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1

Chaos without nonlinear dynamics.

A linear, second-order filter driven by randomly polarized pulses is shown to generate a waveform that is chaotic under time reversal. That is, the filter output exhibits determinism and a positive Lyapunov exponent when viewed backward in time. The filter is demonstrated experimentally using a passive electronic circuit, and the resulting waveform exhibits a Lorenz-like butterfly structure. This phenomenon suggests that chaos may be connected to physical theories whose underlying framework is not that of a traditional deterministic nonlinear dynamical system. PMID:16907450

Corron, Ned J; Hayes, Scott T; Pethel, Shawn D; Blakely, Jonathan N

2006-07-14

2

Pathological tremors : Deterministic chaos or nonlinear

Pathological tremors : Deterministic chaos or nonlinear stochastic oscillators? Jens Timmer \\Lambda Hospital of Freiburg, Breisacher Str. 64, 79110 Freiburg, Germany Abstract. Pathological tremors exhibit apply methods from linear and nonlinear time series analysis to tremor time series. The results

Timmer, Jens

3

Scaling of chaos in strongly nonlinear lattices

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

Mulansky, Mario, E-mail: mulansky@pks.mpg.de [Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Str. 24, D-14476 Potsdam-Golm (Germany) [Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Str. 24, D-14476 Potsdam-Golm (Germany); Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden (Germany); Institut für Theoretische Physik, TU Dresden, Zellescher Weg 17, D-01069 Dresden (Germany)

2014-06-15

4

Scaling of Chaos in Strongly Nonlinear Lattices

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

Mario Mulansky

2013-12-16

5

Detecting nonlinearity and chaos in epidemic data

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

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

1993-08-01

6

Chaos Based Nonlinear Analysis of Epileptic Seizure

Feature extraction and classification of electro-physiological signals is an important issue in development of disease diagnostic expert system (DDES). In this paper we propose a method based on chaos methodology for EEG signal classification. The nonlinear dynamics of original EEGs are quantified in the form of entropy, largest Lyapunov exponent (LLE), correlation dimension (CD), capacity dimension (CAD) and were considered

R. Sahu; T. Parija; B. Mohapatra; B. Rout; S. Sahu; R. Panda; P. Pal; T. Gandhi

2010-01-01

7

Parameter identification using experimental nonlinear dynamics and chaos

Parameter identification using experimental nonlinear dynamics and chaos was applied to a piecewise-linear oscillator; application to cracked beams was attempted. Electronic integration circuitry was constructed to provide velocity and displacement...

Chancellor, Roy Scott

1993-01-01

8

Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?

Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators? J. Timmera Received 17 May 1999; accepted for publication 15 October 1999 Pathological tremors exhibit a nonlinear methods from linear and nonlinear time series analysis to tremor time series. The results of the different

Timmer, Jens

9

Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators?

Pathological tremors: Deterministic chaos or nonlinear stochastic oscillators? J. Timmer a# Pathological tremors exhibit a nonlinear oscillation that is not strictly periodic. We investigate whether dynamics. To do so, we apply various methods from linear and nonlinear time series analysis to tremor time

Timmer, Jens

10

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

11

Chaos and Nonlinear Dynamics in a Quantum Artificial Economy

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

Carlos Pedro Gonçalves

2012-02-29

12

Instabilities, dynamics and chaos in nonlinear optical systems

NASA Astrophysics Data System (ADS)

Some of the topics considered at the International Workshop on Instabilities, Dynamics, and Chaos in Nonlinear Optical Systems (held July 8-10, 1987 in Lucca, Italy) are briefly discussed. Particular consideration is given to laser instabilities, dynamics in optical bistability, the characterization of chaotic signals, quantum chaos, the effects of classical and quantum noise, spatial instabilities, polarization effects, and four-wave mixing and phase conjugation.

Abraham, N. B.; Arimondo, E.; Boyd, R. W.

13

Nonlinear system vibration---The appearance of chaos

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

14

Chaos in Nonlinear Dynamical Systems Helicopter Flight-data Analysis

Chaos in Nonlinear Dynamical Systems Â Helicopter Flight-data Analysis James H. Taylor1 and S dynamic behaviour of a modern, multi-purpose helicopter is considered in this article. The main objective of this study is to characterize the helicopter's vibration mechanism(s) Â i.e., to determine if the vibrations

Taylor, James H.

15

Nonlinear Perspectives on Family Process: Chaos and Catastrophe Theories.

ERIC Educational Resources Information Center

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

Ward, Margaret; Koopmans, Matthijs

16

Controlling chaos using nonlinear approximations and delay coordinate embedding

NASA Astrophysics Data System (ADS)

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

Yagasaki, Kazuyuki; Uozumi, Tomotsugu

1998-10-01

17

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

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

Rothman, Daniel H.

18

Nonlinear dynamics, chaos and complex cardiac arrhythmias

NASA Technical Reports Server (NTRS)

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

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

1987-01-01

19

Shear-induced chaos in nonlinear Maxwell-model fluids

NASA Astrophysics Data System (ADS)

A generalized model for the behavior of the stress tensor in non-Newtonian fluids is investigated for spatially homogeneous plane Couette flow, showing a variety of nonlinear responses and deterministic chaos. Mapping of chaotic solutions is achieved through the largest Lyapunov exponent for the two main parameters: The shear rate and the temperature and/or density. Bifurcation diagrams and stability analysis are used to reveal some of the rich dynamics that can be found. Suggested mechanisms for stability loss in these complex fluids include Hopf, saddle-node, and period-doubling bifurcations.

Goddard, Chris; Hess, Ortwin; Balanov, Alexander G.; Hess, Siegfried

2008-02-01

20

Nonlinearly-enhanced energy transport in many dimensional quantum chaos.

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

Brambila, D S; Fratalocchi, A

2013-01-01

21

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

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

22

NASA Astrophysics Data System (ADS)

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, Arun V.

23

Integrability and chaos in nonlinearly coupled optical beams

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

David, D.

1989-01-01

24

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

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

H. Kröger

2003-02-21

25

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

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

26

Parental ADHD Symptomology and Ineffective Parenting: The Connecting Link of Home Chaos

SYNOPSISObjective. This study examines links between maternal and paternal attention-deficit\\/hyperactivity disorder (ADHD) symptoms and parenting practices that require inhibition of impulses, sustained attention, and consistency; the role of home chaos in these associations is also assessed. Design. ADHD symptoms, the level of home chaos, and parenting practices (e.g., involvement, inconsistent discipline, supportive and nonsupportive responses to children's negative emotions, and

Irina Mokrova; Marion OBrien; Susan Calkins; Susan Keane

2010-01-01

27

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

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

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

2012-01-01

28

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

We applied nonlinear and chaos analysis to fingertip pulse wave data. The largest Lyapunov exponent, a measure of the ``divergence'' of the trajectory of the attractor in phase space, was found to be a useful index of mental health in humans, particularly for the early detection of dementia and depressive psychosis, and for monitoring mental changes in healthy persons. Most

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

2007-01-01

29

Calls out of chaos: the adaptive significance of nonlinear phenomena in mammalian vocal production

Recent work on human vocal production demonstrates that certain irregular phenomena seen in human pathological voices and baby crying result from nonlinearities in the vocal production system. Equivalent phenomena are quite common in nonhuman mammal vocal repertoires. In particular, bifurcations and chaos are ubiquitous aspects of the normal adult repertoire in many primate species. Here we argue that these phenomena

W. Tecumseh Fitch; Jürgen Neubauer; Hanspeter Herzel

2002-01-01

30

NASA Technical Reports Server (NTRS)

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

Hooker, John C.

1991-01-01

31

Testing for Nonlinearity and Deterministic Chaos in Monthly Japanese Stock Market Data

It has been widely recognised that the randomness of a stock market may actually be an indicator of an underlying strange attractor which has a fractal structure and supports chaotic motion. The application of non-linear methods to such financial data may indicate the presence of nonlinearities and low-dimensional chaos. These methods include rescaled range (R\\/S) analysis, correlation dimension calculation and

Teo Jasic

1998-01-01

32

Household chaos moderates the link between maternal attribution bias and parenting

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

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

2013-01-01

33

Deterministic Chaos in Nonlinear Optical Wave-mixing

Propagation in a Kerr medium of a system of equal-frequency light waves has been studied, each of the waves being involved in two four-wave mixing processes. Competition of these processes is shown to result in non-integrability and chaos. A stochastic regime of evolution sets in if the input values of the wave amplitudes differ strongly enough from the ones corresponding

K. N. Alekseev; G. P. Berman; A. V. Butenko; A. K. Popov; V. M. Shalaev; V. Z. Yakhnin

1990-01-01

34

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.

35

12.006J / 18.353J / 2.050J Nonlinear Dynamics I: Chaos, Fall 2006

This course provides an introduction to the theory and phenomenology of nonlinear dynamics and chaos in dissipative systems. The content is structured to be of general interest to undergraduates in science and engineering.

Rothman, Daniel

36

Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 17, No. 2, pp. 223-232.1 © 2013 Society for Chaos Theory in Psychology & Life Sciences.2 3 Is Chaos Good for Learning?4 5 J. C. Sprott 1 chaos allows the exploration of a wider range of conditions while26 still retaining a degree of memory

Sprott, Julien Clinton

37

Controlling chaos of nonlinear domain-wall motion

NASA Astrophysics Data System (ADS)

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

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

1999-04-01

38

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

NASA Astrophysics Data System (ADS)

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

Farshidianfar, A.; Saghafi, A.

