in gene networks.  

PubMed

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

2013-02-06

223

Adaptive functional systems: Learning with chaos  

NASA Astrophysics Data System (ADS)

We propose a new model of adaptive behavior that combines a winnerless competition principle and chaos to learn new functional systems. The model consists of a complex network of nonlinear dynamical elements producing sequences of goal-directed actions. Each element describes dynamics and activity of the functional system which is supposed to be a distributed set of interacting physiological elements such as nerve or muscle that cooperates to obtain certain goal at the level of the whole organism. During ``normal'' behavior, the dynamics of the system follows heteroclinic channels, but in the novel situation chaotic search is activated and a new channel leading to the target state is gradually created simulating the process of learning. The model was tested in single and multigoal environments and had demonstrated a good potential for generation of new adaptations.

Komarov, M. A.; Osipov, G. V.; Burtsev, M. S.

2010-12-01

224

The Chaos Within Sudoku  

PubMed Central

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

225

Nonlinear dynamics established in the ENSO  

SciTech Connect

A time series describing the El-Nino-Southern Oscillation (ENSO) is analyzed using the latest techniques of chaos theory. The methods which rely on resampling statistics were developed to more finely distinguish between nonlinearity and linear correlated noise. From the results significant nonlinear structure arising from ENSO dynamics on the monthly time scale is established. 14 refs., 4 figs.

Elsner, J.B. (Florida State Univ., Tallahassee (United States)); Tsonis, A.A. (Univ. of Wisconsin, Milwaukee (United States))

1993-02-05

226

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

227

Heart rate chaos as a mortality predictor in mild to moderate heart failure.  

PubMed

Linear and nonlinear indices of heart rate variability (HRV) have been shown to predict mortality in congestive heart failure (CHF). However, most nonlinear indices describe only the fractality or complexity of HRV but not the intrinsic chaotic properties. In the present study, we performed linear (time- and frequency-domain), complexity (sample entropy), fractal (detrended fluctuation analysis) and chaos (numerical titration) analyses on the HRV of 50 CHF patients from the United Kingdom heart failure evaluation and assessment of risk trial database. Receiver operating characteristic and survival analysis yielded the chaos level to be the best predictor of mortality (followed by low/high frequency power ratio, LF/HF), such that these indices were significant in both univariate and multivariate models. These results indicate the power of heart rate chaos analysis as a potential prognostic tool for CHF. PMID:18003141

Arzeno, Natalia M; Kearney, Mark T; Eckberg, Dwain L; Nolan, James; Poon, Chi-Sang

2007-01-01

228

Nonlinear waves: Dynamics and evolution  

NASA Astrophysics Data System (ADS)

Papers on nonlinear waves are presented, covering topics such as the history of studies on nonlinear dynamics since Poincare, attractors, pattern formation and the dynamics of two-dimensional structures in nonequilibirum dissipative media, the onset of spatial chaos in one-dimensional systems, and self-organization phenomena in laser thermochemistry. Additional topics include criteria for the existence of moving structures in two-component reaction-diffusion systems, space-time structures in optoelectronic devices, stimulated scattering and surface structures, and distributed wave collapse in the nonlinear Schroedinger equation. Consideration is also given to dimensions and entropies in multidimensional systems, measurement methods for correlation dimensions, quantum localization and dynamic chaos, self-organization in bacterial cells and populations, nonlinear phenomena in condensed matter, and the origin and evolutionary dynamics of Uranian rings.

Gaponov-Grekhov, A. V.; Rabinovich, M. I.

229

Nonlinear systems in medicine.  

PubMed Central

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

230

Pattern dynamics and spatiotemporal chaos in the quantum Zakharov equations  

SciTech Connect

The dynamical behavior of the nonlinear interaction of quantum Langmuir waves (QLWs) and quantum ion-acoustic waves (QIAWs) is studied in the one-dimensional quantum Zakharov equations. Numerical simulations of coupled QLWs and QIAWs reveal that many coherent solitary patterns can be excited and saturated via the modulational instability of unstable harmonic modes excited by a modulation wave number of monoenergetic QLWs. The evolution of such solitary patterns may undergo the states of spatially partial coherence (SPC), coexistence of temporal chaos and spatiotemporal chaos (STC), as well as STC. The SPC state is essentially due to ion-acoustic wave emission and due to quantum diffraction, while the STC is caused by the combined effects of SPC and quantum diffraction, as well as by collisions and fusions among patterns in stochastic motion. The energy in the system is strongly redistributed, which may switch on the onset of weak turbulence in dense quantum plasmas.

Misra, A. P.; Shukla, P. K. [Department of Mathematics, Visva-Bharati University, Santiniketan 731 235 (India); Institut fuer Theoretische Physik IV and Centre for Plasma Science and Astrophysics, Fakultaet fuer Physik and Astronomie, Ruhr-Universitaet Bochum, D-44780 Bochum (Germany)

2009-05-15

231

Sub-Poissonian statistics in order-to-chaos transition  

SciTech Connect

We study the phenomena at the overlap of quantum chaos and nonclassical statistics for the time-dependent model of nonlinear oscillator. It is shown in the framework of Mandel Q parameter and Wigner function that the statistics of oscillatory excitation numbers is drastically changed in the order-to-chaos transition. The essential improvement of sub-Poissonian statistics in comparison with an analogous one for the standard model of driven anharmonic oscillator is observed for the regular operational regime. It is shown that in the chaotic regime, the system exhibits the range of sub-Poissonian and super-Poissonian statistics which alternate one to other depending on time intervals. Unusual dependence of the variance of oscillatory number on the external noise level for the chaotic dynamics is observed. The scaling invariance of the quantum statistics is demonstrated and its relation to dissipation and decoherence is studied.

Kryuchkyan, Gagik Yu. [Yerevan State University, Manookyan 1, Yerevan 375049, (Armenia); Institute for Physical Research, National Academy of Sciences, Ashtarak-2 378410, (Armenia); Manvelyan, Suren B. [Institute for Physical Research, National Academy of Sciences, Ashtarak-2 378410, (Armenia)

2003-07-01

232

Atomic motion in magneto-optical double-well potentials: A testing ground for quantum chaos  

Microsoft Academic Search

We have identified ultracold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement at the quantum level and chaos at the classical level arise from nonseparable couplings between the atomic spin and its center of mass motion.

Shohini Ghose; Paul M. Alsing; Ivan H. Deutsch

2001-01-01

233

Atomic Motion in Magneto-Optical Double-Well Potentials: A Testing Ground for Quantum Chaos  

Microsoft Academic Search

We have identified ultracold atoms in magneto-optical double-well potentials as a very clean setting in which to study the quantum and classical dynamics of a nonlinear system with multiple degrees of freedom. In this system, entanglement at the quantum level and chaos at the classical level arise from nonseparable couplings between the atomic spin and its center of mass motion.

Shohini Ghose; Paul M. Alsing; Ivan H. Deutsch

2001-01-01

234

INTRODUCTION: The Physics of Chaos and Related Problems: Proceedings of the 59th Nobel Symposium  

Microsoft Academic Search

The physics of non-linear phenomena has developed in a remarkable way over the last couple of decades and has accelerated over the last few years, in particular because of the recent progress in the study of chaotic behaviour. In particular the discovery of the universal properties of the transition into chaos for certain classes of systems has stimulated much recent

Stig Lundqvist

1985-01-01

235

Multi-algorithmic Cryptography using Deterministic Chaos with Applications to Mobile Communications  

Microsoft Academic Search

In this extended paper, we present an overview of the principal issues associated with cryptography, providing historically significant examples for illustrative purposes as part of a short tutorial for readers that are not familiar with the subject matter. This is used to introduce the role that nonlinear dynamics and chaos play in the design of encryption engines which utilize different

Jonathan Blackledge

2008-01-01

236

Dynamical Chaos in the Solar System: Past, Current, and Future Research  

Microsoft Academic Search

In the last two decades remarkable advances in computer speed, the development of new numerical techniques, and the application of modern nonlinear dynamics techniques to classical problems of celestial mechanics have permitted the discovery and exploration of a number of examples of dynamical chaos in our own solar system. Perhaps the most interesting is the result that the orbits of

M. Holman

1999-01-01

237

Continuous control of ionization wave chaos by spatially derived feedback signals  

Microsoft Academic Search

In the positive column of a neon glow discharge, two different types of ionization waves occur simultaneously. The low-dimensional chaos arising from the nonlinear interaction between the two waves is controlled by a continuous feedback technique. The control strategy is derived from the time-delayed autosynchronization method. Two spatially displaced points of observation are used to obtain the control infor- mation,

A. Piel; A. Atipo; G. Bonhomme

238

Continuous control of ionization wave chaos by spatially derived feedback signals  

Microsoft Academic Search

In the positive column of a neon glow discharge, two different types of ionization waves occur simultaneously. The low-dimensional chaos arising from the nonlinear interaction between the two waves is controlled by a continuous feedback technique. The control strategy is derived from the time-delayed autosynchronization method. Two spatially displaced points of observation are used to obtain the control information, using

Th. Mausbach; Th. Klinger; A. Piel; A. Atipo; Th. Pierre; G. Bonhomme

1997-01-01

239

Low dimensional chaos in the AT and GC skew profiles of DNA sequences  

Microsoft Academic Search

This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed using continuous wavelet transform and then nonlinear time series methods. The invariant measures of correlation dimension and the largest Lyapunov exponent are calculated. It is demonstrated

Qian Zhou; Zeng-Qiang Chen

2010-01-01

240

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

PubMed

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

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

2013-07-08

241

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

NASA Astrophysics Data System (ADS)

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

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

2013-07-01

242

Chaos Reigns in Russia  

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.

243

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

PubMed

The landmarks in the use of chaos and related constructs in psychology were entwined with the growing use of other nonlinear dynamical constructs, especially catastrophes and self-organization. The growth in substantive applications of chaos in psychology is partially related to the development of methodologies that work within the constraints of psychological data. The psychological literature includes rigorous theory with testable propositions, lighter-weight metaphorical uses of the construct, and colloquial uses of "chaos" with no particular theoretical intent. The current state of the chaos construct and supporting empirical research in psychological theory is summarized in neuroscience, psychophysics, psychomotor skill and other learning phenomena, clinical and abnormal psychology, and group dynamics and organizational behavior. Trends indicate that human systems do not remain chaotic indefinitely; they eventually self-organize, and the concept of the complex adaptive system has become prominent. Chaotic turbulence is generally higher in healthy systems compared to unhealthy systems, although opposite appears true in mood disorders. Group dynamics research shows trends consistent with the complex adaptive system, whereas organizational behavior lags behind in empirical studies relative to the quantity of its theory. Future directions for research involving the chaos construct and other nonlinear dynamics are outlined. PMID:19527620

Guastello, Stephen J

2009-07-01

244

On the use of chaos to reduce idle-channel tones in delta-sigma modulators  

Microsoft Academic Search

Delta-sigma modulators are popular circuits for constructing high precision analog-to-digital and digital-to-analog converters. These systems contain a single nonlinear element (a quantizer) embedded in an otherwise linear system, and can exhibit such nonlinear behavior as limit cycles, subharmonics, phase-locking and chaos. Due to the discrete spectra that result when limit cycles are present, human listeners perceive objectionable tones in the

Richard Schreier

1994-01-01

245

Dynamic chaos in the solution of the Gross-Pitaevskii equation for a periodic potential  

SciTech Connect

We analytically and numerically investigate the solution to the stationary Gross-Pitaevskii equation for a one-dimensional potential of the optical lattice in the case of repulsive nonlinearity. From the mathematical viewpoint, this problem is similar to the well-known problem of the classical mathematical Kapitza pendulum perturbed by a weak high-frequency force. At certain values of the parameters, dynamic chaos is produced in the considered problem. It is modeled analytically by a nonlinear diffusion equation.

Ishkhanyan, H. A.; Krainov, V. P., E-mail: vpkrainov@mail.ru [Moscow Institute of Physics and Technology (State University) (Russian Federation)

2011-09-15

246

Nonlinear Time Series Analysis  

NASA Astrophysics Data System (ADS)

The time variability of many natural and social phenomena is not well described by standard methods of data analysis. However, nonlinear time series analysis uses chaos theory and nonlinear dynamics to understand seemingly unpredictable behavior. The results are applied to real data from physics, biology, medicine, and engineering in this volume. Researchers from all experimental disciplines, including physics, the life sciences, and the economy, will find the work helpful in the analysis of real world systems. First Edition Hb (1997): 0-521-55144-7 First Edition Pb (1997): 0-521-65387-8

Kantz, Holger; Schreiber, Thomas

2004-01-01

247

Chaos, decoherence and quantum cosmology  

NASA Astrophysics Data System (ADS)

In this topical review we discuss the connections between chaos, decoherence and quantum cosmology. We understand chaos as classical chaos in systems with a finite number of degrees of freedom, decoherence as environment induced decoherence and quantum cosmology as the theory of the Wheeler-DeWitt equation or else the consistent history formulation thereof, first in mini super spaces and later through its extension to midi super spaces. The overall conclusion is that consideration of decoherence is necessary (and probably sufficient) to sustain an interpretation of quantum cosmology based on the wavefunction of the Universe adopting a Wentzel-Kramers-Brillouin form for large Universes, but a definitive account of the semiclassical transition in classically chaotic cosmological models is not available in the literature yet.

Calzetta, Esteban

2012-07-01

248

Managing chaos in complex systems  

NASA Astrophysics Data System (ADS)

Controlling critical systems generally requires incorporating a feedback and response mechanism as an integral part of the primary system. Heart pacemakers and nuclear reactors are examples. Once feedback determines that limit-parameters are violated, an immediate response is made to re-synchronize the system and prevent the effects of chaos. In other systems, the quality of the product takes precedence over a need for an immediate feedback and response system. This case study involves the effectiveness of methods used to control chaos in a large relational database. Control methods include software tools, process improvements, and adoption of quality standards for acceptance. The research concluded that focusing on the system's external environment is an effective approach to controlling chaos, especially where the quality of the product, not response time, is the primary concern.

Mueller, Theodore H.

249

Chaos: A historical perspective  

NASA Astrophysics Data System (ADS)

In this introductory lecture I'd like to offer a broad historical perspective regarding the relatively recent general recognition: (a) that mechanical systems satisfying Newton's laws may be subject to the essentially unpredictable type of behavior which the word CHAOS describes—in other words, the recognition (b) that quantum effects are not required; (c) so that, notwithstanding Heisenberg, uncertainty is there on the basis of the good old classical mechanics based on Newton's Laws. But first of all I'll remind you that there are two kinds of laws in science, which we may exemplify by Kepler's Laws and Newton's Laws. Kepler in 1609 completed some very detailed observations of the motions of Mars; together with a full geometrical description of them, in the Copernican sun-centered flame of reference, as motions in a constant orbit in the shape of an ellipse with the Sun as focus. A decade later Kepler had published the Epitome Astronomiae Copernicanae (a rather more substantial work than the Dialogo which later got Galileo into some difficulties), and had there described in detail his most famous discovery: Kepler's three empirical laws concerning planetary orbits. These laws, of the elliptical shapes of orbits, of the radius covering equal areas in equal times, and of the proportionality of the square of the orbital period to the cube of the major axis, were shown from the observations to be closely satisfied by the Earth and by the five then known planets; and furthermore, by the four satellites of Jupiter which Galileo had recently discovered.

Lighthill, James

250

Bistability and chaos at low levels of quanta.  

PubMed

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

2013-08-12

251

THE STRANGE ATTRACTION OF CHAOS  

Microsoft Academic Search

The idea of chaos, as formulated in research on dynamical systems, is causing great excitement among architects and designers. This is because this conception may permit the development and application of an open-ended, nondeterministic yet rigorous “scientific” approach to several “scientific” problems. This paper briefly explores the philosophical, strategic, and technical promise inherent in dynamical systems and suggests a possible

James M. Bradburne

1990-01-01

252

The Chaos Theory of Careers  

ERIC Educational Resources Information Center

|The Chaos Theory of Careers (CTC; Pryor & Bright, 2011) construes both individuals and the contexts in which they develop their careers in terms of complex dynamical systems. Such systems perpetually operate under influences of stability and change both internally and in relation to each other. The CTC introduces new concepts to account for…

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

2011-01-01

253

Chao Formalism & Kondratenko Crossing Tests  

NASA Astrophysics Data System (ADS)

We recently started testing Chao's proposed new matrix formalism for describing the spin dynamics due to a single spin resonance; this seems to be the first generalization of the Froissart-Stora equation since it was published in 1960. The Chao matrix formalism allows one to calculate analytically the polarization's behavior inside a resonance, which is not possible using the Froissart-Stora equation. We recently tested some Chao formalism predictions using a 1.85 GeV/c polarized deuteron beam stored in COSY. We swept an rf dipole's frequency through 200 Hz while varying the distance from the sweep's end frequency to an rf-induced spin resonance's central frequency. While the Froissart-Stora formula can make no prediction in this case, the data seem to support the Chao formalism. We also started investigating the new Kondratenko method to preserve beam polarization during a spin resonance crossing; the method uses 3 rapid changes of the crossing rate near the resonance. With a proper choice of crossing parameters, Kondratenko Crossing may better preserve the polarization than simple fast crossing. We tested Kondratenko's idea using 2.1 GeV/c polarized protons stored in COSY; the frequency of a ferrite rf dipole was swept though an rf-induced spin resonance using Kondratenko's crossing shape. We have not yet observed a significant advantage of Kondratenko Crossing over simple fast crossing. We plan to study it further by choosing better crossing parameters and a smaller momentum spread.