2014-10-01

39

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

NASA Astrophysics Data System (ADS)

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

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

2008-03-01

40

Mutation and Chaos in Nonlinear Models of Heredity

We shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models and observe chaotic behaviors of such models. PMID:25136693

Nawi, Ashraf Mohamed

2014-01-01

41

Study of nonlinear dynamics and chaos in MEMS/NEMS resonators

NASA Astrophysics Data System (ADS)

With the successes in numerous applications from signal filtering to chemical and mass sensing, micro- and nano-electro-mechanical resonators continue to be one of the most widely studied topics of the micro-electro-mechanical systems community. Nonlinearities arising out of different sources such as mid-plane stretching and electrostatic force lead to a rich nonlinear dynamics in the time response of these systems which should be investigated for appropriate design and fabrication of them. Motivated by this need, present study is devoted to analyzing the nonlinear dynamics and chaotic behavior of nano resonators with electrostatic forces on both sides. Based on the potential function and phase portrait of the unperturbed system, the resonator dynamics is categorized to four physical situations and it is shown that the system undergoes homoclinic and heteroclinic orbits which are responsible for the appearance of chaos in the resonator response. Bifurcation diagram of nano resonator is plotted by variation of applied AC actuation voltage and it is shown that the system possess rich dynamic behavior such as periodic doubling, quasi-periodic, bifurcation and chaotic motion which are classified and studied in more details by plotting time response and phase plane of the each category. The main result of this paper indicates that the necessary condition for the creation of chaos in the resonator is intersection of the system steady state response with the homoclinic orbit. This occurs when the system steady state velocity or amplitude reaches to the homoclinic orbit maximum speed or amplitude. The critical oscillating amplitudes corresponding to these situations are derived based on the system parameters which can be used to propose the new analytical criteria for chaos detection in resonators.

Miandoab, Ehsan Maani; Yousefi-Koma, Aghil; Pishkenari, Hossein Nejat; Tajaddodianfar, Farid

2015-05-01

42

Resource Letter: CC-1: Controlling chaos

NASA Astrophysics Data System (ADS)

This Resource Letter provides a guide to the literature on controlling chaos. Journal articles, books, and web pages are provided for the following: controlling chaos, controlling chaos with weak periodic perturbations, controlling chaos in electronic circuits, controlling spatiotemporal chaos, targeting trajectories of nonlinear dynamical systems, synchronizing chaos, communicating with chaos, applications of chaos control in physical systems, and applications of chaos control in biological systems.

Gauthier, Daniel J.

2003-08-01

43

Chaos and related nonlinear noise phenomena in Josephson tunnel junctions

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

44

Nonlinear waves in disordered chains: probing the limits of chaos and spreading.

We probe the limits of nonlinear wave spreading in disordered chains which are known to localize linear waves. We particularly extend recent studies on the regimes of strong and weak chaos during subdiffusive spreading of wave packets [Europhys. Lett. 91, 30001 (2010)] and consider strong disorder, which favors Anderson localization. We probe the limit of infinite disorder strength and study Fröhlich-Spencer-Wayne models. We find that the assumption of chaotic wave packet dynamics and its impact on spreading is in accord with all studied cases. Spreading appears to be asymptotic, without any observable slowing down. We also consider chains with spatially inhomogeneous nonlinearity, which give further support to our findings and conclusions. PMID:21867271

Bodyfelt, J D; Laptyeva, T V; Skokos, Ch; Krimer, D O; Flach, S

2011-07-01

45

Dynamical Systems on Three Manifolds Part I: Knots, Links and Chaos

In this paper, we give an explicit construction of dynamical systems (defined within a solid torus) containing any knot (or link) and arbitrarily knotted chaos. The first is achieved by expressing the knots in terms of braids, defining a system containing the braids and extending periodically to obtain a system naturally defined on a torus and which contains the given knotted trajectories. To get explicit differential equations for dynamical systems containing the braids, we will use a certain function to define a tube neigbourhood of the braid. The second one, generating chaotic systems, is realized by modeling the Smale horseshoe.

Yi Song; S. P. Banks; David Diaz

2007-06-16

46

Ductile Web Fracture Initiation in Steel Shear Links Shih-Ho Chao, S.M.ASCE1

Ductile Web Fracture Initiation in Steel Shear Links Shih-Ho Chao, S.M.ASCE1 ; Kapil Khandelwal, S fracture in the link web, a mode of failure that was not observed in earlier tests. This paper investigates the observed ductile fractures through computational structural simulation. An existing criterion for judging

Chao, Shih-Ho

47

for Chaos Theory in Psychology & Life Sciences Book Review Chaos and Time-Series Analysis. By Julien ClintonNonlinear Dynamics, Psychology, and Life Sciences, Vol.8, No.1, January, 2004. © 2004 Society 5 (hardback),0 19850840 9 (paperback). This book is the most comprehensive and clear text

Sprott, Julien Clinton

48

NASA Astrophysics Data System (ADS)

The efficiency of rotating machines can be improved via precisely manufactured bearings with reduced clearances; consequently, the proclivity for rotor-stator contact is increased. A common model used to investigate rotor-stator contact in previous studies is the two degree-of-freedom (DOF) rotor with symmetric support stiffness, where the contact assumes a linear elastic normal restoring force proportional to the rotor-stator interference and a tangential dry Coulomb friction force. Switching between the contacting and non-contacting states creates strong nonlinearity in the equations of motion, and the dynamic response displays a rich profile of behaviors including periodic, quasiperiodic, and chaotic responses via period-doubling, sudden transitions, quasiperiodicity, and intermittency. For the first time, this work emphasizes an asymmetric support stiffness matrix with cross-coupling between the x and y direction stiffnesses. The influence of support asymmetry on the nonlinear rotor response is shown using rotor orbits, frequency spectra, Poincaré sections, and bifurcation diagrams. It is found that the cross-coupling stiffness coefficient kxy has negligible effect on the dynamic response until its magnitude is on the same order as the direct stiffness coefficients. Direct stiffness coefficient asymmetry is shown to affect the rotor's response, where even small asymmetries can qualitatively change the response. Additionally, the importance of including gravity is investigated, and a method is provided for determining the threshold shaft speed above which gravity can be ignored. The dominant route to chaos is period-doubling for the parameters considered here, though other routes to chaos are seen such as a direct transition from periodic to chaotic motion. Finally, observations pertaining to rotor modeling, design, and fault diagnostics are discussed.

Varney, Philip; Green, Itzhak

2015-02-01

49

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.

50

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

NASA Astrophysics Data System (ADS)

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

Neicu, Toni

2002-09-01

51

\\u000a The flexible rotor modeling has an advantage over rigid rotor modeling, by its suitability to model rotors of complex shapes\\u000a with multiple discs and bearings. In this paper, the non-linear dynamic behavior of a horizontal unbalanced flexible rotor\\u000a supported on deep groove ball bearings is theoretically studied in detail for instability and chaos. A generalized Timoshenko\\u000a beam FE formulation, which

T. C. Gupta; K. Gupta; D. K. Sehgal

52

NASA Astrophysics Data System (ADS)

Axial-grooved gas-lubricated journal bearings have been widely applied to precision instrument due to their high accuracy, low friction, low noise and high stability. The rotor system with axial-grooved gas-lubricated journal bearing support is a typical nonlinear dynamic system. The nonlinear analysis measures have to be adopted to analyze the behaviors of the axial-grooved gas-lubricated journal bearing-rotor nonlinear system as the linear analysis measures fail. The bifurcation and chaos of nonlinear rotor system with three axial-grooved gas-lubricated journal bearing support are investigated by nonlinear dynamics theory. A time-dependent mathematical model is established to describe the pressure distribution in the axial-grooved compressible gas-lubricated journal bearing. The time-dependent compressible gas-lubricated Reynolds equation is solved by the differential transformation method. The gyroscopic effect of the rotor supported by gas-lubricated journal bearing with three axial grooves is taken into consideration in the model of the system, and the dynamic equation of motion is calculated by the modified Wilson- ?-based method. To analyze the unbalanced responses of the rotor system supported by finite length gas-lubricated journal bearings, such as bifurcation and chaos, the bifurcation diagram, the orbit diagram, the Poincaré map, the time series and the frequency spectrum are employed. The numerical results reveal that the nonlinear gas film forces have a significant influence on the stability of rotor system and there are the rich nonlinear phenomena, such as the periodic, period-doubling, quasi-periodic, period-4 and chaotic motion, and so on. The proposed models and numerical results can provide a theoretical direction to the design of axial-grooved gas-lubricated journal bearing-rotor system.

Zhang, Yongfang; Hei, Di; Lü, Yanjun; Wang, Quandai; Müller, Norbert

2014-03-01

53

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

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

2012-12-31

54

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

NASA Astrophysics Data System (ADS)

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

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

2007-11-01

55

Strong and Weak Chaos in Nonlinear Networks with Time-Delayed Couplings

NASA Astrophysics Data System (ADS)

We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for large delay times, and relate this to the condition for stable or unstable chaotic synchronization, respectively. In simulations of laser models and experiments with electronic circuits, we identify transitions from weak to strong and back to weak chaos upon monotonically increasing the coupling strength.

Heiligenthal, Sven; Dahms, Thomas; Yanchuk, Serhiy; Jüngling, Thomas; Flunkert, Valentin; Kanter, Ido; Schöll, Eckehard; Kinzel, Wolfgang

2011-12-01

56

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.