Raymond, R. S.; Chao, A. W.; Krisch, A. D.; Leonova, M. A.; Morozov, V. S.; Sivers, D. W.; Wong, V. K.; Gebel, R.; Lehrach, A.; Lorentz, B.; Maier, R.; Prasuhn, D.; Schnase, A.; Stockhorst, H.; Hinterberger, F.; Ulbrich, K.; Kondratenko, A. M.

2007-06-01

254

Chaos in thermal pulse combustion  

Microsoft Academic Search

An experimental thermal pulse combustor and a differential equation model of this device are shown to exhibit chaotic behavior under certain conditions. Chaos arises in the model by means of a progression of period-doubling bifurcations that occur when operating parameters such as combustor wall temperature or air\\/fuel flow are adjusted to push the system toward flameout. Bifurcation sequences have not

C. Stuart Daw; John F. Thomas; George A. Richards; Lakshmanan L. Narayanaswami

1995-01-01

255

Chaos in thermal pulse combustion  

Microsoft Academic Search

An experimental thermal pulse combustor and a differential equation model of this device are shown to exhibit chaotic behavior under certain conditions. Chaos arises in the model by means of a progression of period-doubling bifurcations that occur when operating parameters such as combustor wall temperature or air\\/fuel flow are adjusted to push the system toward flameout. Bifurcation sequences have not

C. Stuart Daw; John F. Thomas; Lakshmanan L. Narayanaswami

2001-01-01

256

Random matrices and quantum chaos  

PubMed Central

The theory of random matrices has far-reaching applications in many different areas of mathematics and physics. In this note, we briefly describe the state of the theory and two of the perhaps most surprising appearances of random matrices, namely in the theory of quantum chaos and in the theory of prime numbers.

Kriecherbauer, Thomas; Marklof, Jens; Soshnikov, Alexander

2001-01-01

257

Random matrices and quantum chaos.  

PubMed

The theory of random matrices has far-reaching applications in many different areas of mathematics and physics. In this note, we briefly describe the state of the theory and two of the perhaps most surprising appearances of random matrices, namely in the theory of quantum chaos and in the theory of prime numbers. PMID:11553804

Kriecherbauer, T; Marklof, J; Soshnikov, A

2001-09-11

258

STATISTICAL PROPERTIES OF DYNAMICAL CHAOS  

Microsoft Academic Search

This study presents a survey of the results obtained by the au- thors on statistical description of dynamical chaos and the eect of noise on dynamical regimes. We deal with nearly hyperbolic and nonhyperbolic chaotic attractors and discuss methods of diagnosing the type of an attractor. We consider regularities of the relaxation to an invariant probability measure for dieren t

Vadim S. Anishchenko; Tatjana E. Vadivasova; Galina I. Strelkova; George A. Okrokvertskhov

2004-01-01

259

Learning the Uses of Chaos.  

ERIC Educational Resources Information Center

|This paper addresses the issue of learning to write and the need for defining a means of teaching the process of composing. Following a description of what kind of process writing is not, the composing process is presented as a continuum of making meaning out of a chaos of images, half-truths, remembrances, and syntactic fragments. The discovery…

Berthoff, Ann E.

260

More memory under evolutionary learning may lead to chaos  

NASA Astrophysics Data System (ADS)

We show that an increase of memory of past strategy performance in a simple agent-based innovation model, with agents switching between costly innovation and cheap imitation, can be quantitatively stabilising while at the same time qualitatively destabilising. As memory in the fitness measure increases, the amplitude of price fluctuations decreases, but at the same time a bifurcation route to chaos may arise. The core mechanism leading to the chaotic behaviour in this model with strategy switching is that the map obtained for the system with memory is a convex combination of an increasing linear function and a decreasing non-linear function.

Diks, Cees; Hommes, Cars; Zeppini, Paolo

2013-02-01

261

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

262

Meaning Finds a Way: Chaos (Theory) and Composition  

ERIC Educational Resources Information Center

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

Kyburz, Bonnie Lenore

2004-01-01

263

Meaning Finds a Way: Chaos (Theory) and Composition  

ERIC Educational Resources Information Center

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

Kyburz, Bonnie Lenore

2004-01-01

264

Einfuehrung in die Theorie des Deterministischen Chaos (Introduction to the Theory of Deterministic Chaos).  

National Technical Information Service (NTIS)

The theory of deterministic chaos is introduced with a view to astrophysics applications. The emphasis is on the treatment of continuous systems. Deterministic chaos stands for a class of processes the development of which can be described by deterministi...

H. Atmanspacher G. Morfill

1986-01-01

265

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

266

Cooperative dynamics and functions in a collective nonlinear optical element system  

Microsoft Academic Search

An optical ring cavity containing distributed nonlinear elements is proposed as a simple metaphorical model for investigating the dynamic properties of spatial chaos in a system far from thermal equilibrium. If the coupling between the elements is unidirectional, the stability of the disordered structure can be determined by the spatial Liapunov exponent. This fact implies that spatial chaos is almost

Kenju Otsuka; Kensuke Ikeda

1989-01-01

267

Linking actin networks and cell membrane via a reaction-diffusion-elastic description of nonlinear filopodia initiation  

NASA Astrophysics Data System (ADS)

Reaction-diffusion models have been used to describe pattern formation on the cellular scale, and traditionally do not include feedback between cellular shape changes and biochemical reactions. We introduce here a distinct reaction-diffusion-elasticity approach: The reaction-diffusion part describes bistability between two actin orientations, coupled to the elastic energy of the cell membrane deformations. This coupling supports spatially localized patterns, even when such solutions do not exist in the uncoupled self-inhibited reaction-diffusion system. We apply this concept to describe the nonlinear (threshold driven) initiation mechanism of actin-based cellular protrusions and provide support by several experimental observations.

Ben Isaac, Eyal; Manor, Uri; Kachar, Bechara; Yochelis, Arik; Gov, Nir S.

2013-08-01

268

Linking actin networks and cell membrane via a reaction-diffusion-elastic description of nonlinear filopodia initiation.  

PubMed

Reaction-diffusion models have been used to describe pattern formation on the cellular scale, and traditionally do not include feedback between cellular shape changes and biochemical reactions. We introduce here a distinct reaction-diffusion-elasticity approach: The reaction-diffusion part describes bistability between two actin orientations, coupled to the elastic energy of the cell membrane deformations. This coupling supports spatially localized patterns, even when such solutions do not exist in the uncoupled self-inhibited reaction-diffusion system. We apply this concept to describe the nonlinear (threshold driven) initiation mechanism of actin-based cellular protrusions and provide support by several experimental observations. PMID:24032875

Ben Isaac, Eyal; Manor, Uri; Kachar, Bechara; Yochelis, Arik; Gov, Nir S

2013-08-29

269

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

270

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

ERIC Educational Resources Information Center

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

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

2005-01-01

271

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

ERIC Educational Resources Information Center

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

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

2005-01-01

272

Chaos driven Differential Evolution in the task of chaos control optimization  

Microsoft Academic Search

This paper focuses on the application of chaos driven Differential Evolution to the chaos control optimization problem. The focus of this paper is the embedding of chaotic systems in the form of the chaos number generator for Differential Evolution. The aim of this paper is also to show extreme sensitivity of quality of results on the selection of evolutionary algorithm,

Roman Senkerik; Donald Davendra; Ivan Zelinka; Zuzana Oplatková

2010-01-01

273

BOOK REVIEW: Chaos: A Very Short Introduction  

NASA Astrophysics Data System (ADS)

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 science account of research knows that this is a more challenging task than writing an ordinary research article. Lenny Smith brilliantly succeeds to explain in words, in pictures and by using intuitive models the essence of mathematical dynamical systems theory and time series analysis as it applies to the modern world. In a more technical part he introduces the basic terms of nonlinear theory by means of simple mappings. He masterly embeds this analysis into the social, historical and cultural context by using numerous examples, from poems and paintings over chess and rabbits to Olbers' paradox, card games and `phynance'. Fundamental problems of the modelling of nonlinear systems like the weather, sun spots or golf balls falling through an array of nails are discussed from the point of view of mathematics, physics and statistics by touching upon philosophical issues. At variance with Laplace's demon, Smith's 21st century demon makes `real world' observations only with limited precision. This poses a severe problem to predictions derived from complex chaotic models, where small variations of initial conditions typically yield totally different outcomes. As Smith argues, this difficulty has direct implications on decision-making in everyday modern life. However, it also asks for an inherently probabilistic theory, which somewhat reminds us of what we are used to in the microworld. There is little to criticise in this nice little book except that some figures are of poor quality thus not really reflecting the beauty of fractals and other wonderful objects in this field. I feel that occasionally the book is also getting a bit too intricate for the complete layman, and experts may not agree on all details of the more conceptual discussions. Altogether I thoroughly enjoyed reading this book. It was a happy companion while travelling and a nice bedtime literature. It is furthermore an excellent reminder of the `big picture' underlying nonlinear science as it applies to the real world. I will gladly recommend this book as background literature for students in my introductory course on dynamical systems. However, the book will be of interest to anyone who is looking for a very short account on fundamental problems and principles in modern nonlinear science.

Klages, R.

2007-07-01

274

BBC News: Mathematicians Crochet Chaos  

NSDL National Science Digital Library

This article from BBC News discusses how two mathematicians made a crochet model of chaos. The mathematicians, whose research focuses on developing a computer model to describe complex surfaces, were able to represent the Lorenz equations using 25,511 crochet stitches. The pattern was published in the journal Mathematics Intelligencer and the mathematicians are challenging others to repeat the effort. The model stretches almost a meter across and was used as a Christmas decoration.

275

Chaos in a complex plasma  

SciTech Connect

Chaotic dynamics is observed experimentally in a complex (dusty) plasma of three particles. A low-frequency sinusoidal modulation of the plasma density excites both the center-of-mass and breathing modes. Low-dimensional chaos is seen for a 1:2 resonance between these modes. A strange attractor with a dimension of 2.48{+-}0.05 is observed. The largest Lyapunov exponent is positive.

Sheridan, T.E. [Department of Physics and Astronomy, Ohio Northern University, Ada, Ohio 45810 (United States)

2005-08-15

276

Chaos in a double pendulum  

Microsoft Academic Search

A novel demonstration of chaos in the double pendulum is discussed. Experiments to evaluate the sensitive dependence on initial conditions of the motion of the double pendulum are described. For typical initial conditions, the proposed experiment exhibits a growth of uncertainties which is exponential with exponent lambda=7.5+\\/-1.5 s-1. Numerical simulations performed on an idealized model give good agreement, with the

Troy Shinbrot; Celso Grebogi; Jack Wisdom; James A. Yorke

1992-01-01

277

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

278

Nonlinear modeling and bifurcations in the boost converter  

Microsoft Academic Search

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

279

Practical implementation of nonlinear time series methods: The TISEAN package  

Microsoft Academic Search

We describe the implementation of methods of nonlinear time series analysis which are based on the paradigm of deterministic chaos. A variety of algorithms for data representation, prediction, noise reduction, dimension and Lyapunov estimation, and nonlinearity testing are discussed with particular emphasis on issues of implementation and choice of parameters. Computer programs that implement the resulting strategies are publicly available

Rainer Hegger; Holger Kantz; Thomas Schreiber

1999-01-01

280

Comparison of the Nature of Chaos in Experimental [EEG] Data and Theoretical [ANN] Data  

NASA Astrophysics Data System (ADS)

In this paper, nonlinear dynamical tools like largest Lyapunov exponents (LE), fractal dimension, correlation dimension, pointwise correlation dimension will be employed to analyze electroencephalogram [EEG] data and determine the nature of chaos. Results of similar calculations from some earlier works will be produced for comparison with present results. Also, a brief report on difference of opinion among coworkers regarding tools to characterize chaos will be reported; particularly applicability of LE will be reviewed. The issue of nonlinearity present in experimental time series will be addressed by using surrogate data technique. We have extracted another data set which represented chaotic state of the system considered in our earlier work of mathematical modeling of artificial neural network. By comparing the values of measures employed to the two datasets, it can be concluded that EEG represents high dimensional chaos, whereas the experimental data due to its deterministic nature, is of low dimension. Also results give the evidence that LE exponent is applicable for low dimensional chaotic system while for experimental data, due to their stochasticity and presence of noise- LE is not a reliable tool to characterize chaos.

Das, Atin; Das, Pritha

2003-08-01

281

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.

282

Nonlinear science: toward the next frontiers  

Microsoft Academic Search

Nonlinear science has erupted in many directions over recent years, with many successes. Two main themes have been found in many different settings-chaos and solitary phenomena. While found initially in simple models, useful for establishing mathematical methods and the behavior of exact limiting cases, their robust features give us assurance that they are generic. The next frontier then is not

James A. Krumhansl

1993-01-01

283

Present and Future of Nonlinear Dynamics According to a Nonlinear Dynamicist  

NASA Astrophysics Data System (ADS)

The present state and future of “nonlinear dynamics” is explained in this review. First, chaotic vibrations of nonlinear beams are used as a material to demonstrate our present understanding of chaos, compared with the situation of the early stage of its research. Second, two topics, microcantilever dynamics of tapping-mode atomic force microscopy and design of Earth to the Moon transfer trajectories of spacecrafts, are chosen for describing the importance and usefulness of “nonlinear dynamics” in new technologies. Moreover, two applications of “nonlinear dynamics” to biped walking robots and nonlinear optimal control are briefly addressed.

Yagasaki, Kazuyuki

284

Application of Artificial Neural Networks and Chaos in Chemical Processes  

NASA Astrophysics Data System (ADS)

An artificial neural network (ANN) and chaos, conceived and developed independently, are beginning to play essential roles in chemical engineering. Nonetheless, the ANN possesses an appreciable number of deficiencies that need be remedied, and the capability of the ANN to explore and tame chaos or an irregularly behaving system is yet to be fully realized. The present dissertation attempts to make substantial progress toward such ends. The problem of controlling the temperature of an industrial reactor carrying out semibatch polymerization has been solved by an innovative adaptive hybrid control system comprising an ANN and fuzzy expert system (FES) complemented by two supervisory ANN's. The system enhances the strength and compensates for the weaknesses of both the ANN and FES. The system, named dual ANN (DANN), has been proposed for characterizing the nonlinear nature of chaotic time -series data. Its capability to approximate the behavior of a chaotic system has been found to far exceed that of a conventional ANN. A novel approach has been devised for training an ANN through the modified interactive training (MIT) mode. This mode of training has been demonstrated to substantially outperform a conventional interactive training (CIT) mode. A method has been established for synchronizing chaos by resorting to an ANN. This method is capable of causing to be coherent the trajectories of systems whose deterministic governing equations are insufficiently known. This requires training the ANN with a time series and a common driving signal or signals. Examples are given for chaos generated by difference as well as differential equations. An alternative to the OGY method has been proposed for controlling chaos; it meticulously perturbs an accessible parameter of the chaotic system. A single, highly precise ANN suffices to render stable any of an infinite number of unstable periodic orbits embedded in a chaotic or strange attractor. A method for estimating sub-Lyapunov exponents or conditional Lyapunov exponents is presented; it has been developed by exploiting the learning capability of an ANN. For some chaotic systems, the sub-Lyapunov exponents determined by the method are in good accord with the theoretical values.

Otawara, Kentaro

1995-01-01

285

Prediction Model of Chaos Neural Network for Surrounding Rock Pressure in Excavation of Tunnel with Small-interval  

Microsoft Academic Search

Surrounding rock pressure of tunnel is the key factor to analyze the stability of surrounding rock. However, the deformation of surrounding rock is affected by many factors among which there are intense non-linear relation, so it is difficult to predict it effectively. In this paper, the method based on chaos neural network model is put forward, the feasibility of prediction

Yi Liyun

2010-01-01

286

Excitation of dynamic chaos in a monolithic ring chip laser upon periodic modulation of mechanical stresses in the active element  

SciTech Connect

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. (control of laser radiation parameters)

Kravtsov, Nikolai V; Firsov, V V; Chekina, S N [D.V. Skobel'tsyn Institute of Nuclear Physics, M.V. Lomonosov Moscow State University, Moscow (Russian Federation); Sidorov, S S; Pashinin, Pavel P [A.M. Prokhorov General Physics Institute, Russian Academy of Sciences, Moscow (Russian Federation)

2004-04-30

287

Evidence for bifurcation and universal chaotic behavior in nonlinear semiconducting devices  

SciTech Connect

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

288

Iceberg detection using chaos  

NASA Astrophysics Data System (ADS)

Ship navigation through ice-infested waters is a problem of deep concern to the oil exploration industry of the northern countries. Conventional marine radars do not perform satisfactorily in detecting small targets such as small pieces of iceberg. This paper reports a new method for detection in an ocean environment. The approach is based on the recent observation that sea clutter, radar echoes from the sea surface, can be modeled as a nonlinear deterministic dynamical system as an alternative to the conventional stochastic process. Based on this model, detection in sea clutter may be considered as classification of dynamical systems instead of statistical hypothesis testing. Two dynamical detection methods are proposed. The first one uses a dynamical invariant called attractor dimension to distinguish a target and a pure clutter process. The second approach tries to detect the existence of a target by observing the `difference' of the motion of the target and the clutter process. To show the validity of the idea of dynamical detection in sea clutter, real sea clutter and target data were used in this study.

Leung, Henry

1993-11-01

289

Managing the Chaos of Financial Management.  

National Technical Information Service (NTIS)

This paper addresses a two-part research question: Do USAF installation-level financial managers confront undue chaos in budget execution. If so, does this chaos result from recent Department of Defense (DoD) initiatives to decentralize control of previou...

H. D. Arnold J. Fetter K. Rumsey K. Bowling H. Jones

1995-01-01

290

Structures of chaos in open reaction systems.  

PubMed

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

2011-10-12

291

Introduction: Control and synchronization of chaos  

Microsoft Academic Search

The hallmark of deterministic chaos, an extreme sensi- tivity to initial conditions, suggests that chaotic systems might be difficult if not impossible to control, since any per- turbations used for control would grow exponentially in time. Indeed, this quite reasonable view was widely held until only a few years ago. Surprisingly, the basis for con- trolling chaos is provided by

William L. Ditto; Kenneth Showalter

2001-01-01

292

Bringing order to chaos: Communication and health  

Microsoft Academic Search

An ecological theory of health communication is offered that addresses how communications about health interdependently work together to influence health and\\/or health?related behaviors. To explain how a multitude of variables work together in a synergistic manner, the present work borrows heavily from chaos theory. The use of chaos theory concepts represents a significant paradigm shift from previous, more reductionist, health

Kim Witte; Gary Meyer; Helen Bidol; Mary K. Casey; Jenifer Kopfman; Karen Maduschke; Alicia Marshall; Kelly Morrison; Kurt M. Ribisl; Steve Robbins

1996-01-01

293

Chaos in Derrida and Student Texts.  

ERIC Educational Resources Information Center

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

Corbett, Janice M.

294

Chaos in phase-locked loops  

NASA Astrophysics Data System (ADS)

Chaos has been observed in third-order phase-locked loops when the frequency of the received signal is varied linearly with time. Liapunov exponents and dimension are calculated to confirm this result. The appropriate parameter ranges in which chaos could occur in typical designs are indicated.

Chou, J. H.; Chu, Y. H.; Chang, S.

1991-04-01

295

Class, chaos, and the construction of community.  

PubMed

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

2012-08-13

296

Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field  

Microsoft Academic Search

Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called ‘chaos theory’, has now progressed to a stage, where it becomes possible to study self-organization and pattern formation in the complex neuronal networks of the brain. One approach to nonlinear time series analysis consists of reconstructing, from time series of

C. J. Stam

2005-01-01

297

Invited review Nonlinear dynamical analysis of EEG and MEG: Review of an emerging field  

Microsoft Academic Search

Many complex and interesting phenomena in nature are due to nonlinear phenomena. The theory of nonlinear dynamical systems, also called 'chaos theory', has now progressed to a stage, where it becomes possible to study self-organization and pattern formation in the complex neuronal networks of the brain. One approach to nonlinear time series analysis consists of reconstructing, from time series of

C. J. Stam

298

Comment on ``Absence of chaos in a self-organized critical coupled map lattice''  

NASA Astrophysics Data System (ADS)

Csilling and collaborators [Phys. Rev. E 50, 1083 (1994)] present a coupled map lattice representing a collection of linked populations with nonoverlapping generations. They report that their model fails to predict both chaos and spatial organization. In this comment, I highlight a number of published studies using similar models which (by contrast) commonly report both chaos and spatial organization. After careful comparison of two of these models, I suggest that the root of the highly unusual results of Csilling et al. may lie in their separation of the time scales on which dispersal and reproduction occur. Further, I suggest how this theory could be tested.

Ruxton, G. D.

1995-08-01

299

Chaos and Fractal Analysis of Electroencephalogram Signals during Different Imaginary Motor Movement Tasks  

NASA Astrophysics Data System (ADS)

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

Soe, Ni Ni; Nakagawa, Masahiro

2008-04-01

300

Chaos in semiclassical model of multiphoton excitation of spherical top molecules  

Microsoft Academic Search

The dynamical effects of vibration-rotation coupling in multiple photon excitation at lowest order using the simplest molecular model possible: that of an oscillator (triply degenerate) and uncoupled rigid rotor. The molecule-field interactions introduce a vibration-rotation nonlinearity which gives rise to nonconservation of the molecular angular momentum and in some instances consequent chaotic dynamics. The chaos leads to incoherence (widely seen

H. W. Galbraith; J. B. Ackerhalt; P. W. Milonni

1983-01-01

301

Applications of chaos theory on Partial Discharge detection and character analysis  

Microsoft Academic Search

Partial discharge (PD) signals character analyzing and interference suppressing are very important for PD on-line measurement. In this paper, chaos theory is introduced in the PD on-line monitoring. The mechanism of PD phenomena has been researched by series of typical insulation defect PD experiments in the lab. Through calculating the non-linear dynamics character of PD detecting signal time sequence, such

Chelai Yin; Lixing Zhou; Yini Luo

2008-01-01

302

Decoherence, determinism and chaos revisited  

NASA Astrophysics Data System (ADS)

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.

1994-11-01

303

Decoherence, determinism and chaos revisited  

SciTech Connect

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

304

Fractal Neurodyamics and Quantum Chaos : Resolving the Mind-Brain Paradox Through Novel Biophysics  

Microsoft Academic Search

Abstract: A model,of the mind-brain relationship is developed in which novel biophysical principles in,brain function generate a dynamic possessing attributes consistent with consciousness,and free-will. The model,invokes a fractal link between neurodynamical,chaos and quantum,uncertainty. Transactional wave,collapse allows this link to be utilized predictively by the excitable cell, in a way which bypasses and complements formal computation. The formal unpredictabilityof the model

Chris King

1996-01-01

305

Quantifying chaos for ecological stoichiometry  

NASA Astrophysics Data System (ADS)

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing ?1. However, for higher values of ?1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ?) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

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

2010-09-01

306

Competitive coexistence in stoichiometric chaos  

NASA Astrophysics Data System (ADS)

Classical predator-prey models, such as Lotka-Volterra, track the abundance of prey, but ignore its quality. Yet, in the past decade, some new and occasionally counterintuitive effects of prey quality on food web dynamics emerged from both experiments and mathematical modeling. The underpinning of this work is the theory of ecological stoichiometry that is centered on the fact that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P). The ratios of these elements can vary within and among species, providing simple ways to represent prey quality as its C:N or C:P ratios. When these ratios modeled to vary, as they frequently do in nature, seemingly paradoxical results can arise such as the extinction of a predator that has an abundant and accessible prey. Here, for the first time, we show analytically that the reduction in prey quality can give rise to chaotic oscillations. In particular, when competing predators differ in their sensitivity to prey quality then all species can coexist via chaotic fluctuations. The chaos generating mechanism is based on the existence of a junction-fold point on the nullcline surfaces of the species. Conditions on parameters are found for such a point, and the singular perturbation method and the kneading sequence analysis are used to demonstrate the existence of a period-doubling cascade to chaos as a result of the point.

Deng, Bo; Loladze, Irakli

2007-09-01

307

Gaussian Multiplicative Chaos and KPZ Duality  

NASA Astrophysics Data System (ADS)

This paper is concerned with the construction of atomic Gaussian multiplicative chaos and the KPZ formula in Liouville quantum gravity. On the first hand, we construct purely atomic random measures corresponding to values of the parameter ? 2 beyond the transition phase (i.e. ? 2 > 2 d) and check the duality relation with sub-critical Gaussian multiplicative chaos. On the other hand, we give a simplified proof of the classical KPZ formula as well as the dual KPZ formula for atomic Gaussian multiplicative chaos. In particular, this framework allows to construct singular Liouville measures and to understand the duality relation in Liouville quantum gravity.

Barral, Julien; Jin, Xiong; Rhodes, Rémi; Vargas, Vincent

2013-10-01

308

Gaussian Multiplicative Chaos for Symmetric Isotropic Matrices  

NASA Astrophysics Data System (ADS)

Motivated by isotropic fully developed turbulence, we define a theory of symmetric matrix valued isotropic Gaussian multiplicative chaos. Our construction extends the scalar theory developed by J.P. Kahane in 1985.

Chevillard, Laurent; Rhodes, Rémi; Vargas, Vincent

2013-02-01

309

Chaos automata: iterated function systems with memory  

NASA Astrophysics Data System (ADS)

Transforming biological sequences into fractals in order to visualize them is a long standing technique, in the form of the traditional four-cornered chaos game. In this paper we give a generalization of the standard chaos game visualization for DNA sequences. It incorporates iterated function systems that are called under the control of a finite state automaton, yielding a DNA to fractal transformation system with memory. We term these fractal visualizers chaos automata. The use of memory enables association of widely separated sequence events in the drawing of the fractal, finessing the ``forgetfulness'' of other fractal visualization methods. We use a genetic algorithm to train chaos automata to distinguish introns and exons in Zea mays (corn). A substantial issue treated here is the creation of a fitness function that leads to good visual separation of distinct data types.

Ashlock, Dan; Golden, Jim

2003-07-01

310

Chaos-induced true randomness  

Microsoft Academic Search

We investigate functions of type Xn=P(?zn), where P(t) is a periodic function, ? and z are real parameters. We show that these functions produce truly random sequences. We prove that a class of autonomous dynamical systems, containing nonlinear terms described by periodic functions of the variables, can generate random dynamics. We generalize these results to dynamical systems with nonlinearities in

J. A González; L. I. Reyes; J. J. Suárez; L. E Guerrero; G. Gutiérrez

2002-01-01

311

Chaos synchronization of general complex dynamical networks  

Microsoft Academic Search

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

Jinhu Luu; Xinghuo Yu; G. Chen

2004-01-01

312

Chaos synchronization of general complex dynamical networks  

Microsoft Academic Search

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

Jinhu Lü; Xinghuo Yu; Guanrong Chen

2004-01-01

313

Chaos from phase-locked loops  

Microsoft Academic Search

The authors present a rigorous analysis and a detailed experimental study of a chaotic attractor observed from a widely-used practical circuit: namely, a second-order phase-locked loop as an FM demodulation. The existence of chaos in this system proven rigorously by using Melnikov's method, and explicit expressions are derived which specify the possible region of chaos, or, more accurately, the region

T. Endo; L. O. Chua

1988-01-01

314

Noise-induced enhancement of chemical reactions in nonlinear flows.  

PubMed

Motivated by the problem of ozone production in atmospheres of urban areas, we consider chemical reactions of the general type: A+B-->2C, in idealized two-dimensional nonlinear flows that can generate Lagrangian chaos. Our aims differ from those in the existing work in that we address the role of transient chaos versus sustained chaos and, more importantly, we investigate the influence of noise. We find that noise can significantly enhance the chemical reaction in a resonancelike manner where the product of the reaction becomes maximum at some optimal noise level. We also argue that chaos may not be a necessary condition for the observed resonances. A physical theory is formulated to understand the resonant behavior. (c) 2002 American Institute of Physics. PMID:12779572

Liu, Zonghua; Lai, Ying-Cheng; Lopez, Juan M.

2002-06-01

315

Embracing chaos and complexity: a quantum change for public health.  

PubMed

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

Resnicow, Kenneth; Page, Scott E

2008-06-12

316

Different routes to chaos in the Ti:sapphire laser  

SciTech Connect

Kerr-lens mode-locked, femtosecond Ti:sapphire lasers can operate in two coexistent pulsed modes of operation, named P1 (transform limited output pulses) and P2 (chirped output pulses). We study, both theoretically and experimentally, the transition to chaotic behavior for each of these two modes of operation as the net intracavity group velocity dispersion parameter approaches to zero. We find that P1 reaches chaos through a quasiperiodic route, while P2 does it through intermittency. The modulation frequencies involved, the size of the transition regions in the parameter's space, and the embedding and correlation dimensions of the attractors (and also the kurtosis for the intermittent regime) are theoretically predicted and also measured, showing a satisfactory agreement. We consider that this finding of a low-dimensional system of widespread practical use with (at least) two coexistent chaotic scenarios will have a broad impact on the studies on nonlinear dynamics.

Kovalsky, Marcelo G.; Hnilo, Alejandro A. [Centro de Investigaciones en Laseres y Aplicaciones (CEILAP), Instituto de Investigaciones Cientificas y Tecnicas de las Fuerzas Armadas (CITEFA), Consejo Nacional de Investigaciones Cientificas y Tecnicas - CONICET, Universidad Nacional de San Martin - UNSAM, San Martin (Argentina)

2004-10-01

317

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

318

Transient chaos in optical metamaterials  

NASA Astrophysics Data System (ADS)

We investigate the dynamics of light rays in two classes of optical metamaterial systems: (1) time-dependent system with a volcano-shaped, inhomogeneous and isotropic refractive-index distribution, subject to external electromagnetic perturbations and (2) time-independent system consisting of three overlapping or non-overlapping refractive-index distributions. Utilizing a mechanical-optical analogy and coordinate transformation, the wave-propagation problem governed by the Maxwell's equations can be modeled by a set of ordinary differential equations for light rays. We find that transient chaotic dynamics, hyperbolic or nonhyperbolic, are common in optical metamaterial systems. Due to the analogy between light-ray dynamics in metamaterials and the motion of light in matter as described by general relativity, our results reinforce the recent idea that chaos in gravitational systems can be observed and studied in laboratory experiments.

Ni, Xuan; Lai, Ying-Cheng

2011-09-01

319

Temporal chaos in Boussinesq magnetoconvection  

SciTech Connect

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

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

2007-01-15

320

Defect Statistics in Undulation Chaos  

NASA Astrophysics Data System (ADS)

We report experimental results on thermally driven convection in a large aspect ratio inclined layer with a fluid of Prandtl number ? ? 1. At intermediate angles of inclination we find, very close to onset, the unpredicted defect turbulent state of undulating (wavy) chaos. We report measurements of the probability distribution function of the defect density. We do not find the predicted squared Poisson distribution (Gil, Lega, and Meunier, Phys Rev E 41:1138). To resolve this issue we measure bulk nucleation rates, annihilation rates, and the influence of the boundaries. Images and MPEG movies are available at http://milou.msc.cornell.edu/incline.html. This work is supported by NSF grant DMR-9705410.

Daniels, Karen E.; Bodenschatz, Eberhard

2000-03-01

321

Teaching nonlinear dynamics through elastic cords  

NASA Astrophysics Data System (ADS)

We experimentally studied the restoring force of a length of stretched elastic cord. A simple analytical expression for the restoring force was found to fit all the experimental results for different elastic materials. Remarkably, this analytical expression depends upon an elastic-cord characteristic parameter which exhibits two limiting values corresponding to two nonlinear springs with different Hooke's elastic constants. Additionally, the simplest model of elastic cord dynamics is capable of exhibiting a great diversity of nonlinear phenomena, including bifurcations and chaos, thus providing a suitable alternative model system for discussing the basic essentials of nonlinear dynamics in the context of intermediate physics courses at university level.

Chacón, R.; Galán, C. A.; Sánchez-Bajo, F.

2011-01-01

322

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

SciTech Connect

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

323

Critical phenomenon, crisis and transition to spatiotemporal chaos in plasmas  

NASA Astrophysics Data System (ADS)

In a driven/damped drift-wave system a steady wave induces nonlinear variation of the dispersion of a perturbation wave (PW). Competition between the nonlinear dispersion with self-nonlinearity of the PW results in rich wave dynamic behaviors. In particular, a steady wave at the negative tangency slope of a hysteresis becomes unstable due to a saddle instability. It is found that such saddle steady wave (SSW) plays an important role in the discontinuous transition from a spatially coherent state to spatiotemporal chaos (STC). The transition is caused by a crisis due to a collision of the PW attactor to an unstable orbit of the SSW. In the time evolution, it is a ‘pattern resonance’ of the realized wave with the virtual SSW that triggers the crisis. The transition also displays as a critical phenomenon in parameter space, which is related to the change in the symmetry property of the motion of master mode (k = 1) of the PW with respect to that of SSW. In the spatially coherent state the former is trapped by the SSW partial wave, while in the STC it can become free from the latter, its trajectory crosses two unstable orbits of the SSW frequently, causing very turbulent behavior.