57

Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 13, No. 3, pp. 271-278. © 2009 Society for Chaos Theory in Psychology & Life Sciences Simplifications of the Lorenz Attractor J. C. Sprott1.5723). This system has been widely studied, and there is a whole book devoted to it (Sparrow, 1982

Sprott, Julien Clinton

58

for Chaos Theory in Psychology & Life Sciences Book Review Images of a Complex World: The Art and Poetry405 Nonlinear Dynamics, Psychology, and Life Sciences, Vol.10, No.3, pp.405-407. © 2006 Society Longino extended these methods to the social sciences in her book Science as Social Knowledge: Values

Sprott, Julien Clinton

59

Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 12, No. 1, pp. 117-129. © 2008 Society for Chaos Theory in Psychology & Life Sciences Biophilic Fractals and the Visual Journey of Organic Screen, Draves regards his images as evolving artificial life forms and the parameters that generate them

Taylor, Richard

60

Nonlinear Dynamics, Psychology, and Life Sciences, Vol. 16, No. 1, pp.91-96. © 2012 Society for Chaos Theory in Psychology & Life Sciences. The Transience of Virtual Fractals R. P. Taylor 1 to life. This will be done by incorporating her prints of fractal patterns into zoetropes

Taylor, Richard

61

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

NASA Astrophysics Data System (ADS)

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

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

2005-11-01

62

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

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

George Sugihara; Robert M. May

1990-01-01

63

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

64

NASA Astrophysics Data System (ADS)

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

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

2009-02-01

65

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.

Glenn Elert

66

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.

67

Higher order adaptive filter characterization of microwave fiber optic link nonlinearity

Microwave Fiber Optic (MFO) links have attracted much attention recently with their application in wireless access. When a wireless link is in series with the optical link, nonlinear distortion (NLD) of the MFO link becomes the biggest concern. The linearity requirement is high due to the large variations in the RF power through the link. Laser intrinsic nonlinearity is usually

Xavier N. Fernando; Abu B. Sesay

2000-01-01

68

Chaos is a general phenomenon in nonlinear dynamical systems. Accelerators--storage rings in particular--in which particles are stored for 10{sup 10} revolutions constitute a particularly intricate nonlinear dynamical system. (In comparison, the earth has revolved around the sun for only 10{sup 9} turns.) Storage rings therefore provide an ideal testing ground for chaos physics. In fact, it is the chaos phenomenon that imposes one of the key design criteria for these accelerators. One might arguably say that the demise of the Superconducting Super Collider project originated from a misjudgement in its chaos analysis at one point along its design path, leading to its first substantial cost escalation. This talk gives an elementary introduction to the study of chaos in accelerators.

Chao, Alex

1999-05-11

69

NASA Astrophysics Data System (ADS)

In this paper, controlling chaos when chaotic ferroresonant oscillations occur in a voltage transformer with nonlinear core loss model is performed. The effect of a parallel metal oxide surge arrester on the ferroresonance oscillations of voltage transformers is studied. The metal oxide arrester (MOA) is found to be effective in reducing ferroresonance chaotic oscillations. Also the multiple scales method is used to analyze the chaotic behavior and different types of fixed points in ferroresonance of voltage transformers considering core loss. This phenomenon has nonlinear chaotic dynamics and includes sub-harmonic, quasi-periodic, and also chaotic oscillations. In this paper, the chaotic behavior and various ferroresonant oscillation modes of the voltage transformer is studied. This phenomenon consists of different types of bifurcations such as period doubling bifurcation (PDB), saddle node bifurcation (SNB), Hopf bifurcation (HB), and chaos. The dynamic analysis of ferroresonant circuit is based on bifurcation theory. The bifurcation and phase plane diagrams are illustrated using a continuous method and linear and nonlinear models of core loss. To analyze ferroresonance phenomenon, the Lyapunov exponents are calculated via the multiple scales method to obtain Feigenbaum numbers. The bifurcation diagrams illustrate the variation of the control parameter. Therefore, the chaos is created and increased in the system.

Hamid, Reza Abbasi; Ahmad, Gholami; Seyyed, Hamid Fathi; Ataollah, Abbasi

2014-01-01

70

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

71

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

NASA Technical Reports Server (NTRS)

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

Unal, A.; Tobak, M.

1987-01-01

72

We study the discrete nonlinear Schröinger equation with weak disorder, focusing on the regime when the nonlinearity is, on the one hand, weak enough for the normal modes of the linear problem to remain well resolved but, on the other, strong enough for the dynamics of the normal mode amplitudes to be chaotic for almost all modes. We show that in this regime and in the limit of high temperature, the macroscopic density ? satisfies the nonlinear diffusion equation with a density-dependent diffusion coefficient, D(?) = D(0)?(2). An explicit expression for D(0) is obtained in terms of the eigenfunctions and eigenvalues of the linear problem, which is then evaluated numerically. The role of the second conserved quantity (energy) in the transport is also quantitatively discussed. PMID:25353559

Basko, D M

2014-02-01

73

NASA Astrophysics Data System (ADS)

We briefly review two aspects of string cosmology: (1) the presence of chaos in the generic cosmological solutions of the tree-level low-energy effective actions coming out of string theory, and (2) the remarkable link between the latter chaos and the Weyl groups of some hyperbolic Kac-Moody algebras.

Damour, Thibault

74

NASA Astrophysics Data System (ADS)

We briefly review recent work which established the existence of chaos in the generic cosmological solutions of the tree-level low-energy effective actions coming out of string theory, and linked this chaos to the Weyl groups of some hyperbolic Kac-Moody algebras.

Damour, Thibault

75

NASA Astrophysics Data System (ADS)

We briefly review two aspects of string cosmology: 1) the presence of chaos in the generic cosmological solutions of the tree-level low-energy effective actions coming out of string theory, and 2) the remarkable link between the latter chaos and the Weyl groups of some hyperbolic Kac-Moody algebras.

Damour, T.

2003-10-01

76

Self-oscillation and chaos in nonlinear fabry-perot resonators with finite response time

We report results of a detailed analysis of the dynamic response of folded Fabry-Pérot resonators containing a cubic nonlinear medium with finite time constant. Under different conditions, we find steady, oscillatory and chaotic responses to a steady driving field. Oscillation periods of many optical round-trip times are observed for sluggish media. Instability thresholds are well described by a complex characteristic

E. Abraham; W. J. Firth; J. Carr

1982-01-01

77

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

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

Philippe Faure; Henri Korn

2001-01-01

78

Modelling Laser-Diode Non-linearity in a Radio-over-Fibre Link

Modelling Laser-Diode Non-linearity in a Radio-over-Fibre Link G. Baghersalimi, V. Postoyalko, T- diode non-linearity. Based on theory, an analytical model of the laser-diode input/output function]. In the optical part of a RoF system the main sources of non-linearity include the laser-diode light source

Haddadi, Hamed

79

Identification of nonlinear dynamic systems using functional link artificial neural networks

We have presented an alternate ANN structure called functional link ANN (FLANN) for nonlinear dynamic system identification using the popular backpropagation algorithm. In contrast to a feedforward ANN structure, i.e., a multilayer perceptron (MLP), the FLANN is basically a single layer structure in which nonlinearity is introduced by enhancing the input pattern with nonlinear functional expansion. With proper choice of

Jagdish Chandra Patra; Ranendal N. Pal; B. N. Chatterji; Ganapati Panda

1999-01-01

80

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

81

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

NASA Technical Reports Server (NTRS)

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

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

1992-01-01

82

Nonlinear vibration and radiation from a panel with transition to chaos

NASA Technical Reports Server (NTRS)

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

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

1992-01-01

83

(Quantum) chaos theory and statistical physics far from equilibrium

(Quantum) chaos theory and statistical physics far from equilibrium: Introducing the group for Non (Nonlinear dynamics, chaos theory) Quantum information theory Our group is also a part of the bigger program Quantum maps, quantum chaos, random matrix theory: wave-dynamics, wave-chaos, PT-symmetric Hamiltonians

Â?umer, Slobodan

84

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

85

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

Bradley, Elizabeth

1990-12-01

86

Links between nonlinear dynamics and statistical mechanics in a simple one-dimensional model

We consider the links between nonlinear dynamics and thermodynamics in the framework of a simple nonlinear model for DNA. Two analyses of the phase transition, either with the transfer integral approach or by considering the instability of a nonlinear particular solution, are discussed. Conversely, the computation of the largest Lyapunov exponent is obtained within a thermodynamic treatment. Differences with the Peyrard-Bishop model are also discussed.

Hicham Qasmi; Julien Barre'; Thierry Dauxois

2004-07-26

87

Coherence and chaos in condensed matter

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

Bishop, A.R.

1989-01-01

88

Nonlinear distortion compensation of microwave fiber optic links with asymmetric adaptive filters

Microwave fiber optic (MFO) links are being increasingly used in microcellular wireless access. However, their nonlinear distortions (NLD) limit the dynamic range. In this paper a baseband adaptive post nonlinearity compensation scheme is described for the uplink. For cost sharing the compensation is done at the central base station. Measurement and simulation results show that 3rd order memoryless filters efficiently

Xavier N. Fernando; Abu B. Sesay

2000-01-01

89

Deterministic polarization chaos from a laser diode

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

Martin Virte; Krassimir Panajotov; Hugo Thienpont; Marc Sciamanna

2014-07-22

90

OSNR margin brought by nonlinear regenerators in optical communication links

Computation using a semianalytical model of the optical signal-to-noise ratio margins brought by the introduction of a generic 2R regenerator in an optical transmission link is presented. The optimization of the discriminating level of the regenerator depending on the link conditions is discussed and a regenerator characterization method that can be used in system design is presented

Benoît Charbonnier; Nayla El Dahdah; Michel Joindot

2006-01-01

91

Nonlinear Viscoelastic Mechanics of Cross-linked Rubbers

NASA Technical Reports Server (NTRS)

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

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

2002-01-01

92

Higher order adaptive filter characterization of microwave fiber optic link nonlinearity

NASA Astrophysics Data System (ADS)

Microwave Fiber Optic (MFO) links have attracted much attention recently with their application in wireless access. When a wireless link is in series with the optical link, nonlinear distortion (NLD) of the MFO link becomes the biggest concern. The linearity requirement is high due to the large variations in the RF power through the link. Laser intrinsic nonlinearity is usually the major concern in a directly modulated link. However, in wireless applications significant amplification is required at the antenna site, which introduces additional NLD. In this paper a higher order adaptive fiber is proposed to model the entire MFO link considering all cascaded nonlinearities. The FIR filter runs at the baseband symbol rate and trains itself from the input/output amplitude and phase relationships of the microwave modulated symbols. Thus no accurate knowledge of the link physical parameters is required. The powerful recursive least square algorithm converges quickly, tracking any modification or drift in the link parameters. Simulation results show that, third order Volterra adaptive filters are adequate to model measured AM-AM and AM-PM characteristics of a MFL link under steady state conditions. The link consists of a directly modulated InGaAsP DFB laser and PIN diode receiver with a high gain amplifier.