He, Kaifen

2003-04-01

324

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

325

Nonlinear dynamics and chaos in boiling water reactors  

SciTech Connect

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

326

Non-linear protocell models: synchronization and chaos  

Microsoft Academic Search

.  \\u000a We consider generic protocells models allowing linear and non-linear\\u000a kinetics for the main involved chemical reactions. We are interested\\u000a in understanding if and how the protocell division and the metabolism\\u000a do synchronise to give rise to sustainable evolution of the protocell.

Alessandro Filisetti; Roberto Serra; Timoteo Carletti; Marco Villani; Irene Poli

2010-01-01

327

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

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

328

Chaos theory as a model for managing issues and crises  

Microsoft Academic Search

This article uses chaos theory to model public relations situations whose salient feature is the volatility of public perceptions. After discussing the central premises of the theory itself, it applies chaos theory to issues management, the evolution of interest groups, crises, and rumors. It concludes that chaos theory is most useful as an analogy to structure persistent image problems and

Priscilla Murphy

1996-01-01

329

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

ERIC Educational Resources Information Center

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

Willhauck, Susan

2010-01-01

330

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

ERIC Educational Resources Information Center

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

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

2010-01-01

331

Water quality situation in the Chao Phraya Delta  

Microsoft Academic Search

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

Wijarn Simachaya; Pimon Watanamahart; Vuttichai Kaewkrajang

332

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

ERIC Educational Resources Information Center

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

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

2010-01-01

333

Enhancing supply chain solutions with the application of chaos theory  

Microsoft Academic Search

Purpose – The purpose of this article is to expand the base of supply chain knowledge by applying chaos theory principles to selected supply chain functions. Design\\/methodology\\/approach – Researchers borrow chaos theory from the natural sciences, provide a basic explanation, and then examine how it may be applied to enhance supply chain management techniques. Findings – Chaos theory principles are

Drew Stapleton; Joe B. Hanna; Jonathan R. Ross

2006-01-01

334

Chaos Theory as a Model for Managing Issues and Crises.  

ERIC Educational Resources Information Center

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

Murphy, Priscilla

1996-01-01

335

Studying the connection between Aram Chaos and Ares Vallis  

Microsoft Academic Search

An unusual canyon (˜2.9° N, 341.7° E) with a complex geomorphic history connects Aram Chaos and Ares Vallis. Aram Chaos (centered on 2° N, 339° E) is a circular depression filled with irregular blocks. Ares Vallis, to the east of and slightly lower in elevation than Arem Chaos, is a long valley with a complex hydrologic history. A ˜100 km

E. Kraal; M. Kleinhans; T. Zegers; J. Oosthoek; A. Rossi

2006-01-01

336

Controlling chaos in a defined trajectory using adaptive fuzzy logic algorithm  

NASA Astrophysics Data System (ADS)

Chaos is a nonlinear behavior of chaotic system with the extreme sensitivity to the initial conditions. Chaos control is so complicated that solutions never converge to a specific numbers and vary chaotically from one amount to the other next. A tiny perturbation in a chaotic system may result in chaotic, periodic, or stationary behavior. Modern controllers are introduced for controlling the chaotic behavior. In this research an adaptive Fuzzy Logic Controller (AFLC) is proposed to control the chaotic system with two equilibrium points. This method is introduced as an adaptive progressed fashion with the full ability to control the nonlinear systems even in the undertrained conditions. Using AFLC designers are released to determine the precise mathematical model of system and satisfy the vast adaption that is needed for a rapid variation which may be caused in the dynamic of nonlinear system. Rules and system parameters are generated through the AFLC and expert knowledge is downright only in the initialization stage. So if the knowledge was not assuring the dynamic of system it could be changed through the adaption procedure of parameters values. AFLC methodology is an advanced control fashion in control yielding to both robustness and smooth motion in nonlinear system control.

Sadeghi, Maryam; Menhaj, Bagher

2012-09-01

337

CONTROL OF LASER RADIATION PARAMETERS: Excitation of dynamic chaos in a monolithic ring chip laser upon periodic modulation of mechanical stresses in the active element  

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

338

The Capabilities of Chaos and Complexity  

PubMed Central

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

339

Variational approach to nonlinear evolution of modulational instability using one-dimensional Zakharov equations  

Microsoft Academic Search

The Ritz variational method has been applied to the Zakharov equations to construct a model for the nonlinear evolution of modulational instability. Spatiotemporal chaos and nonlinear evolution patterns of the modulational instability are investigated theoretically by choosing an appropriate trial function for the field for periodic field and density perturbations. The spatially periodic field trial function was chosen in the

R. P. Sharma; K. Batra; S. S. Das

2005-01-01

340

Misfire detection of locomotive diesel engine by non-linear analysis  

Microsoft Academic Search

The paper describes the measurements of vibroacoustic exhaust locomotive engine signals for misfire phenomenon simulation and some results of their non-linear analysis. The misfire was simulated by disconnection of fuel supply of one cylinder of the engine. The analysis consists of non-linear methods that are based on the deterministic chaos theory. The results of the analysis demonstrate the dominant Lyapunov

Piotr Bogus; Jerzy Merkisz

2005-01-01

341

Nonlinear Response of the Upper Mesospheric Photochemical System Under Action of Diffusion  

Microsoft Academic Search

Choosing a simple oxygen-hydrogen model of the upper mesosphere, we study conditions necessary to create nonlinear effects like period doublings and chaos. The model is 1-dimensional and takes into account diffusion and diurnally periodic excitation by solar radiation. The air density decreasing with height acts as a control parameter. The computations show that the height range of nonlinear response of

G. R. Sonnemann; A. M. Feigin

1999-01-01

342

Nonlinear response of the upper mesospheric photochemical system under action of diffusion  

Microsoft Academic Search

Choosing a simple oxygen-hydrogen model of the upper mesosphere, we study conditions necessary to create nonlinear effects like period doublings and chaos. The model is 1-dimensional and takes into account diffusion and diurnally periodic excitation by solar radiation. The air density decreasing with height acts as a control parameter. The computations show that the height range of nonlinear response of

G. R. Sonnemann; A. M. Feigin

1999-01-01

343

Irreversible evolution of quantum chaos.  

PubMed

The pendulum is the simplest system having all the basic properties inherent in dynamic stochastic systems. In the present paper we investigate the pendulum with the aim to reveal the properties of a quantum analogue of dynamic stochasticity or, in other words, to obtain the basic properties of quantum chaos. It is shown that a periodic perturbation of the quantum pendulum (similarly to the classical one) in the neighborhood of the separatrix can bring about irreversible phenomena. As a result of recurrent passages between degenerate states, the system gets self-chaotized and passes from the pure state to the mixed one. Chaotization involves the states, the branch points of whose levels participate in a slow "drift" of the system along the Mathieu characteristics this "drift" being caused by a slowly changing variable field. Recurrent relations are obtained for populations of levels participating in the irreversible evolution process. It is shown that the entropy of the system first grows and, after reaching the equilibrium state, acquires a constant value. PMID:16089638

Ugulava, A; Chotorlishvili, L; Nickoladze, K

2005-05-26

344

Chaos, Chaos Control and Synchronization of Electro-Mechanical Gyrostat System  

NASA Astrophysics Data System (ADS)

The dynamic behavior of electro-mechanical gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, Period-T maps, and Lyapunov exponents are presented to observe periodic and chaotic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. Several methods, the delayed feedback control, adaptive control algorithm (ACA) control are used to control chaos effectively. Anticontrol of chaos destroyed the periodic motions and replaced by chaotic motion effectively by adding constant motor torque and adding periodic motor torque. Finally, synchronization of chaos in the electro-mechanical gyrostat system is studied.

Ge, Z.-M.; Lin, T.-N.

2003-01-01

345

Flank wear detection of cutting tool inserts in turning operation: application of nonlinear time series analysis  

Microsoft Academic Search

It has been established that turning process on a lathe exhibits low dimensional chaos. This study reports the results of\\u000a nonlinear time series analysis applied to sensor signals captured real time. The purpose of this chaos analysis is to differentiate\\u000a three levels of flank wears on cutting tool inserts—fresh, partially worn and fully worn—utilizing the single value index\\u000a extracted from

V. G. Rajesh; V. N. Narayanan Namboothiri

2010-01-01

346

Chaos, dynamical structure, and climate variability  

SciTech Connect

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

347

Control mechanisms for a nonlinear model of international relations  

SciTech Connect

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

348

The Application of Nonlinear Dynamics in Nursing Research  

Microsoft Academic Search

In this article, the authors present an overview of the applications of chaos theory and nonlinear dynamics to problems of relevance not only to nurses, but to anyone dealing with human functioning and interaction. These applications have been in the areas of epidemiology, nursing management and physiological functioning. In some cases, the applications were successful in identifying information that would

Patti Hamilton; Jane Englebright Pollock; De Ann F. Mitchell; Angela E. Vicenzi; Bruce J. West

1997-01-01

349

Applications of nonlinear time series analysis in solar physics  

Microsoft Academic Search

We applied methods of nonlinear time series analysis to different aspects of the solar phenomenology, as the solar cycle, the solar granulation and solar radio bursts. The methods include tests for deterministic chaos hidden in the data, as the determination of global attractor dimensions. However, in solar physics we deal with \\

A. Veronig; M. Messerotti; A. Hanslmeier

2000-01-01

350

Evidence for universal chaotic behavior of a driven nonlinear oscillator  

Microsoft Academic Search

A bifurcation diagram for a driven nonlinear semiconductor oscillator is measured directly, showing successive subharmonic bifurcations to f\\/32, onset of chaos, noise band merging, and extensive noise-free windows. The overall diagram closely resembles that computed for the logistic model. Measured values of universal numbers are reported, including effects of added noise.

James Testa; José Pérez; Carson Jeffries

1982-01-01

351

Invariant measure of a driven nonlinear oscillator with external noise  

Microsoft Academic Search

The effect of external white Gaussian noise on the invariant measure of a periodically driven damped nonlinear oscillator is studied by solving for the first time the full three-dimensional Fokker-Planck equation by numerical means. We critically discuss and interpret deterministic concepts and stochastic notions in the presence of noise and chaos.

Peter Jung; Peter Hänggi

1990-01-01

352

Nonlinear analysis and prediction of pulsatile hormone secretion  

SciTech Connect

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

353

Applications of nonlinear time-series analysis  

Microsoft Academic Search

In this work, new applications in chaos theory and nonlinear time-series analysis are explored. Tools for attractor-based analysis are developed along with a complete description of invariant measures. The focus is on the computation of dimension and Lyapunov spectra from a single time-history for the purposes of system identification. The need for accurate attractor reconstruction is stressed as it may

Jonathan Michael Nichols

2002-01-01

354

Dynamics of Flow: A Nonlinear Perspective  

Microsoft Academic Search

The aims of this study are to consider the experience of flow from a nonlinear dynamics perspective. The processes and temporal\\u000a nature of intrinsic motivation and flow, would suggest that flow experiences fluctuate over time in a dynamical fashion. Thus\\u000a it can be argued that the potential for chaos is strong. The sample was composed of 20 employees (both full

Lucia Ceja; José Navarro

2009-01-01

355

Covariant Description of the Inhomogeneous Mixmaster Chaos  

NASA Astrophysics Data System (ADS)

We outline the covariant nature of the chaos characterizing the generic cosmological solution near the initial singularity. Our analysis is based on a "gauge" independent ADM-reduction of the dynamics to the physical degrees of freedom, and shows that the dynamics is isomorphic point by point in space to a billiard on a Lobachevsky plane. The Jacobi metric associated to the geodesic flow is constructed and a non-zero Lyapunov exponent is explicitly calculated. The chaos covariance emerges from the independence of the form of the lapse function and the shift vector.

Benini, R.; Montani, G.

2008-09-01

356

Wave chaos in rapidly rotating stars.  

PubMed

The effects of rapid stellar rotation on acoustic oscillation modes are poorly understood. We study the dynamics of acoustic rays in rotating polytropic stars and show using quantum chaos concepts that the eigenfrequency spectrum is a superposition of regular frequency patterns and an irregular frequency subset respectively associated with near-integrable and chaotic phase space regions. This opens fresh perspectives for rapidly rotating star seismology and also provides a potentially observable manifestation of wave chaos in a large-scale natural system. PMID:18764043

Lignières, François; Georgeot, Bertrand

2008-07-31

357

Quasiperiodicity and chaos in cardiac fibrillation.  

PubMed Central

In cardiac fibrillation, disorganized waves of electrical activity meander through the heart, and coherent contractile function is lost. We studied fibrillation in three stationary forms: in human chronic atrial fibrillation, in a stabilized form of canine ventricular fibrillation, and in fibrillation-like activity in thin sheets of canine and human ventricular tissue in vitro. We also created a computer model of fibrillation. In all four studies, evidence indicated that fibrillation arose through a quasiperiodic stage of period and amplitude modulation, thus exemplifying the "quasiperiodic transition to chaos" first suggested by Ruelle and Takens. This suggests that fibrillation is a form of spatio-temporal chaos, a finding that implies new therapeutic approaches.

Garfinkel, A; Chen, P S; Walter, D O; Karagueuzian, H S; Kogan, B; Evans, S J; Karpoukhin, M; Hwang, C; Uchida, T; Gotoh, M; Nwasokwa, O; Sager, P; Weiss, J N

1997-01-01

358

Resurvey of order and chaos in spinning compact binaries  

SciTech Connect

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

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

2008-05-15

359

Bifurcations and chaos in register transitions of excised larynx experiments  

NASA Astrophysics Data System (ADS)

Experimental data from an excised larynx are analyzed in the light of nonlinear dynamics. The excised larynx provides an experimental framework that enables artificial control and direct observation of the vocal fold vibrations. Of particular interest in this experiment is the coexistence of two distinct vibration patterns, which closely resemble chest and falsetto registers of the human voice. Abrupt transitions between the two registers are typically accompanied by irregular vibrations. Two approaches are presented for the modeling of the excised larynx experiment; one is the nonlinear predictive modeling of the experimental time series and the other is the biomechanical modeling (three-mass model) that takes into account basic mechanisms of the vocal fold vibrations. The two approaches show that the chest and falsetto vibrations correspond to two coexisting limit cycles, which jump to each other with a change in the bifurcation parameter. Irregular vibrations observed at the register jumps are due to chaos that exists near the two limit cycles. This provides an alternative mechanism to generate chaotic vibrations in excised larynx experiment, which is different from the conventionally known mechanisms such as strong asymmetry between the left and right vocal folds or excessively high subglottal pressure.

Tokuda, Isao T.; Horá?ek, Jaromir; Švec, Jan G.; Herzel, Hanspeter

2008-03-01

360

Prospects for chaos control of machine tool chatter  

SciTech Connect

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

361

Exponential power spectra, deterministic chaos and Lorentzian pulses in plasma edge dynamics  

NASA Astrophysics Data System (ADS)

Exponential spectra have been observed in the edges of tokamaks, stellarators, helical devices and linear machines. The observation of exponential power spectra is significant because such a spectral character has been closely associated with the phenomenon of deterministic chaos by the nonlinear dynamics community. The proximate cause of exponential power spectra in both magnetized plasma edges and nonlinear dynamics models is the occurrence of Lorentzian pulses in the time signals of fluctuations. Lorentzian pulses are produced by chaotic behavior in the separatrix regions of plasma E × B flow fields or the limit cycle regions of nonlinear models. Chaotic advection, driven by the potential fields of drift waves in plasmas, results in transport. The observation of exponential power spectra and Lorentzian pulses suggests that fluctuations and transport at the edge of magnetized plasmas arise from deterministic, rather than stochastic, dynamics.

Maggs, J. E.; Morales, G. J.

2012-12-01

362

Source of human ventilatory chaos: lessons from switching controlled mechanical ventilation to inspiratory pressure support in critically ill patients.  

PubMed

Ventilatory flow measured at the airway opening in humans exhibits a complex dynamics that has the features of chaos. Currently available data point to a neural origin of this feature, but the role of respiratory mechanics has not been specifically assessed. In this aim, we studied 17 critically ill mechanically ventilated patients during a switch form an entirely machine-controlled assistance mode (assist-controlled ventilation ACV) to a patient-driven mode (inspiratory pressure support IPS). Breath-by-breath respiratory variability was assessed with the coefficient of variation of tidal volume, total cycle time, inspiratory time, expiratory time, mean inspiratory flow, duty cycle. The detection of chaos was performed with the noise titration technique. When present, chaos was characterized with numerical indexes (correlation dimension, irregularity; largest Lyapunov exponent, sensitivity to initial conditions). Expectedly, the coefficients of variations of the respiratory variables were higher during IPS than during ACV. During ACV, noise titration failed to detect nonlinearities in 12 patients who did not exhibit signs of spontaneous respiratory activity. This indicates that the mechanical properties of the respiratory system were not sufficient to produce ventilatory chaos in the presence of a nonlinear command (ventilator clock). A positive noise limit was found in the remaining 5 cases, but these patients exhibited signs of active expiratory control (highly variable expiratory time, respiratory frequency higher than the set frequency). A positive noise limit was also observed in 16/17 patients during IPS (p<0.001). These observations suggest that ventilatory chaos predominantly has a neural origin (intrinsic to the respiratory central pattern generators, resulting from their perturbation by respiratory afferents, or both), with little contribution of respiratory mechanics, if any. PMID:18387347

Mangin, Laurence; Fiamma, Marie-Noëlle; Straus, Christian; Derenne, Jean-Philippe; Zelter, Marc; Clerici, Christine; Similowski, Thomas

2008-02-29

363

Unified model and reverse recovery nonlinearities of the driven diode resonator  

NASA Astrophysics Data System (ADS)

We study the origins of period doubling and chaos in the driven series resistor-inductor-varactor diode (RLD) nonlinear resonant circuit. We find that resonators driven at frequencies much higher than the diode reverse recovery rate do not show period doubling. Models of chaos based on the nonlinear capacitance of the varactor diode display a reverse-recovery-like effect, and this effect strongly resembles reverse recovery of real diodes. We find for the first time that in addition to the known dependence of the reverse recovery time on past current maxima, there are also important nonlinear dependencies on pulse frequency, duty cycle, and dc voltage bias. Similar nonlinearities are present in the nonlinear capacitance models of these diodes. We conclude that a history-dependent and nonlinear reverse-recovery time is an essential ingredient for chaotic behavior of this circuit, and demonstrate for the first time that all major competing models have this effect, either explicitly or implicitly. Besides unifying the two major models of RLD chaos, our work reveals that the nonlinearities of the reverse-recovery time must be included for a complete understanding of period doubling and chaos in this circuit.

de Moraes, Renato Mariz; Anlage, Steven M.

2003-08-01

364

Chaos in three species food chains  

Microsoft Academic Search

We study the dynamics of a three species food chain using bifurcation theory to demonstrate the existence of chaotic dynamics in the neighborhood of the equilibrium where the top species in the food chain is absent. The goal of our study is to demonstrate the presence of chaos in a class of ecological models, rather than just in a specific

Aaron Klebanoff; Alan Hastings

1994-01-01

365

Chaos theory, informational needs, and natural disasters  

Microsoft Academic Search

This study applies chaos theory to a system-wide analysis of crisis communication in a natural disaster. Specifically, we analyze crisis communication during the 1997 Red River Valley flood in Minnesota and North Dakota. This flood, among the worst in modern American history, consumed entire metropolitan areas, displacing thousands of people. The conditions and decisions leading to the disaster, and the

Timothy L. Sellnow; Matthew W. Seeger; Robert R. Ulmer

2002-01-01

366

Divergence of classical trajectories and quantum chaos  

Microsoft Academic Search

This paper reviews our recent studies of the logarithmical in ? effects in the statistical description of quantum chaos. We concentrate on the deviations from the universality in the level statistics and in the quantum correction to the conductivity. For the latter, we find that the weak localization correction to the current response is delayed by the large time tE

I. L. Aleiner; A. I. Larkin

1997-01-01

367

An expose on discrete Wiener chaos expansions  

Microsoft Academic Search

In this note we review and compare dierent versions of expansions in discrete Wiener chaos. We relate these expansions to the Rota-Wallstrom combinatorial approach to stochastic integration and to extended Haar systems. At the end we present some simple applications. 1 Preliminaries Discrete stochastic calculus has seen a revival during the last decade or so, and several lines of work

Henryk Gzyl

2006-01-01

368

Integrability and Chaos: The Classical Uncertainty  

ERIC Educational Resources Information Center

|In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now referred to as deterministic chaos. There is still substantial interest in a matter that is included in many graduate and even undergraduate courses on classical…

Masoliver, Jaume; Ros, Ana

2011-01-01

369

A Framework for Chaos Theory Career Counselling  

ERIC Educational Resources Information Center

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

Pryor, Robert G. L.

2010-01-01

370

Poincaré's contributions to chance and chaos.  

NASA Astrophysics Data System (ADS)

In this paper a short and condensed biography of Henri Poincaré is presented with detailed information concerning several biographical references. This is followed by a review of his publications emphasizing his work in celestial mechanics and on the problem of three bodies. His article "Le Hasard" is reviewed in detail discussing his contributions to chaos.

Szebehely, V.

371

Somalia after state collapse: Chaos or improvement?  

Microsoft Academic Search

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

Benjamin Powell; Ryan Ford; Alex Nowrasteh

2008-01-01

372

Chaos: Connecting Science and the Humanities  

NSDL National Science Digital Library

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

Paddy, David; Lagan, Seamus

2005-01-01

373

Integrability and Chaos: The Classical Uncertainty  

ERIC Educational Resources Information Center

In recent years there has been a considerable increase in the publishing of textbooks and monographs covering what was formerly known as random or irregular deterministic motion, now referred to as deterministic chaos. There is still substantial interest in a matter that is included in many graduate and even undergraduate courses on classical…

Masoliver, Jaume; Ros, Ana

2011-01-01

374

Chaos: Connecting Science and the Humanities  

ERIC Educational Resources Information Center

We describe a team-taught course entitled Chaos in Science and Literature. Our course goals were to place science in a nontechnological context, emphasizing its intellectual and cultural aspects, and to provide a forum for the exchange of ideas between "scientists" and "humanists," with the authors serving as role models. (Contains 4 figures.)

Lagan, Seamus; Paddy, David

2005-01-01

375

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

376

On Stable Chaos in the Asteroid Belt  

Microsoft Academic Search

Recent numerical integration of Sidlichovsky and Nesvorny showed that 26 out of the first one hundred numbered asteroids have Lyapunov time TL shorter than 50 thousand years. Calculations were performed taking into account both outer and inner planets (without Mercury and Pluto). As the proper elements are reasonably stable for several 10^7 years we have the case of stable chaos.

M. Sidlichovský

1999-01-01

377

RADEMACHER CHAOS: TAIL ESTIMATES VS LIMIT THEOREMS  

Microsoft Academic Search

We study Rademacher chaos indexed by a sparse set which has a fractional combinatorial dimension. We obtain tail estimates for finite sums and a normal limit theorem as the size tends to infinity. The tails for finite sums may be much larger that the tails of the limit.

RON BLEI; SVANTE JANSON

2003-01-01

378

Electronic circuit implementation of chaos synchronization  

NASA Astrophysics Data System (ADS)

In this paper, an electronic circuit implementation of a robustly chaotic two-dimensional map is presented. Two such electronic circuits are realized. One of the circuits is configured as the driver and the other circuit is configured as the driven system. Synchronization of chaos between the driver and the driven system is demonstrated.

Ranjan, R.; Mishra, S.; Madhekar, S.

2013-07-01

379

Chaos in an Eulerian Based Model of Sickle Cell Blood Flow  

NASA Astrophysics Data System (ADS)

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

Apori, Akwasi; Harris, Wesley

2001-11-01

380

Barriers in the transition to global chaos in collisionless magnetic reconnection. II. Field line spectroscopy  

SciTech Connect

The transitional phase from local to global chaos in the magnetic field of a reconnecting current layer is investigated. The identification of the ridges in the field of the finite time Lyapunov exponent as barriers to the field line motion is carried out adopting the technique of field line spectroscopy to analyze the radial position of a field line while it winds its way through partial stochastic layers and to compare the frequencies of the field line motion with the corresponding frequencies of the distinguished hyperbolic field lines that are the nonlinear generalizations of linear X-lines.

Borgogno, D. [Dipartimento di Energetica, Politecnico di Torino, Torino (Italy); Grasso, D. [CNR Consiglio Nazionale delle Ricerche, Istituto dei Sistemi Complessi, Dipartimento di Energetica, Politecnico di Torino, Torino (Italy); Pegoraro, F. [Department of Physics, Pisa University, Pisa CNISM (Italy); Schep, T. J. [Department of Physics, Eindhoven University of Technology, Eindhoven (Netherlands)

2011-10-15

381

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

382

Controlling chaos in spatially extended beam-plasma system by the continuous delayed feedback  

SciTech Connect

In this paper we discuss the control of complex spatio-temporal dynamics in a spatially extended nonlinear system (fluid model of Pierce diode) based on the concepts of controlling chaos in the systems with few degrees of freedom. A presented method is connected with stabilization of unstable homogeneous equilibrium state and the unstable spatio-temporal periodical states analogous to unstable periodic orbits of chaotic dynamics of the systems with few degrees of freedom. We show that this method is effective and allows to achieve desired regular dynamics chosen from a number of possible in the considered system.

Hramov, Alexander E.; Koronovskii, Alexey A.; Rempen, Irene S. [Department of Nonlinear Processes, Saratov State University, Astrakhanskaya, 83, Saratov, 410012 (Russian Federation)

2006-03-15

383

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

NASA Astrophysics Data System (ADS)

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

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

2009-03-01

384

Low dimensional chaos in the AT and GC skew profiles of DNA sequences  

NASA Astrophysics Data System (ADS)

This paper investigates the existence of low-dimensional deterministic chaos in the AT and GC skew profiles of DNA sequences. It has taken DNA sequences from eight organisms as samples. The skew profiles are analysed using continuous wavelet transform and then nonlinear time series methods. The invariant measures of correlation dimension and the largest Lyapunov exponent are calculated. It is demonstrated that the AT and GC skew profiles of these DNA sequences all exhibit low dimensional chaotic behaviour. It suggests that chaotic properties may be ubiquitous in the DNA sequences of all organisms.

Zhou, Qian; Chen, Zeng-Qiang

2010-09-01

385

Hyperbolic Kac-Moody algebras and chaos in Kaluza-Klein models  

NASA Astrophysics Data System (ADS)

Some time ago, it was found that the never-ending oscillatory chaotic behaviour discovered by Belinskii, Khalatnikov and Lifshitz (BKL) for the generic solution of the vacuum Einstein equations in the vicinity of a spacelike (``cosmological'') singularity disappears in spacetime dimensions /D?d+1>10. Recently, a study of the generalization of the BKL chaotic behaviour to the superstring effective Lagrangians has revealed that this chaos is rooted in the structure of the fundamental Weyl chamber of some underlying hyperbolic Kac-Moody algebra. In this Letter we show that the same connection applies to pure gravity in any spacetime dimension />=4, where the relevant algebras are AEd. In this way the disappearance of chaos in pure gravity models in /D>=11 dimensions becomes linked to the fact that the Kac-Moody algebras AEd are no longer hyperbolic for /d>=10.

Damour, T.; Henneaux, M.; Julia, B.; Nicolai, H.

2001-06-01

386

Nonlinear Dynamic Processes as a Source of Uncertainty for Flow Simulations through Partially Saturated Fractured-Porous Media  

Microsoft Academic Search

The concept of nonlinear dynamics and chaos can be used to provide an alternative explanation for the irreducible uncertainty of seemingly erratic temporal and spatial oscillations of variables characterizing unsaturated flow and transport within fractured-porous media. The goals of this presentation are to discuss the physical processes and to quantify the uncertainty of flow characteristics caused by deterministic-chaotic, nonlinear dynamic

B. Faybishenko

2007-01-01

387

Chaos Cryptography with Dynamical Systems  

NASA Astrophysics Data System (ADS)

Cryptography is a subject that draws strength from an amazing variety of different mathematical fields, including such deep results as the Weil-Dwork-Deligne theorem on the zeta function. Physical theories have recently entered the subject as well, an example being the subject of quantum cryptography, motivated in part by Shor's insight into the vulnerability of prime number factorization based crypto systems. In this contribution we describe a cryptographic algorithm which is based on the dynamics of a class of physical models that exhibit chaotic behavior. More precisely, we consider dissipative systems which are described by nonlinear three-dimensional systems of differential equations with strange attractor surfaces of non-integer Lyapunov dimension. The time evolution of such systems in part of the moduli space shows unpredictable behavior, which suggests that they might be useful as pseudorandom number generators. We will show that this is indeed the case and illustrate our procedure mainly with the Lorenz attractor, though we also briefly mention the Rössler system. We use this class of nonlinear models to construct an extremely fast stream cipher with a large keyspace, which we test with Marsaglia's battery of DieHard tests.

Anderson, Robert; Morse, Jack; Schimmrigk, Rolf

2001-11-01

388

Chaos as a social determinant of child health: Reciprocal associations?  

PubMed

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

2013-03-14

389

Ray and wave chaos in underwater acoustic waveguides  

NASA Astrophysics Data System (ADS)

In the 1990s, the study of the chaotic behavior of ray trajectories in inhomogeneous waveguides emerged as a new field in ocean acoustics. It turned out that at ranges on the order of or larger than 1000 km ray chaos is well developed and should be taken into account when describing long-range sound propagation in the ocean. The theoretical analysis of ray chaos and of its finite-wavelength manifestation, wave chaos, is to a large extent based on well-known methods and ideas from the theory of dynamical and quantum chaos. Concrete examples are used to review the results obtained in this field over the last two decades.

Virovlyansky, Anatolii L.; Makarov, Denis V.; Prants, Sergei V.

2012-01-01

390

Chaos-assisted tunnelling with cold atoms  

NASA Astrophysics Data System (ADS)

In the context of quantum chaos, both theory and numerical analysis predict large fluctuations of the tunnelling transition probabilities when irregular dynamics is present at the classical level. We consider here the non-dissipative quantum evolution of cold atoms trapped in a time-dependent modulated periodic potential generated by two laser beams. We give some precise guidelines for the observation of chaos assisted tunnelling between invariant phase space structures paired by time-reversal symmetry. The recent experiments done by Phillips's team from the National Institute of Standards and Technology, Maryland [Nature vol.412 (2001) p.52] and by Raizen's team from the University of Texas [Science vol.293 (2001) p.274] will also be discussed.

Mouchet, Amaury; Miniatura, Christian; Kaiser, Robin; Grémaud, Benoît; Delande, Dominique

2002-05-01

391

Finding equilibrium statistical mechanics in spatiotemporal chaos  

NASA Astrophysics Data System (ADS)

Ruelle has argued that the extensivity of the complicated dynamics of spatiotemporal chaos is evidence that these systems can be viewed as a gas of weakly-interacting regions of a characteristic size. We have performed large-scale computational studies of spatiotemporal chaos in the 1D complex Ginzburg-Landau equation and have found that histograms of the number of maxima in the amplitude are well-described by an equilibrium Tonks gas (and variants) in the grand canonical ensemble. Furthermore, for small system sizes, the average number of particles in the Tonks gas (with particle sizes and temperatures determined from fits to the CGL histograms) exhibits oscillatory, decaying deviations from extensivity in agreement with the deviations in the fractal dimension found by Fishman and Egolf. This result not only supports Ruelle's picture but also suggests that the coarse-grained behavior of this far-from-equilibrium system might be understood using equilibrium statistical mechanics.

Esty, C. Clark; Ballard, Christopher C.; Kerin, John A.; Egolf, David A.

2013-03-01

392

Dimensions Associated with Defects in Spatiotemporal Chaos  

NASA Astrophysics Data System (ADS)

In recent work,(David A. Egolf. Building blocks of spatiotemporal chaos: the dimension of defects in the 2D complex Ginzburg-Landau equation. In preparation. 1996.) we defined a finite-time Lyapunov dimension D^T based on the evolution of Lyapunov vectors over short time intervals of length T. For the complex Ginzburg-Landau equation in two spatial dimensions, we showed that on average D^T is linearly related to the mean number of defects in the system during the same time interval. The average dimension per defect is about 2 over a wide range of parameter values. We review this work and present new calculations comparing values of D^T to the average number of spirals present in the spiral defect chaos state in a generalized Swift-Hohenberg model of convection. This work is supported by NSF-ASC-9503963 and the Cornell Theory Center.

Egolf, David A.; Bodenschatz, Eberhard

1996-11-01

393

Nonlinear Acoustic NDE Using Complete Nonclassical Spectra  

NASA Astrophysics Data System (ADS)

In the presence of cracked defects, material nonlinear response is determined by local contact dynamics which strongly depends on the amplitude of acoustic wave. At moderate driving amplitude, the contact acoustic nonlinearity suggests a fully deterministic scenario of higher harmonic generation and/or wave modulation. Unlike classical nonlinear materials, these effects feature much higher efficiency, specific dynamic characteristics, modulated spectra, and unconventional acoustic waveform distortion. At higher excitation, the contact vibrations acquire a dynamic instability which is a forerunner of transition to chaos. Such a dynamics is interpreted on the basis of nonlinear resonance phenomena for a defect conceived as a set of coupled oscillators. It is shown to result in a decay of external excitation into either a combination frequency pair or a subharmonic mode. For higher-order contact nonlinearity, the nonlinear spectrum expands considerably to include the ultra-subharmonic and ultra-frequency pair modes. Experiments show that even a moderate acoustic excitation of realistic cracked defects gives rise to the instability vibration modes which exhibit threshold behavior and distinctive hysteretic dynamics. All the modes-contributors to such non-classical nonlinear spectra display a high localization in the areas of nonlinear contacts and visualize readily various fractured defects in solids. The case studies presented include Hi-tech and constructional materials and demonstrate their applicability for defect-selective imaging in nonlinear NDE.