Fernando, Xavier N.; Sesay, Abu B.

2000-04-01

93

A novel nonlinear adaptive filter with pipelined Chebyshev functional link artificial recurrent neural network (PCFLARNN) is presented in this paper, which uses a modification real-time recurrent learning algorithm. The PCFLARNN consists of a number of simple small-scale Chebyshev functional link artificial recurrent neural network (CFLARNN) modules. Compared to the standard recurrent neural network (RNN), those modules of PCFLARNN can simultaneously

Haiquan Zhao; Jiashu Zhang

2010-01-01

94

Exploring Chaos: Theory and Experiment

In the past few years there has been an explosion of books on chaos: the `strange' behaviour of nonlinear dynamical systems. Our understanding of nonlinear dynamics has been aided by the availability of computers with graphical displays on which one can study the iteration of maps and the solution of ordinary differential equations (ODEs). This book is a useful addition

P Borcherds

2000-01-01

95

Deterministic polarization chaos from a laser diode

NASA Astrophysics Data System (ADS)

Fifty years after the invention of the laser diode, and forty years after the butterfly effect signified the unpredictability of deterministic chaos, it is commonly believed that a laser diode behaves like a damped nonlinear oscillator and cannot be driven into chaotic operation without additional forcing or parameter modulation. Here, we counter that belief and report the first example of a free-running laser diode generating chaos. The underlying physics comprises a nonlinear coupling between two elliptically polarized modes in a vertical-cavity surface-emitting laser. We identify chaos in experimental time series and show, theoretically, the bifurcations leading to single- and double-scroll attractors with characteristics similar to Lorenz chaos. The reported polarization chaos resembles noise-driven mode hopping, but shows opposite statistical properties. Our findings open up new research areas for the creation of controllable and integrated sources of optical chaos.

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

2013-01-01

96

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

97

Strange Attractors: Chaos Theory and Composition Studies.

ERIC Educational Resources Information Center

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

Hesse, Doug

98

Properties of nonlinear noise in long, dispersion-uncompensated fiber links

Properties of nonlinear noise in long, dispersion-uncompensated fiber links Ronen Dar,1 Meir Feder) in fiber-optic communications systems with large accumulated dispersion. Our focus is on settling the discrepancy between the results of the Gaussian noise (GN) model (according to which NLIN is additive Gaussian

Feder, Meir

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 of

Madhok, Vaibhav

100

In this paper we propose, discuss and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy", and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy, to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.

Brian R. Hunt; Edward Ott

2015-02-16

101

A method and some results of numeric simulations of magnetostatic spin waves in ferromagnetic films are exponded, in comparison with the theory earlier presented in arXiv preprint 1204.0200. In particular, roles of films finiteness (edges) and defects in formation of linear and non-linear magnetostatic wave patterns, excitation and evolution of two-dimensional solitons, and chaotic non-linear ferromagnetic resonance are considered.

Yu. E. Kuzovlev; Yu. V. Medvedev; N. I. Mezin

2012-04-11

102

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

Katsuhiro Nakamura

2007-01-01

103

Nonlinear optimization-based device-free localization with outlier link rejection.

Device-free localization (DFL) is an emerging wireless technique for estimating the location of target that does not have any attached electronic device. It has found extensive use in Smart City applications such as healthcare at home and hospitals, location-based services at smart spaces, city emergency response and infrastructure security. In DFL, wireless devices are used as sensors that can sense the target by transmitting and receiving wireless signals collaboratively. Many DFL systems are implemented based on received signal strength (RSS) measurements and the location of the target is estimated by detecting the changes of the RSS measurements of the wireless links. Due to the uncertainty of the wireless channel, certain links may be seriously polluted and result in erroneous detection. In this paper, we propose a novel nonlinear optimization approach with outlier link rejection (NOOLR) for RSS-based DFL. It consists of three key strategies, including: (1) affected link identification by differential RSS detection; (2) outlier link rejection via geometrical positional relationship among links; (3) target location estimation by formulating and solving a nonlinear optimization problem. Experimental results demonstrate that NOOLR is robust to the fluctuation of the wireless signals with superior localization accuracy compared with the existing Radio Tomographic Imaging (RTI) approach. PMID:25853406

Xiao, Wendong; Song, Biao; Yu, Xiting; Chen, Peiyuan

2015-01-01

104

Generalized Statistical Mechanics at the Onset of Chaos

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

Alberto Robledo

2013-12-03

105

Nuclear fission and spatial chaos

Nuclear fission is the most fundamental reaction between neutrons and atomic nuclei of nuclear fuel in a reactor. In this paper, according to the nonlinear dynamical behavior of the neutron transport system in space (or the distribution behavior of neutrons in the reactor) which reveals this essential reaction, we investigate the relation between nuclear fission and spatial chaos, neutron multiplication

Shu Tang Liu

2006-01-01

106

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

107

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

NASA Astrophysics Data System (ADS)

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

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

2013-12-01

108

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

109

Many travelling wave solutions of nonlinear evolution equations can be written as a polynomial in several elementary or special functions which satisfy a first order nonlinear ordinary differential equation with a sixth-degree nonlinear term. From that property, we deduce an algebraic method for constructing those solutions by determining only a finite number of coefficients. Being concise and straightforward, the method

Ding-Jiang Huang; Hong-Qing Zhang

2006-01-01

110

Chaos in World Politics: A Reflection

NASA Astrophysics Data System (ADS)

Chaos theory results from natural scientists' findings in the area of non-linear dynamics. The importance of related models has increased in the last decades, by studying the temporal evolution of non-linear systems. In consequence, chaos is one of the concepts that most rapidly have been expanded in what research topics respects. Considering that relationships in non-linear systems are unstable, chaos theory aims to understand and to explain this kind of unpredictable aspects of nature, social life, the uncertainties, the nonlinearities, the disorders and confusion, scientifically it represents a disarray connection, but basically it involves much more than that. The existing close relationship between change and time seems essential to understand what happens in the basics of chaos theory. In fact, this theory got a crucial role in the explanation of many phenomena. The relevance of this kind of theories has been well recognized to explain social phenomena and has permitted new advances in the study of social systems. Chaos theory has also been applied, particularly in the context of politics, in this area. The goal of this chapter is to make a reflection on chaos theory - and dynamical systems such as the theories of complexity - in terms of the interpretation of political issues, considering some kind of events in the political context and also considering the macro-strategic ideas of states positioning in the international stage.

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

111

and Chaos Group. Universidad Rey Juan Carlos, 28933 Mo´stoles, Madrid, Spain J. M. Guerra Departamento de Optica, Facultad de Ciencias Fi´sicas, Universidad Complutense de Madrid, 28040 Madrid, Spain Received 15

Rey Juan Carlos, Universidad

112

Ventilatory Chaos Is Impaired in Carotid Atherosclerosis

Ventilatory chaos is strongly linked to the activity of central pattern generators, alone or influenced by respiratory or cardiovascular afferents. We hypothesized that carotid atherosclerosis should alter ventilatory chaos through baroreflex and autonomic nervous system dysfunctions. Chaotic dynamics of inspiratory flow was prospectively evaluated in 75 subjects undergoing carotid ultrasonography: 27 with severe carotid stenosis (>70%), 23 with moderate stenosis

Laurence Mangin; Guy Lesèche; Alain Duprey; Christine Clerici

2011-01-01

113

Visually-induced illusions of self-motion (vection) can be compelling for some people, but they are subject to large individual variations in strength. Do these variations depend, at least in part, on the extent to which people rely on vision to maintain their postural stability? We investigated by comparing physical posture measures to subjective vection ratings. Using a Bertec balance plate in a brightly-lit room, we measured 13 participants' excursions of the centre of foot pressure (CoP) over a 60-second period with eyes open and with eyes closed during quiet stance. Subsequently, we collected vection strength ratings for large optic flow displays while seated, using both verbal ratings and online throttle measures. We also collected measures of postural sway (changes in anterior-posterior CoP) in response to the same visual motion stimuli while standing on the plate. The magnitude of standing sway in response to expanding optic flow (in comparison to blank fixation periods) was predictive of both verbal and throttle measures for seated vection. In addition, the ratio between eyes-open and eyes-closed CoP excursions during quiet stance (using the area of postural sway) significantly predicted seated vection for both measures. Interestingly, these relationships were weaker for contracting optic flow displays, though these produced both stronger vection and more sway. Next we used a non-linear analysis (recurrence quantification analysis, RQA) of the fluctuations in anterior-posterior position during quiet stance (both with eyes closed and eyes open); this was a much stronger predictor of seated vection for both expanding and contracting stimuli. Given the complex multisensory integration involved in postural control, our study adds to the growing evidence that non-linear measures drawn from complexity theory may provide a more informative measure of postural sway than the conventional linear measures. PMID:25462216

Apthorp, Deborah; Nagle, Fintan; Palmisano, Stephen

2014-01-01

114

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

115

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.

116

Chaos in an imperfectly premixed model combustor.

This article reports nonlinear bifurcations observed in a laboratory scale, turbulent combustor operating under imperfectly premixed mode with global equivalence ratio as the control parameter. The results indicate that the dynamics of thermoacoustic instability correspond to quasi-periodic bifurcation to low-dimensional, deterministic chaos, a route that is common to a variety of dissipative nonlinear systems. The results support the recent identification of bifurcation scenarios in a laminar premixed flame combustor (Kabiraj et al., Chaos: Interdiscip. J. Nonlinear Sci. 22, 023129 (2012)) and extend the observation to a practically relevant combustor configuration. PMID:25725637

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

2015-02-01

117

Chaos in an imperfectly premixed model combustor

NASA Astrophysics Data System (ADS)

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

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

2015-02-01

118

Physics and applications of laser diode chaos

NASA Astrophysics Data System (ADS)

This Review Article provides an overview of chaos in laser diodes by surveying experimental achievements in the area and explaining the theory behind the phenomenon. The fundamental physics underpinning laser diode chaos and also the opportunities for harnessing it for potential applications are discussed. The availability and ease of operation of laser diodes, in a wide range of configurations, make them a convenient testbed for exploring basic aspects of nonlinear and chaotic dynamics. It also makes them attractive for practical tasks, such as chaos-based secure communications and random number generation. Avenues for future research and development of chaotic laser diodes are also identified.

Sciamanna, M.; Shore, K. A.

2015-03-01

119

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

NASA Astrophysics Data System (ADS)

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

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

2009-07-01

120

Proceedings of the 2nd Experimental Chaos Conference

NASA Astrophysics Data System (ADS)

The Table of Contents for the full book PDF is as follows: * Introduction * Spatiotemporal Phenomena * Experimental Studies of Chaotic Mixing * Using Random Maps in the Analysis of Experimental Fluid Flows * Transition to Spatiotemporal Chaos in a Reaction-Diffusion System * Ion-Dynamical Chaos in Plasmas * Optics * Chaos in a Synchronously Driven Optical Resonator * Chaos, Patterns and Defects in Stimulated Scattering Phenomena * Test of the Normal Form for a Subcritical Bifurcation * Observation of Bifurcations and Chaos in a Driven Fiber Optic Coil * Applications -- Communications * Robustness and Signal Recovery in a Synchronized Chaotic System * Synchronizing Nonautonomous Chaotic Circuits * Synchronization of Pulse-Coupled Chaotic Oscillators * Ocean Transmission Effects on Chaotic Signals * Controlling Symbolic Dynamics for Communication * Applications -- Control * Analysis of Nonlinear Actuators Using Chaotic Waveforms * Controlling Chaos in a Quasiperiodic Electronic System * Control of Chaos in a CO2 Laser * General Research * Video-Based Analysis of Bifurcation Phenomena in Radio-Frequency-Excited Inert Gas Plasmas * Transition from Soliton to Chaotic Motion During the Impact of a Nonlinear Structure * Sonoluminescence in a Single Bubble: Periodic, Quasiperiodic and Chaotic Light Source * Quantum Chaos Experiments Using Microwave Cavities * Experiments on Quantum Chaos With and Without Time Reversibility * When Small Noise Imposed on Deterministic Dynamics Becomes Important * Biology * Chaos Control for Cardiac Arrhythmias * Irregularities in Spike Trains of Cat Retinal Ganglion Cells * Broad-Band Synchronization in Monkey Neocortex * Applicability of Correlation Dimension Calculations to Blood Pressure Signal in Rats * Tests for Deterministic Chaos in Noisy Time Series * The Crayfish Mechanoreceptor Cell: A Biological Example of Stochastic Resonance * Chemistry * Chaos During Heterogeneous Chemical Reactions * Stabilizing and Tracking Unstable Periodic Orbits and Stationary States in Chemical Systems * Recursive Proportional-Feedback and Its Use to Control Chaos in an Electrochemical System * Temperature Patterns on Catalytic Surfaces * Meteorology/Oceanography * Nonlinear Evolution of Water Waves: Hilbert's View * Fractal Properties of Isoconcentration Surfaces in a Smoke Plume * Fractal Dimensions of Remotely Sensed Atmospheric Signals * Are Ocean Surface Waves Chaotic? * Dynamical Attractor Reconstruction for a Marine Stratocumulus Cloud

Ditto, William; Pecora, Lou; Shlesinger, Michael; Spano, Mark; Vohra, Sandeep

1995-02-01

121

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

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

Sharp, L F; Priesmeyer, H R

1995-01-01

122

Protein folding produces characteristic and functional three-dimensional structures from unfolded polypeptides or disordered coils. The emergence of extraordinary complexity in the protein folding process poses astonishing challenges to theoretical modeling and computer simulations. The present work introduces molecular nonlinear dynamics (MND), or molecular chaotic dynamics, as a theoretical framework for describing and analyzing protein folding. We unveil the existence of intrinsically low dimensional manifolds (ILDMs) in the chaotic dynamics of folded proteins. Additionally, we reveal that the transition from disordered to ordered conformations in protein folding increases the transverse stability of the ILDM. Stated differently, protein folding reduces the chaoticity of the nonlinear dynamical system, and a folded protein has the best ability to tame chaos. Additionally, we bring to light the connection between the ILDM stability and the thermodynamic stability, which enables us to quantify the disorderli...

Xia, Kelin

2013-01-01

123

NASA Astrophysics Data System (ADS)

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

Maldonado, Armando; Bixler, David

2012-03-01

124

Chaos and Forecasting - Proceedings of the Royal Society Discussion Meeting

NASA Astrophysics Data System (ADS)

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

Tong, Howell

1995-04-01

125

Monitoring chaos of cardiac rhythms

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

Mayer-Kress, G.

1989-01-01

126

A highly stable second-order nonlinear optical multilayer film was constructed on insulating substrates using the electric-field-induced layer-by-layer assembly technique. The substrates used in this method could be arbitrary. In another, the substrates could be modified with polyanion solution by spin coating as cladding layer. Then, the nonlinear optical multilayer films were assembled on the cladding layer directly by the electric-field-induced layer-by-layer assembly technique. The resulting cross-linked multilayer films fabricated by this method displayed high optical transparency, good thermal stability, and excellent nonlinear optical properties which can be made into waveguide devices directly. PMID:22005346

Wang, Shiwei; Zhao, Lisha; Cui, Zhanchen

2012-01-15

127

Quantum chaos in an ultra-strongly coupled bosonic junction

The classical and quantum dynamics of two ultra-strongly coupled and weakly nonlinear resonators cannot be explained using the Discrete Nonlinear Schr\\"odinger Equation or the Bose-Hubbard model, respectively. Instead, a model beyond the Rotating Wave Approximation must be studied. In the classical limit this model is not integrable and becomes chaotic for a finite window of parameters. For the quantum dimer we find corresponding regions of stability and chaos. The more striking consequence for both classical and quantum chaos is that the tunneling time between the sites becomes unpredictable. These results, including the transition to chaos, can be tested in experiments with superconducting microwave resonators.

Uta Naether; Juan José García-Ripoll; Juan José Mazo; David Zueco

2014-03-12

128

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

129

ERIC Educational Resources Information Center

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

Huwe, Terence K.

2009-01-01

130

Chaos Experiments Wave Chaos and Electromagnetic

Dimensional Quarter Bow Tie Wave Chaotic cavity Â· Classical ray trajectories are chaotic - short wavelengthChaos Experiments Â Wave Chaos and Electromagnetic Interference in Enclosures Â·Faculty: Steven M Â· Coupling of external radiation to computer circuits is a complex processes: apertures resonant cavities

Anlage, Steven

131

High-dimensional chaos from self-sustained collisions of solitons

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

Yildirim, O. Ozgur, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Cavium, Inc., 600 Nickerson Rd., Marlborough, Massachusetts 01752 (United States); Ham, Donhee, E-mail: donhee@seas.harvard.edu, E-mail: oozgury@gmail.com [Harvard University, 33 Oxford St., Cambridge, Massachusetts 02138 (United States)

2014-06-16

132

High-dimensional chaos from self-sustained collisions of solitons

NASA Astrophysics Data System (ADS)

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

Yildirim, O. Ozgur; Ham, Donhee

2014-06-01

133

Subharmonics, chaos and beyond

NASA Astrophysics Data System (ADS)

While studying finite amplitude ultrasonic wave resonance in a one dimensional liquid-filled cavity formed by a narrow band transducer and a plane reflector, subharmonics of the driver's frequency were observed (1,2) in addition to the expected harmonic structure. Subsequently, it was realized that the system was one of the many examples of parametric resonance in which the observed subharmonics are parametrically generated. The generation mechanism also requires a sufficiently high threshold value of the driving amplitude so that the system becomes increasingly nonlinear in response. The nonlinear features were recently investigated and are the focus of this paper. An ultrasonic interferometer with optical precision was built. The transducers were compressional, undamped quartz and Lithium Niobate crystals ranging from 1-10 MHz, driven by a high power amplifier. Both an optical diffraction system and a receiver transducer attached to an aligned reflector were used to observe the generated frequency components in the cavity. There are at least 5 regions of excitation that were identified. It is shown that from a region of oscillation stability into an unstable region leads to a cascade of bifurcations (subharmonics) culminating in chaotic oscillations. A further increase in the amplitude results in a reversion of the chaos into a second region of stability. A first-principle based explanation of the experimental findings is presented.