Solodov, I.; Pfleiderer, K.; Busse, G.

2006-05-01

394

Controlling spatiotemporal chaos in coupled map lattices  

SciTech Connect

A simple method is presented for controlling spatiotemporal chaos in coupled map lattices to a homogeneous state. This method can be applied to many kinds of models such as coupled map lattices (CML), one-way open CML (the open-flow model), and globally coupled map. We offer the stability analysis of the homogeneous state. Simple and sufficient conditions are obtained for controlling the above mentioned models. Our theoretical results agree well with numerical simulations.

Zhu, KaiEn; Chen, Tianlun

2001-06-01

395

Oscillations, Synchrony and DeterministicChaos  

Microsoft Academic Search

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

396

Stein’s method on Wiener chaos  

Microsoft Academic Search

We combine Malliavin calculus with Stein’s method, in order to derive explicit bounds in the Gaussian and Gamma approximations\\u000a of random variables in a fixed Wiener chaos of a general Gaussian process. Our approach generalizes, refines and unifies the\\u000a central and non-central limit theorems for multiple Wiener–Itô integrals recently proved (in several papers, from 2005 to\\u000a 2007) by Nourdin, Nualart,

Ivan Nourdin; Giovanni Peccati

2009-01-01

397

Detecting chaos in irregularly sampled time series  

NASA Astrophysics Data System (ADS)

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.

Kulp, C. W.

2013-09-01

398

Detecting chaos in irregularly sampled time series.  

PubMed

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

399

A new method for line spectra reduction similar to generalized synchronization of chaos  

NASA Astrophysics Data System (ADS)

Line spectra in the radiated noise of marine vessels are the most visible signs, which can be detected, tracked and identified by enemy's passive sonar, and hence it is of great significance to reduce the line spectra for improving the acoustic stealth of marine vessels. In this paper, a driving parameter scheme using an external chaotic signal to drive a nonlinear vibration isolation system (VIS) of onboard machinery is presented to make the chaotic motion in the nonlinear VIS persistent, which is similar to generalized synchronization of chaos in some sense. In this way, the line spectra in the radiated noise can be reduced effectively because the response spectrum of a chaotic system under harmonic excitations is a continuous and reduced one. Numerical simulations are carried out and the results confirm the effectiveness of this method. The maximum conditional Lyapunov exponent is calculated numerically and its negative value indicates the stability of this driving parameter control scheme.

Yu, Xiang; Zhu, Shijian; Liu, Shuyong

2007-10-01

400

Chaos in the heart: the interaction between body and mind  

NASA Astrophysics Data System (ADS)

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

Redington, Dana

1993-11-01

401

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

PubMed

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

402

Amplifier similariton fiber laser with nonlinear spectral compression.  

PubMed

We propose a new concept of a fiber laser architecture supporting self-similar pulse evolution in the amplifier and nonlinear spectral pulse compression in the passive fiber. The latter process allows for transform-limited picosecond pulse generation, and improves the laser's power efficiency by preventing strong spectral filtering from being highly dissipative. Aside from laser technology, the proposed scheme opens new possibilities for studying nonlinear dynamical processes. As an example, we demonstrate a clear period-doubling route to chaos in such a nonlinear laser system. PMID:23114353

Boscolo, Sonia; Turitsyn, Sergei K; Finot, Christophe

2012-11-01

403

Sights and sounds of chaos [autonomous and nonautonomous circuits  

Microsoft Academic Search

The concept of chaos is introduced using actual circuit experiments. Several well-known chaotic circuits are used as vehicles to demonstrate the many phenomena associated with chaos. They are divided into two classes, autonomous and nonautonomous. For the simplest autonomous circuits the authors examine strange attractors, the Lorenz circuit, Lyapunov exponents, and fractals. For the simplest nonautonomous circuits they consider period-doubling,

L. O. Chua; R. N. Madan

1988-01-01

404

New Math for Leaders: Useful Ideas from Chaos Theory.  

National Technical Information Service (NTIS)

This research project is a study of the implications of modern chaos theory on military management and leadership for the next century. The critical elements of chaos theory are presented in a non-mathematical treatment to reach the broadest audience. The...

G. W. Mitchell

1998-01-01

405

Chaos Theory as a Lens for Advancing Quality Schooling.  

ERIC Educational Resources Information Center

Chaos theory provides a useful mental model for guiding change as leaders garner the energy from unpredictable events for realizing transformation goals. The paper considers chaos theory as a framework for managing school change toward Total Quality Management work cultures. Change is possible to manage when plans are made and then followed by a…

Snyder, Karolyn J.; Acker-Hocevar, Michele; Wolf, Kristen M.

406

Chaos: A Topic for Interdisciplinary Education in Physics  

ERIC Educational Resources Information Center

Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…

Bae, Saebyok

2009-01-01

407

Chaos in multiple-photon excitation of molecules  

Microsoft Academic Search

With use of a Hamiltonian model system to represent IR laser excitation of a molecule it is shown that chaos is a fundamental aspect of this physical process. On average the chaos leads to a fluence-dependent absorption which previously was attributed to rapid statistical equilibration of energy in the quasicontinuum and was modeled by population rate equations. The origin of

J. R. Ackerhalt; H. W. Galbraith; P. W. Milonni

1983-01-01

408

Chaos in multiple-photon excitation of molecules  

Microsoft Academic Search

With use of a Hamiltonian model system to represent ir laser excitation of a molecule it is shown that chaos is a fundamental aspect of this physical process. On average the chaos leads to a fluence-dependent absorption which previously was attributed to rapid statistical equilibration of energy in the quasicontinuum and was modeled by population rate equations. The origin of

Jay Ackerhalt; Harold Galbraith; Peter Milonni

1983-01-01

409

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

410

The Chaos Theory of Careers: A User's Guide  

ERIC Educational Resources Information Center

|The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…

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

2005-01-01

411

Chaos: A Topic for Interdisciplinary Education in Physics  

ERIC Educational Resources Information Center

|Since society and science need interdisciplinary works, the interesting topic of chaos is chosen for interdisciplinary education in physics. The educational programme contains various university-level activities such as computer simulations, chaos experiment and team projects besides ordinary teaching. According to the participants, the programme…

Bae, Saebyok

2009-01-01

412

Integration of chaos theory and mathematical models in building simulation  

Microsoft Academic Search

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on

Xiaoshu Lu; Derek Clements-Croome; Martti Viljanen

2010-01-01

413

The Chaos Theory of Careers: A User's Guide  

ERIC Educational Resources Information Center

The purpose of this article is to set out the key elements of the Chaos Theory of Careers. The complexity of influences on career development presents a significant challenge to traditional predictive models of career counseling. Chaos theory can provide a more appropriate description of career behavior, and the theory can be applied with clients…

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

2005-01-01

414

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

415

Uncertainty Propagation in CFD Using Polynomial Chaos Decomposition  

Microsoft Academic Search

Uncertainty quantication (UQ) in CFD computations is receiving increased in- terest, due in large part to the increasing complexity of physical models, and the inherent introduction of random model data. This paper focuses on recent applica- tion of Polynomial Chaos (PC) methods for uncertainty representation and propa- gation in CFD computations. The fundamental concept on which Polynomial Chaos (PC) representations

O. M. Knio

2005-01-01

416

Master Teachers: Making a Difference on the Edge of Chaos  

ERIC Educational Resources Information Center

|The No Child Left Behind legislation, by legitimizing a stark, one-size-fits-all, industrial model of education, has denied the inherent complexity and richness of what teachers do. Discussing teaching in terms of Chaos Theory, Chapin explains that while excellent teaching may occur at the edge of chaos, it is not chaotic. There are patterns…

Chapin, Dexter

2008-01-01

417

Evidence for Multiple Depositional Periods in Aram Chaos, Mars  

Microsoft Academic Search

Analysis of CTX, HiRISE, OMEGA, and CRISM data over Aram Chaos shows that monohydrated sulfate-bearing materials mixed with nanophase iron oxides were unconformably overlain onto chaos blocks that define the basement of the crater floor. After a period of considerable wind erosion, a section of polyhydrated materials was deposited. This stratigraphic section is interpreted to indicate that at least two

K. A. Lichtenberg; R. E. Arvidson; R. V. Morris; S. L. Murchie; J. L. Bishop; D. C. Fernandez-Remolar; T. D. Glotch; E. Z. Noe Dobrea; J. F. Mustard; J. C. Andrews-Hanna; L. Roach

2009-01-01

418

Optical double-sideband modulation to single-sideband modulation conversion using period-one nonlinear dynamics of semiconductor lasers for radio-over-fiber links.  

PubMed

To distribute microwaves over fibers, optical single-sideband (SSB) modulation signals are preferred to optical double-sideband (DSB) modulation signals. This study investigates an optically injected semiconductor laser at period-one nonlinear dynamics for optical DSB-to-SSB conversion. For the operating microwave frequencies up to 40 GHz investigated in this study, the proposed system regenerates or even enhances the microwave features of an optical DSB input while converting its optical feature into SSB with an intensity difference of at least 20 dB. The bit-error ratio at 622 Mb/s is down to 10(-9) with a sensitivity improvement of up to 3 dB. The proposed system can be self-adapted to certain changes in the operating microwave frequency and can operate stably under certain fluctuations in the input optical power and frequency. PMID:23632525

Hung, Yu-Han; Chu, Cheng-Hao; Hwang, Sheng-Kwang

2013-05-01

419

Random matrices and chaos in nuclear physics: Nuclear structure  

SciTech Connect

Evidence for the applicability of random-matrix theory to nuclear spectra is reviewed. In analogy to systems with few degrees of freedom, one speaks of chaos (more accurately, quantum chaos) in nuclei whenever random-matrix predictions are fulfilled. An introduction into the basic concepts of random-matrix theory is followed by a survey over the extant experimental information on spectral fluctuations, including a discussion of the violation of a symmetry or invariance property. Chaos in nuclear models is discussed for the spherical shell model, for the deformed shell model, and for the interacting boson model. Evidence for chaos also comes from random-matrix ensembles patterned after the shell model such as the embedded two-body ensemble, the two-body random ensemble, and the constrained ensembles. All this evidence points to the fact that chaos is a generic property of nuclear spectra, except for the ground-state regions of strongly deformed nuclei.

Weidenmueller, H. A.; Mitchell, G. E. [Max-Planck-Institut fuer Kernphysik, D-69029 Heidelberg (Germany); North Carolina State University, Raleigh, North Carolina 27695 (United States) and Triangle Universities Nuclear Laboratory, Durham, North Carolina 27706 (United States)

2009-04-15

420

Dynamic modeling of chaos and turbulence  

Microsoft Academic Search

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

421

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

422

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

ERIC Educational Resources Information Center

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

Adams, Helen M.; Russ, John C.

1992-01-01

423

Reducing or enhancing chaos using periodic orbits.  

PubMed

A method to reduce or enhance chaos in Hamiltonian flows with two degrees of freedom is discussed. This method is based on finding a suitable perturbation of the system such that the stability of a set of periodic orbits changes (local bifurcations). Depending on the values of the residues, reflecting their linear stability properties, a set of invariant tori is destroyed or created in the neighborhood of the chosen periodic orbits. An application on a paradigmatic system, a forced pendulum, illustrates the method. PMID:16822007

Bachelard, R; Chandre, C; Leoncini, X

2006-06-01

424

Geometry in the large and hyperbolic chaos  

SciTech Connect

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

425

Method of controlling chaos in laser equations  

NASA Astrophysics Data System (ADS)

A method of controlling chaotic to laminar flows in the Lorenz equations using fixed points dictated by minimizing the Lyapunov functional was proposed by Singer, Wang, and Bau [Phys. Rev. Lett. 66, 1123 (1991)]. Using different fixed points, we find that the solutions in a chaotic regime can also be periodic. Since the laser equations are isomorphic to the Lorenz equations we use this method to control chaos when the laser is operated over the pump threshold. Furthermore, by solving the laser equations with an occasional proportional feedback mechanism, we recover the essential laser controlling features experimentally discovered by Roy, Murphy, Jr., Maier, Gills, and Hunt [Phys. Rev. Lett. 68, 1259 (1992)].

Duong-van, Minh

1993-01-01

426

Has Non-linear Analysis of Heart Rate Variability Any Practical Value?  

Microsoft Academic Search

In this article, we focus on the recent advances in the assessment of the heart rate variability (HRV). Speci~cally, we review some of the new methods to assess heart rate dynamics based on non-linear mathematics and chaos theory. These methods do not quantify the actual magnitude of HRV but describe the complexity and dynamics of heart rate _uctuation. Although the

Antti E. Hedman; Juha E. K. Hartikainen

1999-01-01

427

Nonlinear panel flutter in a turbulent boundary layer of a weakly compressible flow  

NASA Astrophysics Data System (ADS)

Nonlinear panel flutter and flutter of a system of two adjacent panels with fixed edges in a turbulent boundary layer of a subsonic compressible flow are studied. Panels are successively butt-jointed downstream at one level with a rigid flat surface. The possibility of dynamical chaos in such a system is analyzed using analytical approximations for matrix elements of adjoint elasticities.

Reutov, V. P.

1993-04-01

428

Modeling of chaotic DC-DC converters by iterated nonlinear mappings  

Microsoft Academic Search

In parameter ranges where conventional methods break down, DC-DC converters may be described by iterated mappings, a nonlinear discrete modeling technique. The underlying principles are explained and are applied to the example of a PWM-controlled buck converter. Stable behavior and bifurcations to chaos are predicted by numerical evaluation of the governing mapping and are confirmed by experiment

David C. Hamill; Jonathan H. B. Deane; David J. Jefferies

1992-01-01

429

Nonlinear behavior of a reaction-diffusion system of the photochemistry within the mesopause region  

Microsoft Academic Search

The photochemistry of the mesopause region entails a driven chemical oscillator enforced by solar short-wave irradiation. Zero-dimensional calculations show that this oscillator is able to produce nonlinear reactions like cascades of subharmonics or chaos. We investigate what will happen if this system is subjected to atmospheric diffusion. We discuss the system response and introduce different kinds of bifurcations.

G. Sonnemann; A. M. Feigin

1999-01-01

430

RAPID DYNAMICAL CHAOS IN AN EXOPLANETARY SYSTEM  

SciTech Connect

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

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

2012-08-10

431

Rapid Dynamical Chaos in an Exoplanetary System  

NASA Astrophysics Data System (ADS)

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

Deck, Katherine M.; Holman, Matthew J.; Agol, Eric; Carter, Joshua A.; Lissauer, Jack J.; Ragozzine, Darin; Winn, Joshua N.

2012-08-01

432

Chaos and structure of level densities  

SciTech Connect

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

433

Interactions destroy dynamical localization with strong and weak chaos  

NASA Astrophysics Data System (ADS)

Bose-Einstein condensates loaded into kicked optical lattices can be treated as quantum kicked-rotor systems. Noninteracting rotors show dynamical localization in momentum space. The experimentally tunable condensate interaction is included in a qualitative Gross-Pitaevskii-type model based on two-body interactions. We observe strong- and weak-chaos regimes of wave packet spreading in momentum space. In the intermediate strong-chaos regime the condensate energy grows as t1/2. In the asymptotic weak-chaos case the growth crosses over into a t1/3 law. The results do not depend on the details of the kicking.

Gligori?, G.; Bodyfelt, J. D.; Flach, S.

2011-11-01

434

Manifestation of resonance-related chaos in coupled Josephson junctions  

NASA Astrophysics Data System (ADS)

Manifestation of chaos in the temporal dependence of the electric charge is demonstrated through the calculation of the maximal Lyapunov exponent, phase-charge and charge-charge Lissajous diagrams and correlation functions. It is found that the number of junctions in the stack strongly influences the fine structure in the current-voltage characteristics and a strong proximity effect results from the nonperiodic boundary conditions. The observed resonance-related chaos exhibits intermittency. The criteria for a breakpoint region with no chaos are obtained. Such criteria could clarify recent experimental observations of variations in the power output from intrinsic Josephson junctions in high temperature superconductors.

Shukrinov, Yu. M.; Hamdipour, M.; Kolahchi, M. R.; Botha, A. E.; Suzuki, M.

2012-11-01

435

Absorption of light by a quantum chaos system  

NASA Astrophysics Data System (ADS)

A simple quantum chaos system is examined as a model with which a realistic process of light absorption can be simulated. A typical quantum chaos system composed of two degrees of freedom does not absorb light stationarily, that is, at a constant rate. However, when it is coupled with only one or two other degrees of freedom, the results of simulation strongly suggest that the chaotic system absorbs light stationarily even though the coupling strength is quite weak. This fact provides a direct evidence that quantum chaos may be an origin of dissipation in quantum systems with a few degrees of freedom.