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

2012-05-01

134

Dynamical Systems, Stability, and Chaos

In this expository and resources chapter we review selected aspects of the mathematics of dynamical systems, stability, and chaos, within a historical framework that draws together two threads of its early development: celestial mechanics and control theory, and focussing on qualitative theory. From this perspective we show how concepts of stability enable us to classify dynamical equations and their solutions and connect the key issues of nonlinearity, bifurcation, control, and uncertainty that are common to time-dependent problems in natural and engineered systems. We discuss stability and bifurcations in three simple model problems, and conclude with a survey of recent extensions of stability theory to complex networks.

R. Ball; P. Holmes

2007-04-26

135

ERIC Educational Resources Information Center

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

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

2010-01-01

136

Distributional uncertainty analysis using power series and polynomial chaos expansions

This paper provides an overview of computationally efficient approaches for quantifying the influence of parameter uncertainties on the states and outputs of nonlinear dynamical systems with finite-time control trajectories, focusing primarily on computing probability distributions. The advantages and disadvantages of various uncertainty analysis approaches, which use approximate representations of the full nonlinear model using power series or polynomial chaos expansions,

Z. K. Nagy; R. D. Braatz

2007-01-01

137

Parabolic Resonance: A Route to Hamiltonian Spatiotemporal Chaos

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

138

Chaos in oil prices? Evidence from futures markets

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

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

2001-01-01

139

The missing link: a nonlinear post-Friedmann framework for small and large scales

We present a nonlinear post-Friedmann framework for structure formation, generalizing to cosmology the weak-field (post-Minkowskian) approximation, unifying the treatment of small and large scales. We consider a universe filled with a pressureless fluid and a cosmological constant $\\Lambda$, the theory of gravity is Einstein's general relativity and the background is the standard flat $\\Lambda$CDM cosmological model. We expand the metric and the energy-momentum tensor in powers of $1/c$, keeping the matter density and peculiar velocity as exact fundamental variables. We assume the Poisson gauge, including scalar and tensor modes up to $1/c^4$ order and vector modes up to $1/c^5$ terms. Through a redefinition of the scalar potentials as a resummation of the metric contributions at different orders, we obtain a complete set of nonlinear equations, providing a unified framework to study structure formation from small to superhorizon scales, from the nonlinear Newtonian to the linear relativistic regime. We expli...

Milillo, Irene; Bruni, Marco; Maselli, Andrea

2015-01-01

140

. Two different chaotic time series analysis methods – the correlation dimension and nonlinear forecasting – are introduced\\u000a and then used to process the interspike intervals (ISI) of the action potential trains propagated along a single nerve fiber\\u000a of the anesthetized rat. From the results, the conclusion is drawn that compared with the correlation dimension, nonlinear\\u000a forecasting is more efficient

Yunfan Gong; Jianxue Xu; Wei Ren; Sanjue Hu; Fuzhou Wang

1998-01-01

141

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

Oestreicher, Christian

2007-01-01

142

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

143

NASA Astrophysics Data System (ADS)

The publication by Ott, Grebogi and Yorke(E. Ott, C. Grebogi and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).) of their theory of chaos control in 1990 led to an explosion of experimental work applying their theory to mechanical systems and electronic circuits, lasers and chemical reactors, and heart and brain tissue, to name only a few. In this talk the basics of chaos control as implemented in a simple mechanical system will be described, as well as extensions of the method to biological applications. Finally, current advances in the field, including the maintenance of chaos and the control of high dimensional chaos, will be discussed.

Spano, Mark

1997-04-01

144

THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT

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

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

2011-09-20

145

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

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

2014-04-01

146

Decoherence, determinism and chaos

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

Noyes, H.P.

1994-01-01

147

NASA Astrophysics Data System (ADS)

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

Schuch, Dieter

2014-04-01

148

Observational Manifestation of Chaos in Astrophysical Objects

NASA Astrophysics Data System (ADS)

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

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

2002-12-01

149

Chaotic operation and chaos control of travelling wave ultrasonic motor.

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

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

2013-08-01

150

Quantum Chaos in Non-Symmetric Potential Well in a Tilted Magnetic Field

In this paper, the dynamical behavior of a non-symmetric double potential well in a tilted magnetic field is studied. The classical Poincare section is given to exhibit the chaotic behavior of the system, and non-linear resonant lead to chaos. The paper has also given the energy spectral statistics which satisfies Brody's distribution, tunnelling effect develops quantum chaos and also holds

Guoyong Yuan; Shiping Yang; Hongling Fan; Hong Chang

2004-01-01

151

Cyberterrorism: Postmodern State of Chaos

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

152

What makes chaos border sticky?

A ``microscopic'' investigation of long-time correlations near the chaos border of a particular model system has been carried out. Apparent stickiness of chaos border seems to be due to the influence of nearby hyperbolic orbits which are convergent to the invariant curve which constitutes the chaos border. The diffusion near the chaos border can be described by a one-dimensional biased

Koo-Chul Lee

1989-01-01

153

Understanding chaos via nuclei

We use two models of nuclear collective dynamics-the geometric collective model and the interacting boson model-to illustrate principles of classical and quantum chaos. We propose these models as a suitable testing ground for further elaborations of the general theory of chaos in both classical and quantum domains.

Cejnar, Pavel [Institute of Particle and Nuclear Physics, Faculty of Mathematics and Physics, Charles University, V Holešovi?kách 2, 18000 Prague (Czech Republic); Stránský, Pavel [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, 04510, México, D.F. (Mexico)

2014-01-08

154

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

155

Properties of nonlinear noise in long, dispersion-uncompensated fiber links.

We study the properties of nonlinear interference noise (NLIN) in fiber-optic communications systems with large accumulated dispersion. Our focus is on settling the discrepancy between the results of the Gaussian noise (GN) model (according to which NLIN is additive Gaussian) and a recently published time-domain analysis, which attributes drastically different properties to the NLIN. Upon reviewing the two approaches we identify several unjustified assumptions that are key in the derivation of the GN model, and that are responsible for the discrepancy. We derive the true NLIN power and verify that the NLIN is not additive Gaussian, but rather it depends strongly on the data transmitted in the channel of interest. In addition we validate the time-domain model numerically and demonstrate the strong dependence of the NLIN on the interfering channels' modulation format. PMID:24216794

Dar, Ronen; Feder, Meir; Mecozzi, Antonio; Shtaif, Mark

2013-11-01

156

Controlling spatiotemporal chaos via small external forces

The spatiotemporal chaos in the system described by a one-dimensional nonlinear drift-wave equation is controlled by directly adding a periodic force with appropriately chosen frequencies. By dividing the solution of the system into a carrier steady wave and its perturbation, we find that the controlling mechanism can be explained by a slaving principle. The critical controlling time for a perturbation mode increases exponentially with its wave number.

Shunguang Wu; Kaifen He; Zuqia Huang

1999-08-08

157

Harnessing quantum transport by transient chaos.

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. PMID:23556962

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

2013-03-01

158

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

NASA Astrophysics Data System (ADS)

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

Simon, A.

2010-12-01

159

Probability Simulations by Non-Lipschitz Chaos

NASA Technical Reports Server (NTRS)

It has been demonstrated that classical probabilities, and in particular, probabilistic Turing machine, can be simulated by combining chaos and non-Lipschitz dynamics, without utilization of any man-made devices. Self-organizing properties of systems coupling simulated and calculated probabilities and their link to quantum computations are discussed.

Zak, Michail

1996-01-01

160

Decrease of cardiac chaos in congestive heart failure

NASA Astrophysics Data System (ADS)

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

Poon, Chi-Sang; Merrill, Christopher K.

1997-10-01

161

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

162

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

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

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

2008-09-29

163

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

164

Chaos and Unpredictability in Evolution

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

Iaroslav Ispolatov; Michael Doebeli

2013-09-24

165

NASA Astrophysics Data System (ADS)

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

Tauxe, L.

2002-12-01

166

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

167

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

168

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

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

2013-01-01

169

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

170

Household chaos is a construct often overlooked in studies of human development, despite its theoretical links with the integrity of individual well-being, family processes, and child development. The present longitudinal study examined relations between household chaos and well-established correlates of chaos (sociodemographic risk, major life events, and personal distress) and several constructs that, to date, are theoretically linked with chaos but never before assessed as correlates (quality of coparenting and emotional availability with infants at bedtime). In addressing this aim, we introduce a new measure of household chaos (the Descriptive In-home Survey of Chaos-Observer ReporteD, or DISCORD), wholly reliant on independent observer report, which draws from household chaos theory and prior empirical work but extends the measurement of chaos to include information about families' compliance with a home visiting protocol. Household chaos was significantly associated with socioeconomic risk, negative life events, less favorable coparenting, and less emotionally available bedtime parenting, but not with personal distress. These findings emphasize the need to examine household chaos as a direct and indirect influence on child and family outcomes, as a moderator of intervention attempts to improving parenting and child development, and as a target of intervention in its own right. (PsycINFO Database Record PMID:25705790

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

2015-04-01

171

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

172

Chaos in a three-species food chain

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

173

Chaos and bifurcation in Power Electronics Medical Instruments Implications

Chaos and bifurcation in Power Electronics Medical Instruments Implications Titi Trandafir, MSEE Consultant Microtrend Systems Inc. http://www.microtrendsys.com #12;Number of Variables n = 1 n = 2 n 3 n) Predator-Prey cycles Nonlinear electronics (van der Pol,Josephson) #12;PoincarÃ© in 1899 first glimpsed

Gajic, Zoran

174

Organisational Leadership and Chaos Theory: Let's Be Careful

ERIC Educational Resources Information Center

This article addresses issues associated with applications of ideas from "chaos theory" to educational administration and leadership as found in the literature. Implications are considered in relation to claims concerning the behaviour of non-linear dynamic systems, and to the nature of the interpretations and recommendations that are made. To aid…

Galbraith, Peter

2004-01-01

175

New Directions in Systems Theory: Chaos and Complexity.

ERIC Educational Resources Information Center

"Nonlinear dynamics," chaos and complexity theories, and their accompanying research methods provide new ways to understand systems theory and study complex human systems. This article presents an overview of these approaches, their sophisticated mathematical methods, and their relevance to social work practice and research. The advantages are…

Warren, Keith; Franklin, Cynthia; Streeter, Calvin L.

1998-01-01

176

Quantum Chaos & Quantum Computers

The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergodicity are determined. In spite the fact that this phenomenon is rather dangerous for quantum computing it is shown that the quantum chaos border for inter-qubit coupling is exponentially larger than the energy level spacing between quantum computer eigenstates and drops only linearly with the number of qubits n. As a result the ideal multi-qubit structure of the computer remains rather robust against imperfections. This opens a broad parameter region for a possible realization of quantum computer. The obtained results are related to the recent studies of quantum chaos in such many-body systems as nuclei, complex atoms and molecules, finite Fermi systems and quantum spin glass shards which are also reviewed in the paper.

D. L. Shepelyansky

2000-06-15

177

NASA Astrophysics Data System (ADS)

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

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

2011-02-01

178

Intramolecular and nonlinear dynamics

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

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

1993-12-01

179

The Chaos Hypertextbook: Mathematics in the Age of the Computer

NSDL National Science Digital Library

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

Elert, Glenn.

180

Open-loop sustained chaos and control: a manifold approach.

We present a general method for preserving chaos in nonchaotic parameter regimes as well as preserving periodic behavior in chaotic regimes using a multifrequency phase control. The systems considered are nonlinear systems driven at a base frequency. Multifrequency phase control is defined as the addition of small subharmonic amplitude modulation coupled with a phase shift. By implementing multifrequency control, stable and unstable manifold intersections in postcrisis regimes may be manipulated to sustain chaos as well as to sustain periodic behavior. The theory and a preliminary experiment are demonstrated for a CO2 driven laser. PMID:12241273

Schwartz, Ira B; Triandaf, Ioana; Meucci, Riccardo; Carr, Thomas W

2002-08-01

181

NASA Astrophysics Data System (ADS)

Further modifications of the method proposed by Ott, Grebogi and Yorke to control chaos [Phys. Rev. Lett. 64, 1196 (1990)] have been achieved allowing us to stabilize and characterize unstable states (stationary or periodic) in their whole domain of existence. We demonstrate the possibility of stabilizing unstable periodic orbits in an experiment by applying a continuous feedback method. It has been checked experimentally on a CO2 laser with a modulated parameter. This kind of method is very attractive opening the way to the control of chaos in very fast systems.

Bielawski, Serge; Derozier, Dominique; Glorieux, Pierre

1993-12-01

182

NASA Astrophysics Data System (ADS)

The method for stabilizing an unstable periodic orbit in chaotic dynamical systems originally formulated by Ott, Grebogi, and Yorke (OGY) is not directly applicable to chaotic Hamiltonian systems. The reason is that an unstable periodic orbit in such systems often exhibits complex-conjugate eigenvalues at one or more of its orbit points. In this paper we extend the OGY stabilization method to control Hamiltonian chaos by incorporating the notion of stable and unstable directions at each periodic point. We also present an algorithm to calculate the stable and unstable directions. Other issues specific to the control of Hamiltonian chaos are also discussed.

Lai, Ying-Cheng; Ding, Mingzhou; Grebogi, Celso

1993-01-01

183

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

184

Chaos in a Fractional Order Chua System

NASA Technical Reports Server (NTRS)

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

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

1996-01-01

185

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

186

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

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

187

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

188

Converting transient chaos into sustained chaos by feedback control

NASA Astrophysics Data System (ADS)

A boundary crisis is a catastrophic event in which a chaotic attractor is suddenly destroyed, leaving a nonattracting chaotic saddle in its place in the phase space. Based on the controlling-chaos idea [E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990)], we present a method for stabilizing chaotic trajectories on the chaotic saddle by applying only small parameter perturbations. This strategy enables us to convert transient chaos into sustained chaos, thereby restoring attracting chaotic motion.

Lai, Ying-Cheng; Grebogi, Celso

1994-02-01

189

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

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

Ustinov, Alexey B.; Kondrashov, Alexandr V.; Nikitin, Andrey A.; Kalinikos, Boris A. [Department of Physical Electronics and Technology, St. Petersburg Electrotechnical University, St. Petersburg 197376 (Russian Federation)

2014-06-09

190

Noise tolerant spatiotemporal chaos computing.

We introduce and design a noise tolerant chaos computing system based on a coupled map lattice (CML) and the noise reduction capabilities inherent in coupled dynamical systems. The resulting spatiotemporal chaos computing system is more robust to noise than a single map chaos computing system. In this CML based approach to computing, under the coupled dynamics, the local noise from different nodes of the lattice diffuses across the lattice, and it attenuates each other's effects, resulting in a system with less noise content and a more robust chaos computing architecture. PMID:25554030

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

2014-12-01

191

Noise tolerant spatiotemporal chaos computing

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

192

NASA Technical Reports Server (NTRS)

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

2002-01-01

193

Wireless communication with chaos.

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

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

2013-05-01

194

Chaos synchronization and hyperchaos

NASA Astrophysics Data System (ADS)

We discuss the relation between phenomena of chaos synchronization in coupled systems and creation of hyperchaotic attractors (attractors with at least two positive Lyapunov exponents. Such attractors are common in higher-dimensional dynamical systems (at least two-dimensional maps or four-dimensional flows). Riddling bifurcation i.e., the bifurcation in which one of the unstable periodic orbits embedded in a chaotic attractor located on the invariant manifold becomes unstable transversely to the attractor leads to the loss of chaos synchronization in coupled identical systems. We show that generalized riddling bifurcation defined as the bifurcation in which one of the unstable periodic orbits embedded in a higher-dimensional chaotic attractor (not necessarily located on the invariant manifold) becomes unstable transversely to the attractor explains mechanism of the creation of hyperchaotic attractors. Additionally we show that the generalized riddling bifurcation can give physical mechanism explaining interstellar journeys described in science-fiction literature.

Kapitaniak, Tomasz

2005-01-01

195

Chaos and unpredictability in evolution.

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

Doebeli, Michael; Ispolatov, Iaroslav

2014-05-01

196

NASA Technical Reports Server (NTRS)

23 October 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows light-toned rock outcrops, possibly sedimentary rocks, in the Arsinoes Chaos region east of the Valles Marineris trough system. These rocky materials were once below the martian surface. These features are located near 7.2oS, 27.9oW. The image covers an area about 3 km (1.9 mi) wide. Sunlight illuminates the scene from the upper left.

2004-01-01

197

The 2014 International Nursing Administration Research Conference, "Pioneering Through Chaos: Leadership for a Changing World," was held at the Texas Woman's University in Dallas, Texas, in the fall of 2014. The program drew more than 100 attendees from 4 countries. The conference informed attendees from both academe and practice about the role of nursing administration in navigating the dynamic healthcare climate. This article will report on the insights from the conference presenters. PMID:25689497

Warshawsky, Nora E; Joseph, M Lindell; Fowler, Debra L; Edmonson, Cole; Nelson-Brantley, Heather V; Kowalski, Karren

2015-03-01

198

Much of the foundational work on quantum cosmology employs a simple minisuperspace model describing a Friedmann-Robertson-Walker universe containing a massive scalar field. We show that the classical limit of this model exhibits deterministic chaos and explore some of the consequences for the quantum theory. In particular, the breakdown of the WKB approximation calls into question many of the standard results in quantum cosmology.

Neil Cornish; Paul Shellard

1998-10-05

199

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

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

2014-06-23

200

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

Sudarshan, E.C.G.

1993-12-31

201

Chaos Experiments at Microwave Frequencies

-band? Localized modes in trapezoidal cavities Investigate the effects of slight irregularities in the shape Square Meeting 14 June, 2001 #12;Two Types of Experiments "Quantum Chaos" Basic study of wave dynamics: Breaking of degeneracy, Scars, Strong eigenfunction fluctuations ii ii qHp pHq -= = / / #12;Wave Chaos

Anlage, Steven

202

Quantum Chaos and Quantum Computers

The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability.

D. L. Shepelyansky

2001-01-01

203

Quantum chaos and quantum computers

The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability.

D. L. Shepelyansky

2001-01-01

204

Quantum chaos in quantum dots coupled to bosons

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

S. Ahadpour; N. Hematpour

2012-07-24

205

NASA Technical Reports Server (NTRS)

8 September 2005 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows outcrops of light-toned, sedimentary rock among darker-toned mesas in Aram Chaos. Dark, windblown *megaripples* -- large ripples -- are also present at this location.

*Location near*: 3.0oN, 21.6oW *Image width*: width: 3 km (1.9 mi) *Illumination from*: lower left *Season*: Northern Autumn

2005-01-01

206

NASA Technical Reports Server (NTRS)

15 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows the results of a small landslide off of a hillslope in the Aureum Chaos region of Mars. Mass movement occurred from right (the slope) to left (the lobate feature pointed left). Small dark dots in the landslide area are large boulders. This feature is located near 2.6oS, 24.5oW. This picture covers an area approximately 3 km (1.9 mi) across and is illuminated by sunlight from the left/upper left.