Ikeda, K.; Adachi, S.; Toda, M.

1990-07-01

436

Analysis on the nonlinear response of cracked rotor in hover flight  

Microsoft Academic Search

The motion equations for a Jeffcott rotor in hover flight are derived. A periodically sampled peak-to-peak value diagram is\\u000a used for characterizing and distinguishing different types of nonlinear responses in hovering state. The nonlinear responses\\u000a become more apparent when the rotor is running above the critical speed in flat flight. There are three ways for rotor responses\\u000a going to chaos,

Yongfeng Yang; Xingmin Ren; Weiyang Qin; Yafeng Wu; Xizhe Zhi

2010-01-01

437

Tunnel-diode loaded split-ring resonators as a foundation for nonlinear metamaterials  

NASA Astrophysics Data System (ADS)

The nonlinear electromagnetic response is one of the foundations of modern technology and it arises in natural materials at the atomic scale. We briefly present some of the fundamentals of nonlinearity in natural materials and then we present experimental studies of analogous behavior in meta-atoms, the fundamental building block of metamaterials. Specifically tunnel-diode loaded, microwave split-ring resonators are shown to enable various nonlinear phenomena including self-sustained oscillation, harmonic/comb generation, frequency locking/pulling, and quasi-chaos generation. We discuss the possible adaptation of these unit cells to create bulk nonlinear metamaterials.

O'Hara, John F.; Reiten, Matthew T.; Colestock, Patrick; Earley, Lawrence; Taylor, Antoinette

2011-09-01

438

A Newly Discovered Hematite-rich Unit in Aureum Chaos: Comparison of Hematite and Associated Units with Those in Aram Chaos  

Microsoft Academic Search

A new hematite-rich deposit in Aureum Chaos has been discovered with data from the Thermal Emission Spectrometer. Additionally, a caprock unit resembling that in Aram Chaos is seen. A comparison of the units in Aram and Aureum Chaos is presented.

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

2005-01-01

439

A Newly Discovered Hematite-rich Unit in Aureum Chaos: Comparison of Hematite and Associated Units with Those in Aram Chaos  

NASA Astrophysics Data System (ADS)

A new hematite-rich deposit in Aureum Chaos has been discovered with data from the Thermal Emission Spectrometer. Additionally, a caprock unit resembling that in Aram Chaos is seen. A comparison of the units in Aram and Aureum Chaos is presented.

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

2005-03-01

440

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

SciTech Connect

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

441

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

SciTech Connect

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

442

Sediment carrying capacity prediction based on chaos optimization support vector machines  

NASA Astrophysics Data System (ADS)

Correct calculation of sediment carrying capacity in natural rivers is of great significance to the simulation of sediment movement and river-bed deformation by mathematical model. Peak recognition support vector machines, an improved support vector machines, was proposed considering the complication and nonlinearity between sediment carrying capacity and its impact factors; peak recognition least square support vector machines sediment carrying capacity prediction model, which was based on chaos optimization, was built combining with accelerating chaos optimization against questions of support vector machines regression such as parameter optimization, training and test speed. The test data of 30 sets of water tanks with high, medium and low sediment concentrations were trained, and training values agreed well with measured values; four sets of test data were predicted by trained support vector machines model, and training values were pretty much the same with measured values. Theoretical analysis and experimental results show that sediment carrying capacity studying method based on peak recognition support vector machines is more accurate in predication and more reliable than common support vector machines and BP neural network.

Li, Zheng-Zui; Xie, Yue-Bo; Zhang, Jun; Li, Xiao-Lu

2010-07-01

443

Nonlinear intermodulation distortion suppression in coherent analog fiber optic link using electro-optic polymeric dual parallel Mach-Zehnder modulator.  

PubMed

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

444

Understanding the Role of Chaos Theory in Military Decision Making.  

National Technical Information Service (NTIS)

Chaos theory is a poorly understood concept in social science and in military analytical decision making systems. Military decision makers require a multidisciplinary approach of mathematical analysis, modeling and simulation, topology, and post-structura...

D. O. Fuqua

2009-01-01

445

A Case for Hydrothermal Gray Hematite in Aram Chaos  

Microsoft Academic Search

Mars Global Surveyor data suggests that high concentrations of hematite were formed in planar strata in Aram Chaos and have since been exposed by erosion of an overlying light-toned, caprock. Geochemical and geomorphological inferences suggest a hydrothermal formation.

D. C. Catling; J. M. Moore

2003-01-01

446

A Case for Hydrothermal Gray Hematite in Aram Chaos  

NASA Astrophysics Data System (ADS)

Mars Global Surveyor data suggests that high concentrations of hematite were formed in planar strata in Aram Chaos and have since been exposed by erosion of an overlying light-toned, caprock. Geochemical and geomorphological inferences suggest a hydrothermal formation.

Catling, D. C.; Moore, J. M.

2003-07-01

447

Semiclassical chaos in an x sup 4 anharmonic oscillator  

SciTech Connect

This paper reports on the Zaslavskii criterion for quantum chaos to a quartic anharmonic oscillator with dissipation and an external force term in the semiclassical approximation. The semiclassical equilibrium states and integral invariants are related to quantum states in terms of the ratio of h to the semiclassical action. Semiclassical chaos is found to occur with the destruction of integral invariants and equilibrium states but the quantum states are not destroyed.

Anderson, J.T. (Physics Dept., Univ. of the Philippines, Manila (PH))

1992-04-10

448

Philosophical perspectives on quantum chaos: Models and interpretations  

NASA Astrophysics Data System (ADS)

The problem of quantum chaos is a special case of the larger problem of understanding how the classical world emerges from quantum mechanics. While we have learned that chaos is pervasive in classical systems, it appears to be almost entirely absent in quantum systems. The aim of this dissertation is to determine what implications the interpretation of quantum mechanics has for attempts to explain the emergence of classical chaos. There are three interpretations of quantum mechanics that have set out programs for solving the problem of quantum chaos: the standard interpretation, the statistical interpretation, and the deBroglie-Bohm causal interpretation. One of the main conclusions of this dissertation is that an interpretation alone is insufficient for solving the problem of quantum chaos and that the phenomenon of decoherence must be taken into account. Although a completely satisfactory solution of the problem of quantum chaos is still outstanding, I argue that the deBroglie-Bohm interpretation with the help of decoherence outlines the most promising research program to pursue. In addition to making a contribution to the debate in the philosophy of physics concerning the interpretation of quantum mechanics, this dissertation reveals two important methodological lessons for the philosophy of science. First, issues of reductionism and intertheoretic relations cannot be divorced from questions concerning the interpretation of the theories involved. Not only is the exploration of intertheoretic relations a central part of the articulation and interpretation of an individual theory, but the very terms used to discuss intertheoretic relations, such as `state' and `classical limit', are themselves defined by particular interpretations of the theory. The second lesson that emerges is that, when it comes to characterizing the relationship between classical chaos and quantum mechanics, the traditional approaches to intertheoretic relations, namely reductionism and theoretical pluralism, are inadequate. The fruitful ways in which models have been used in quantum chaos research point to the need for a new framework for addressing intertheoretic relations that focuses on models rather than laws.

Bokulich, Alisa Nicole

2001-09-01

449

Different routes from a matter wavepacket to spatiotemporal chaos.  

PubMed

We investigate the dynamics of a quasi-one-dimensional Bose-Einstein condensate confined in a double-well potential with spatiotemporally modulated interaction. A variety of phenomena is identified in different frequency regimes, including the self-compression, splitting, breathing-like, and near-fidelity of the matter wavepacket, which are associated with different routes for the onset of spatiotemporal chaos. The results also reveal that chaos can retain space-inversion symmetry of the system. PMID:23020448

Rong, Shiguang; Hai, Wenhua; Xie, Qiongtao; Zhong, Honghua

2012-09-01

450

Regional mapping and structural analysis of Aram Chaos area  

Microsoft Academic Search

Aram Chaos is a typical chaotic terrain within a ˜280 km crater located 2.5o N and 338.5o E, in the Xanthe and Margaritifer Terrae (XMT) region. Most large craters in the XMT region, such as the Aram Chaos crater, formed in the Noachian Period. In the subsequent Hesperian Period and into the Amazonian Period the XMT region has been dissected

J. H. P. Oosthoek; T. E. Zegers; A. P. Rossi; P. Martin; B. Foing; G. Neukum

2006-01-01

451

Chaos in axially symmetric potentials with octupole deformation  

SciTech Connect

Classical and quantum mechanical results are reported for the single particle motion in a harmonic oscillator potential which is characterized by a quadrupole deformation and an additional octupole deformation. The chaotic character of the motion is strongly dependent on the quadrupole deformation in that for a prolate deformation virtually no chaos is discernible while for the oblate case the motion shows strong chaos when the octupole term is turned on.

Heiss, W.D.; Nazmitdinov, R.G.; Radu, S. (Centre for Nonlinear Studies and Department of Physics, University of Witwatersrand, PO Wits 2050, Johannesburg (South Africa) Departamento de Fisica Teorica C-XI, Universidad Autonoma de Madrid, E-28049, Madrid (Spain))

1994-04-11

452

Experimental survey of chaos in the josephson effect  

SciTech Connect

The range of chaotic behavior in the Josephson effect is investigated experimentally in tin tunnel junctions and indium microbridges subjected to dc and rf bias. Chaos is found to occur between frequencies of 0.1/(2..pi..RC) and the plasma frequency at intermediate hysteresis. The low-hysteresis onset of chaos is studied systematically by varying the critical current of an Sn/ox/Sn tunnel junction as a function of temperature. The results agree with simulations and theoretical predictions.

Noeldecke, C.; Bauer, M.; Gross, R.; Reiner, G.; Seifert, H.

1986-08-01

453

Mg and Fe-Sulfate Layers in Aram Chaos, Mars  

Microsoft Academic Search

The post-chaos layered deposits in Aram Chaos extend laterally approximately 10,000 km2 with a present-day height of ~800 meters above the basement. The deposits experienced significant erosion, in some places down to the basement, indicating a more extensive depositional coverage than evident today. Crystalline hematite, mono- and poly-hydrated sulfate, and pyroxene have been identified in the layered deposits with OMEGA,

K. Lichtenberg; R. Arvidson; J. Bishop; T. Glotch; E. Noe Dobrea; S. Murchie; J. Mustard; L. Roach

2008-01-01

454

Chaos in the Genesis and Maintenance of Cardiac Arrhythmias  

PubMed Central

Dynamical chaos, an irregular behavior of deterministic systems, has been widely shown in nature. It also has been demonstrated in cardiac myocytes in many studies, including rapid pacing induced irregular beat-to-beat action potential alterations and slow pacing induced irregular early afterdepolarizations, etc. Here we review the roles of chaos in the genesis of cardiac arrhythmias, the transition to ventricular fibrillation, and the spontaneous termination of fibrillation, based on evidence from computer simulation of mathematical models and experiments of animal models.

Qu, Zhilin

2010-01-01

455

A novel robust proportional-integral (PI) adaptive observer design for chaos synchronization  

NASA Astrophysics Data System (ADS)

In this paper, chaos synchronization in the presence of parameter uncertainty, observer gain perturbation and exogenous input disturbance is considered. A nonlinear non-fragile proportional-integral (PI) adaptive observer is designed for the synchronization of chaotic systems; its stability conditions based on the Lyapunov technique are derived. The observer proportional and integral gains, by converting the conditions into linear matrix inequality (LMI), are optimally selected from solutions that satisfy the observer stability conditions such that the effect of disturbance on the synchronization error becomes minimized. To show the effectiveness of the proposed method, simulation results for the synchronization of a Lorenz chaotic system with unknown parameters in the presence of an exogenous input disturbance and abrupt gain perturbation are reported.

Mahdi, Pourgholi; Vahid Johari, Majd

2011-12-01

456

Parametric generation of robust chaos with time-delayed feedback and modulated pump source  

NASA Astrophysics Data System (ADS)

We consider a chaos generator composed of two parametrically coupled oscillators whose natural frequencies differ by factor of two. The system is driven by modulated pump source on the third harmonic of the basic frequency, and on each next period of pumping the excitation of the oscillator of doubled frequency is stimulated by the signal from the oscillator of the basic frequency undergoing quadratic nonlinear transformation and time delay. Using qualitative analysis and numerical results, we argue that chaotic dynamics in the system corresponds to hyperbolic strange attractor. It is a kind of Smale-Williams solenoid embedded in the infinite-dimensional state space of the stroboscopic map of the time-delayed system.

Kuznetsov, Alexey S.; Kuznetsov, Sergey P.

2013-03-01

457

Chaos computing in terms of periodic orbits  

NASA Astrophysics Data System (ADS)

The complex dynamics of chaotic systems can perform computations. The parameters and/or the initial conditions of a dynamical system are the data inputs and the resulting system state is the output of the computation. By controlling how inputs are mapped to outputs, a specific function can be performed. Previously no clear connection has been drawn between the structure of the dynamics and the computation. In this paper we demonstrate how chaos computation can be explained, modeled, and even predicted in terms of the dynamics of the underlying chaotic system, specifically the periodic orbit structure of the system. Knowing the dynamical equations of the system, we compute the system's periodic orbits as well as its stability in terms of its eigenvalues, thereby demonstrating how, how well, and what the chaotic system can compute.

Kia, Behnam; Spano, Mark L.; Ditto, William L.

2011-09-01

458

Limit cycles, noise, and chaos in hearing.  

PubMed

Based on insight obtained from a newly developed cochlea model, we argue that noise-driven limit cycles are the basic ingredient in the mammalian cochlea hearing process. For insect audition, we provide evidence in favor of the persistence of this principle. We emphasize the role of bifurcations for the emergence of broad-range sound perception, both in the frequency and amplitude domain, and indicate that this crucially depends on the correct coupling between limit cycles. We review the limit-cycle coupling universality, and outline how it can be used to encode information. Cortical noise is the microscopic basis for this encoding, whereas chaos emerges as the macroscopic expression of computation being done in the network. Large neuron firing variability is one possible consequence of the proposed mechanism that may apply to both vertebrate and insect hearing. PMID:15252881

Stoop, R; Vyver, J-J V D; Kern, A

2004-04-15

459

Chaos-enhanced accelerated particle swarm optimization  

NASA Astrophysics Data System (ADS)

There are more than two dozen variants of particle swarm optimization (PSO) algorithms in the literature. Recently, a new variant, called accelerated PSO (APSO), shows some extra advantages in convergence for global search. In the present study, we will introduce chaos into the APSO in order to further enhance its global search ability. Firstly, detailed studies are carried out on benchmark problems with twelve different chaotic maps to find out the most efficient one. Then the chaotic APSO (CAPSO) will be compared with some other chaotic PSO algorithms presented in the literature. The performance of the CAPSO algorithm is also validated using three engineering problems. The results show that the CAPSO with an appropriate chaotic map can clearly outperform standard APSO, with very good performance in comparison with other algorithms and in application to a complex problem.

Gandomi, Amir Hossein; Yun, Gun Jin; Yang, Xin-She; Talatahari, Siamak

2013-02-01

460

Noodle-map chaos - A simple example  

NASA Astrophysics Data System (ADS)

Chaos-generating folded two-dimensional maps can be generalized to higher dimensions in two ways: as folded-towel (or pancake) maps and as bent-walking-stick (or noddle) maps. The noodle case is of mathematical interest because the topologically one-dimensional attractors involved may, despite their thinness, be of the 'non-sink' type (that is, stand in a bijective relation to their domain of attraction). Moreover, Shtern recently showed that the well-known Kaplan-Yorke conjecture on the fractal dimensionality of chaotic attractors may fail in the case of noodle maps. We present here an explicit 3-variable noodle map with constant divergence (constant Jacobian determinant). The example is a higher analogue to the Henon diffeomorphism. A map of similar shape was recently found experimentally by Rob Shaw in a study of the irregularly dripping faucet.

Roessler, O. E.; Hudson, J. L.; Farmer, J. D.

461

Nonlinear Dynamics of Optical Systems.  

NASA Astrophysics Data System (ADS)

Available from UMI in association with The British Library. The general principle of dynamics and chaos are reviewed in the first chapter. In chapter 2 special effort has been given to the development of a generalized presentation of light-material interaction and its subsequent reduction to various low dimensional dynamic systems; notably two level lasers, nonlinear counterpropagating wave interaction and transverse spatial pattern forming systems. In chapter 3 and 4 original theoretical investigations of nonlinear dynamic and chaotic behaviour of Raman laser systems is presented. A new theoretical model of a single -mode, homogeneously broadened Raman laser is established using the semi-classical laser theory. Bistable features of the Raman emission and its operating condition are determined from steady state analysis. Linear instability analysis shows that dynamics exists over a broad range of parameter space and for broad cavity detuning to the low frequency side of the Raman gain where bistable emission also prevails, the threshold for the dynamics being as low as the first laser threshold. The analysis of the gain and dispersion characteristics in steady state together with the dynamic side mode analysis establish, that the laser and pump field induced distortion and displacement of dispersion profile associated with the laser gain are responsible for the asymmetric steady and dynamical features and also for a low second laser threshold. Oscillatory behaviour and period doubling routes to chaos in both intensity and phase of the Raman emission are found to occur for both good and bad cavity conditions, the dynamics of the phase revealing more complicated oscillatory behaviour to that of intensity. Comparisons of these theoretical results with experimental findings are also made. In general, a good qualitative agreement between them have been established in regard to (a) steady state and bistable features, (b) dependence of instabilities on the operating parameters and (c) dynamic and chaotic formations in unstable regions. In chapter 5 and 6 a general theoretical model of stimulated scattering incorporating the integral effect of nonlinear refraction is originated. Our analysis establishes that nonlinear dynamics is generic to and can be a prevalent feature of stimulated scattering phenomena. Finally Appendix A provides an original contribution on absorptive bistability in coherently pumped three-level lasers. This work, which complements much of the earlier work of the group on three-level systems, is incorporated as an appendix since it deals with steady state rather than dynamic aspects of behaviour. (Abstract shortened by UMI.).

Lu, Weiping

462

SEARCH FOR CHAOS IN NEUTRON STAR SYSTEMS: IS Cyg X-3 A BLACK HOLE?  

SciTech Connect

The accretion disk around a compact object is a nonlinear general relativistic system involving magnetohydrodynamics. Naturally, the question arises whether such a system is chaotic (deterministic) or stochastic (random) which might be related to the associated transport properties whose origin is still not confirmed. Earlier, the black hole system GRS 1915+105 was shown to be low-dimensional chaos in certain temporal classes. However, so far such nonlinear phenomena have not been studied fairly well for neutron stars which are unique for their magnetosphere and kHz quasi-periodic oscillation (QPO). On the other hand, it was argued that the QPO is a result of nonlinear magnetohydrodynamic effects in accretion disks. If a neutron star exhibits chaotic signature, then what is the chaotic/correlation dimension? We analyze RXTE/PCA data of neutron stars Sco X-1 and Cyg X-2, along with the black hole Cyg X-1 and the unknown source Cyg X-3, and show that while Sco X-1 and Cyg X-2 are low dimensional chaotic systems, Cyg X-1 and Cyg X-3 are stochastic sources. Based on our analysis, we argue that Cyg X-3 may be a black hole.

Karak, Bidya Binay; Dutta, Jayanta; Mukhopadhyay, Banibrata, E-mail: bidya_karak@physics.iisc.ernet.i, E-mail: dutta@physics.iisc.ernet.i, E-mail: bm@physics.iisc.ernet.i [Astronomy and Astrophysics Program, Department of Physics, Indian Institute of Science, Bangalore 560012 (India)

2010-01-01

463

Studying the connection between Aram Chaos and Ares Vallis  

NASA Astrophysics Data System (ADS)

An unusual canyon (˜2.9° N, 341.7° E) with a complex geomorphic history connects Aram Chaos and Ares Vallis. Aram Chaos (centered on 2° N, 339° E) is a circular depression filled with irregular blocks. Ares Vallis, to the east of and slightly lower in elevation than Arem Chaos, is a long valley with a complex hydrologic history. A ˜100 km long, ˜10 km wide canyon runs radially, from Aram Chaos connecting it to Ares Vallis. Recently gathered high-resolution Thermal Emission Imaging System Infrared (THEMIS IR) at ˜100m/pixel, THEMIS (Visible Imaging System) VIS at ˜30 m/pixel, and High Resoluting Stereo Camera (HRSC) at ˜12.5 m/pixel images combined with stereo topography (anaglyphs) from HRSC at ˜100 m/pixel reveal that this connection between Aram Chaos and Ares Vallis is extremely complex. At the conference, we will present the preliminary results of our geologic and geomorphic mapping of this feature and analysis of the system. The origin of the canyon has not yet been determined. It originates radially from Aram Chaos. After about 100 km, it bends to the northeast as it connects with Ares Vallis. The canyon has steep walls and a flat bottom. Several observations lead us to believe that this canyon was influenced by fluid flow. One is that it has a very gentle sinuosity, possibly indicating a slight meander during formation. Second, it bends to the northeast, or the downstream direction, as it enters Ares Valles. Finally, at the intersection with Aram Chaos, there is a complex sedimentary feature. Initially, this featured appeared to be a delta within Aram Chaos, however, inspection of the higher resolution images and topography shows that the drainage pattern is actually incised into the feature and drains to the east, out of Aram Chaos. Through careful mapping and sedimentary analysis we hope to determine the origin and modification history of this sedimentary feature. The center section of the canyon is filled with ˜10 landslides. The largest landslide has an apron of about 8km in diameter. All of the landslides originate from the southern wall of the canyon. They cover the top of the floor and are the youngest features in the canyon. Our study of this area will include detailed geologic and geomorphic mapping, an 1 analysis of the sedimentary feature at the intersection of the canyon and Aram Chaos, a sediment transport analysis to estimate formation time scales if the canyon was, indeed, carved by water, and a study of the landslides in an effort to gather more information about the materials in the walls of the canyon. 2

Kraal, E.; Kleinhans, M.; Zegers, T.; Oosthoek, J.; Rossi, A.

464

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

ERIC Educational Resources Information Center

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

Duffy, Jean Ann

2000-01-01

465

75 FR 53013 - Culturally Significant Objects Imported for Exhibition Determinations: “Chaos and Classicism: Art...  

Federal Register 2010, 2011, 2012, 2013

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

2010-08-30

466

Diminished chaos of heart rate time series in patients with major depression  

Microsoft Academic Search

Background: Depression and anxiety have been linked to serious cardiovascular events in patients with preexisting cardiac illness. A decrease in cardiac vagal function as suggested by a decrease in heart rate (HR) variability has been linked to sudden death.Methods: We compared LLE and nonlinearity scores of the unfiltered (UF) and filtered time series (very low, low, and high frequency; VLF,

Vikram Kumar Yeragani; K. A. Radha Krishna Rao; M. Ramesh Smitha; Robert B. Pohl; Richard Balon; K. Srinivasan

2002-01-01

467

Detecting nonlinear structure in time series  

SciTech Connect

We describe an approach for evaluating the statistical significance of evidence for nonlinearity in a time series. The formal application of our method requires the careful statement of a null hypothesis which characterizes a candidate linear process, the generation of an ensemble of surrogate'' data sets which are similar to the original time series but consistent with the null hypothesis, and the computation of a discriminating statistic for the original and for each of the surrogate data sets. The idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets. While some data sets very cleanly exhibit low-dimensional chaos, there are many cases where the evidence is sketchy and difficult to evaluate. We hope to provide a framework within which such claims of nonlinearity can be evaluated. 5 refs., 4 figs.

Theiler, J.

1991-01-01

468

Regional mapping and structural analysis of Aram Chaos area  

NASA Astrophysics Data System (ADS)

Aram Chaos is a typical chaotic terrain within a ˜280 km crater located 2.5o N and 338.5o E, in the Xanthe and Margaritifer Terrae (XMT) region. Most large craters in the XMT region, such as the Aram Chaos crater, formed in the Noachian Period. In the subsequent Hesperian Period and into the Amazonian Period the XMT region has been dissected by five of the circum-Chryse outflow channels: Shalbatana, Simud, Tiu, Ares and Mawrth Valles. We are mapping and analysing the geology of Aram Chaos using (1) HRSC image data from the ESA Mars Express orbiter, (2) THEMIS and MOC image data and MOLA elevation data.. The data was processed and map projected and incorporated in ESRI ArcGIS. HRSC data is particularly important in this mapping study. The large swath width, the high resolution, and the sharpness of the images combine both context and detail in one image. In addition, HRSC anaglyphs were incorporated in the GIS database. Using red/blue glasses, these provide direct detailed elevation information, essential to geometry based geological mapping. Apart from the general mapping the focus of this study is on (1) investigating the structural and geometric relations of the chaotic terrain and the surrounding Noachian cratered terrain, and (2) investigating the light toned deposits in the chaotic terrain and their relation to the chaotic terrain and outflow channels. 5 major units were distinguished: Highland terrain, Fractured highland terrain, Intermediate chaotic terrain, Chaos floor terrain and Light toned deposits. Inside Aram Chaos a morphologically distinct chaotic terrain unit was mapped which also shows a distinct fault pattern. The outflow channels were considered geomorphological units and the channel flow boundaries and directions are shown as lines in the map. Faults and fault blocks were mapped. On the Aram Chaos end of the channel connecting Ares Vallis and Aram Chaos a delta-like feature is located.

Oosthoek, J. H. P.; Zegers, T. E.; Rossi, A. P.; Martin, P.; Foing, B.; Neukum, G.

469

Assessing nonlinear structures in real exchange rates using recurrence plot strategies  

NASA Astrophysics Data System (ADS)

Purchasing power parity (PPP) is an important theory at the basis of a large number of economic models. However, the implication derived from the theory that real exchange rates must follow stationary processes is not conclusively supported by empirical studies. In a recent paper, Serletis and Gogas [Appl. Finance Econ. 10 (2000) 615] show evidence of deterministic chaos in several OECD exchange rates. As a consequence, PPP rejections could be spurious. In this work, we follow a two-stage testing procedure to test for nonlinearities and chaos in real exchange rates, using a new set of techniques designed by Webber and Zbilut [J. Appl. Physiol. 76 (1994) 965], called recurrence quantification analysis (RQA). Our conclusions differ slightly from Serletis and Gogas [Appl. Finance Econ. 10 (2000) 615], but they are also supportive of chaos for some exchange rates.

Belaire-Franch, Jorge; Contreras, Dulce; Tordera-Lledó, Lorena

2002-11-01

470

Chaos in a long-term experiment with a plankton community  

Microsoft Academic Search

Mathematical models predict that species interactions such as competition and predation can generate chaos. However, experimental demonstrations of chaos in ecology are scarce, and have been limited to simple laboratory systems with a short duration and artificial species combinations. Here, we present the first experimental demonstration of chaos in a long-term experiment with a complex food web. Our food web

Elisa Benincà; Jef Huisman; Reinhard Heerkloss; Klaus D. Jöhnk; Pedro Branco; Egbert H. van Nes; Marten Scheffer; Stephen P. Ellner

2008-01-01

471

Chaos in a generalized van der Pol system and in its fractional order system  

Microsoft Academic Search

In this paper, chaos of a generalized van der Pol system with fractional orders is studied. Both nonautonomous and autonomous systems are considered in detail. Chaos in the nonautonomous generalized van der Pol system excited by a sinusoidal time function with fractional orders is studied. Next, chaos in the autonomous generalized van der Pol system with fractional orders is considered.

Zheng-Ming Ge; Mao-Yuan Hsu

2007-01-01

472

Optimization design of hybrid chaos immune algorithm with self-adaptive parameter adjusting  

Microsoft Academic Search

In order to improve the performance of immune algorithm, chaos optimization is integrated into immune clone selection algorithm. Portion antibodies after decoding are mapped into Lozi's chaos field, and then collect every optical value by each of chaos iteration is added into the new antibody group to improve the antibody-antigen fitness value. This paper analyzes the importance of the selection

Daohua Liu; Xin Liu; Li Zhang; Congcong Wei; Danning Wang

2012-01-01

473

Effects of maturation and acidosis on the chaos-like complexity of the neural respiratory output in the isolated brainstem of the tadpole, Rana esculenta  

PubMed Central

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

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

2011-01-01

474

Quantum signatures of chaos in a kicked top.  

PubMed

Chaotic behaviour is ubiquitous and plays an important part in most fields of science. In classical physics, chaos is characterized by hypersensitivity of the time evolution of a system to initial conditions. Quantum mechanics does not permit a similar definition owing in part to the uncertainty principle, and in part to the Schrödinger equation, which preserves the overlap between quantum states. This fundamental disconnect poses a challenge to quantum-classical correspondence, and has motivated a long-standing search for quantum signatures of classical chaos. Here we present the experimental realization of a common paradigm for quantum chaos-the quantum kicked top- and the observation directly in quantum phase space of dynamics that have a chaotic classical counterpart. Our system is based on the combined electronic and nuclear spin of a single atom and is therefore deep in the quantum regime; nevertheless, we find good correspondence between the quantum dynamics and classical phase space structures. Because chaos is inherently a dynamical phenomenon, special significance attaches to dynamical signatures such as sensitivity to perturbation or the generation of entropy and entanglement, for which only indirect evidence has been available. We observe clear differences in the sensitivity to perturbation in chaotic versus regular, non-chaotic regimes, and present experimental evidence for dynamical entanglement as a signature of chaos. PMID:19812668

Chaudhury, S; Smith, A; Anderson, B E; Ghose, S; Jessen, P S

2009-10-01

475

Behavior modeling through CHAOS for simulation of dismounted soldier operations  

NASA Astrophysics Data System (ADS)

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

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

2008-05-01

476

PREFACE: XI Latin American Workshop on Nonlinear Phenomena  

NASA Astrophysics Data System (ADS)

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

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

2010-09-01

477

Hamiltonian reduction and complex behaviour in nonlinear polarization dynamics  

SciTech Connect

The problem of two counterpropagating optical beams in a nonlinear medium is investigated as an Hamiltonian system. The phase space is an eight-dimensional manifold isomorphic to C/sup 2/ /times/ C/sup 2/. Invariance of the system under the action of several copies of the O(1) group allows for its reduction to the two-sphere onto which the resulting induced Hamiltonian system is therefore completely integrable. We determine all the fixed points of the system, corresponding to physical static solutions, and examine the bifurcations that occur as parameters are varied. Orbits connecting hyperbolic fixed points are special and determine physical soliton-like and kink-like solutions. We also look at how chaos, in particular Horseshoe chaos and Arnold diffusion, arises when the system is subject to certain types of perturbations. 6 refs.

David, D.

1988-01-01

478

Quantum Arnol'd diffusion in a simple nonlinear system.  

PubMed

We study the fingerprint of the Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators with a two-frequency external force. In the classical description, this peculiar diffusion is due to the onset of a weak chaos in a narrow stochastic layer near the separatrix of the coupling resonance. We have found that global dependence of the quantum diffusion coefficient on model parameters mimics, to some extent, the classical data. However, the quantum diffusion happens to be slower than the classical one. Another result is the dynamical localization that leads to a saturation of the diffusion after some characteristic time. We show that this effect has the same nature as for the studied earlier dynamical localization in the presence of global chaos. The quantum Arnol'd diffusion represents a new type of quantum dynamics and can be observed, for example, in two-dimensional semiconductor structures (quantum billiards) perturbed by time-periodic external fields. PMID:12366228

Demikhovskii, V Ya; Izrailev, F M; Malyshev, A I

2002-09-20

479

Nonlinear dynamics of modulation instability in distributed resonators under external harmonic driving  

NASA Astrophysics Data System (ADS)

We study the regimes of complex field dynamics upon modulation instability in distributed nonlinear resonators under external harmonic driving. Two regimes are considered: the regime of a nonlinear ring cavity, described by nonlinear Schrödinger equation (NLS) with a delayed boundary condition, and the regime of a one-dimensional Fabri-Perot cavity, described by a system of coupled NLS for the forward and backward waves. Theoretical stability analysis of stationary forced oscillations is carried out. The results of numerical simulation of transition to chaos with increasing input intensity are presented.

Balyakin, A. A.; Ryskin, N. M.; Khavroshin, O. S.

2007-09-01

480

Chaos Synchronization in Navier-Stokes Turbulence  

NASA Astrophysics Data System (ADS)

Chaos synchronization (CS) has been studied for some time now (Pecora & Carroll 1990), for systems with only a few degrees of freedom as well as for systems described by partial differential equations (Boccaletti et al 2002). CS in general is said to be present in coupled dynamical systems when a specific property of each system has the same time evolution for all, even though the evolution itself is chaotic. The Navier-Stokes (NS) equations describe the velocity for a wide range of fluids, and their solutions are usually called turbulent if fluctuation amplitudes decrease as a power of their wavenumber. There have been some studies of CS for continuous systems (Kocarev et al 1997), but CS for NS turbulence seems not to have been investigated so far. We focus on the synchronization of the small scales of a turbulent flow for which the time history of large scales is prescribed. Our DNS results show that high-wavenumbers in turbulence are fully slaved to modes with wavenumbers up to a critical fraction of the Kolmogorov dissipation wavenumber. The motivation for our work is to study deeply sub-Kolmogorov scales in fully developed turbulence (Schumacher 2007), which we found to be recoverable even at very high Reynolds number from simulations with moderate resolutions.

Lalescu, Cristian; Meneveau, Charles; Eyink, Gregory

2013-03-01