2004-01-01

207

NASA Astrophysics Data System (ADS)

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

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

2013-01-01

208

NASA Astrophysics Data System (ADS)

An extensive set of both linear and non-linear mechanical experiments including non-linear stress-strain behavior and non-linear creep/recovery has been carried out on a lightly cross-linked SBR. The results have been obtained for a wide range of temperatures, extension rates and stretch ratios. The data set reveals an unexpectedly rich behavior, which cannot be predicted by the traditional constitutive models that are based on an additive combination of hyperelastic and quasi-linear viscoelastic contributions. The inability of traditional constitutive models to describe the data is particularly striking for a high extension rate deformation followed by a slow extension rate (e.g. creep) as contrasted to deformations at slow extension rates. The hyperelastic model of rubber elasticity is shown to provide a satisfactory description of the equilibrium behavior; thus, the results in the current study indicate the need for the development of a new type viscoelastic model for elastomers. Potential candidates for the needed constitutive description will be discussed.

Caruthers, James; Bhattacharya, Aparajita; Medvedev, Grigori

2010-03-01

209

We present experimental and numerical investigations of Kerr nonlinearity compensation in a 400-km standard single-mode fiber link with distributed Raman amplification with backward pumping. A dual-pump polarization-independent fiber-based optical parametric amplifier is used for mid-link spectral inversion of 5 × 28-GBd polarization-multiplexed 16-QAM signals. Signal quality factor (Q-factor) improvements of 1.1 dB and 0.8 dB were obtained in the cases of a single-channel and a five-channel wavelength-division multiplexing (WDM) system, respectively. The experimental results are compared to numerical simulations with good agreement. It is also shown with simulations that a maximum transmission reach of 2400 km enabled by the optical phase conjugator is possible for the WDM signal. PMID:25401887

Sackey, Isaac; Da Ros, Francesco; Jazayerifar, Mahmoud; Richter, Thomas; Meuer, Christian; Nölle, Markus; Molle, Lutz; Peucheret, Christophe; Petermann, Klaus; Schubert, Colja

2014-11-01

210

Detecting chaos in a complex system

The sequences, given by a 7D map have been analysed by means of the methods, widely used to detect chaos in the real world in order to test their sensitivity to chaotic features of a non-linear system determined by comparatively high number of parameters. The same diagnostic approaches have been applied to the 3D Lorenz map for comparison. The results show that for some of the sequences yielded from the 7D map, the adopted methods were not able to give as straightforward answer to the question if the system is chaotic as in the 3D case. Since the sequences, subject of the analysis, were not contaminated by noise and were sufficiently long, it could be assumed that such difficulties have arisen likely due to specific internal features of the more complex system. It was found also that an increase from 0.01 to 0.5 of the sampling step determining the sequences obtained from the 7D map, masks the chaos in some of them.

Boyan Hristozov Petkov

2013-10-14

211

NASA Astrophysics Data System (ADS)

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

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

2014-06-01

212

Stratified chaos in a sand pile formation

Sand pile formation is often used to describe stratified chaos in dynamic systems due to self-emergent and scale invariant behaviour. Cellular automata (Bak-Tang-Wiesenfeld model) are often used to describe chaotic behaviour, as simulating physical interactions between individual particles is computationally demanding. In this study, we use a state-of-the-art parallel implementation of the discrete element method on the graphical processing unit to simulate sand pile formation. Interactions between individual grains were simulated using a contact model in an Euler integration scheme. Results show non-linear self-emergent behaviour which is in good agreement with experimental results, theoretical work and self organized criticality (SOC) approaches. Moreover, it was found that the fully deterministic model, where the position and forces on every individual particle can be determined every iteration has a brown noise signal in the x and y direction, where the signal is the z direction is closer to a white noise spectrum.

Ate Poortinga; Jan G. Wesseling; Coen J. Ritsema

2014-03-04

213

Semiclassical Foundation of Universality in Quantum Chaos

NASA Astrophysics Data System (ADS)

We sketch the semiclassical core of a proof of the so-called Bohigas-Giannoni-Schmit conjecture: A dynamical system with full classical chaos has a quantum energy spectrum with universal fluctuations on the scale of the mean level spacing. We show how in the semiclassical limit all system specific properties fade away, leaving only ergodicity, hyperbolicity, and combinatorics as agents determining the contributions of pairs of classical periodic orbits to the quantum spectral form factor. The small-time form factor is thus reproduced semiclassically. Bridges between classical orbits and (the nonlinear sigma model of) quantum field theory are built by revealing the contributing orbit pairs as topologically equivalent to Feynman diagrams.

Müller, Sebastian; Heusler, Stefan; Braun, Petr; Haake, Fritz; Altland, Alexander

2004-07-01

214

NSDL National Science Digital Library

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

215

Chao Family Comprehensive Cancer Center

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

216

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

217

Distinguishing Error from Chaos in Ecological Time Series

NASA Astrophysics Data System (ADS)

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

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

1990-11-01

218

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

219

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

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

Shepelyansky, Dima

220

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

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

2007-01-01

221

Human language is a complex communication system with unlimited expressibility. Children spontaneously develop a native language by exposure to linguistic data from their speech community. Over historical time, languages change dramatically and unpredictably by accumulation of small changes and by interaction with other languages. We have previously developed a mathematical model for the acquisition and evolution of language in heterogeneous populations of speakers. This model is based on game dynamical equations with learning. Here, we show that simple examples of such equations can display complex limit cycles and chaos. Hence, language dynamical equations mimic complicated and unpredictable changes of languages over time. In terms of evolutionary game theory, we note that imperfect learning can induce chaotic switching among strict Nash equilibria. PMID:15209103

Mitchener, W. Garrett; Nowak, Martin A.

2004-01-01

222

NASA Technical Reports Server (NTRS)

MGS MOC Release No. MOC2-504, 5 October 2003

This August 2003 Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows a valley near Nilus Chaos, around 25.2oN, 80.3oW. The scene has a uniform albedo, indicating that all of the landforms are probably mantled by fine, bright dust. Dark streaks on the valley walls indicate places where recent dust avalanches have occurred. The ripple-like dune features on the valley floor were formed by wind, but today they are inactive and covered with dust. A few craters, created by impacting debris, have formed on the dunes, again attesting to their inactivity in the modern martian environment. The image covers an area 3 km (1.9 mi) wide; it is illuminated by sunlight from the lower left.

2003-01-01

223

NASA Technical Reports Server (NTRS)

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

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

2006-01-01

224

Optical digital chaos cryptography

NASA Astrophysics Data System (ADS)

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

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

2007-10-01

225

NSDL National Science Digital Library

This chaos game applet features a game board with the Sierpinski triangle computed down to level 2 with nine smaller triangles. One smaller triangle appears green and is the target. The game requires the student to move a point found on the lower right corner of the Sierpinski triangle to the target's interior. Each move consists of clicking one vertex of the large triangle to move the point half the distance to that vertex. The goal is to get the point to the interior of the target in four moves. The student is challenged to find the algorithm for successfully moving the point to the target's interior in four moves. The applet keeps a record of moves and is playable in progressively harder modes and in several variations. Copyright 2005 Eisenhower National Clearinghouse

Johanna Voolich

2003-01-01

226

Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem through partial differential equations difficult. Here we present a simple approach for the activity in inhomogeneously stirred flows. We show that the fractal patterns serving as skeletons and catalysts lead to a rate equation with a universal form that is independent of the flow, of the particle properties, and of the details of the active process. One aspect of the universality of our approach is that it also applies to reactions among particles of finite size (so-called inertial particles). PMID:15003046

Tél, Tamás; Nishikawa, Takashi; Motter, Adilson E; Grebogi, Celso; Toroczkai, Zoltán

2004-03-01

227

Nonlinear waves: Structures and bifurcations

NASA Astrophysics Data System (ADS)

The papers contained in this volume focus on the problems of self-organization, dynamic chaos, and turbulence in relation to various physical applications. Papers are presented on the dynamics of structures in shear flows, two-dimensional vortices in an ideal liquid, interaction of systems with stochastic behavior, and spiral waves in distributed active media. Other topics discussed include solitons and chaos during resonance wave interaction, sound generation by turbulence, three-dimensional structures and nonlinear energy dissipation in strong plasma turbulence, and bifurcations and autowaves.

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

228

Role of chaos for the validity of statistical mechanics laws: diffusion and conduction

Several years after the pioneering work by Fermi Pasta and Ulam, fundamental questions about the link between dynamical and statistical properties remain still open in modern statistical mechanics. Particularly controversial is the role of deterministic chaos for the validity and consistency of statistical approaches. This contribution reexamines such a debated issue taking inspiration from the problem of diffusion and heat conduction in deterministic systems. Is microscopic chaos a necessary ingredient to observe such macroscopic phenomena?

Massimo Cencini; Fabio Cecconi; Massimo Falcioni; Angelo Vulpiani

2008-04-04

229

Photonic Josephson effect, phase transitions, and chaos in optomechanical systems

A photonic analog of the Josephson effect is analyzed for a system formed by a partly transparent mechanical membrane dividing an optical cavity into two halves. Photons tunneling between the two sub-cavities constitute the coherent Jospehson current. The force acting upon the membrane due to the light pressure induces a nonlinearity which results in a rich dynamical structure. For example, contrary to standard bosonic Josephson systems, we encounter chaos. By means of a mean-field approach we identify the various regimes and corresponding phase diagram. At the short time scale, chaos is demonstrated to prevent regular self-trapping, while for longer times a dissipation induced self-trapping effect is possible.

Jonas Larson; Mats Horsdal

2011-08-17

230

Photonic Josephson effect, phase transitions, and chaos in optomechanical systems

NASA Astrophysics Data System (ADS)

A photonic analog of the Josephson effect is analyzed for a system formed by a partly transparent mechanical membrane dividing an optical cavity into two halves. Photons tunneling between the two subcavities constitute the coherent Jospehson current. The force acting upon the membrane due to the light pressure induces a nonlinearity, which results in a rich dynamical structure. For example, contrary to standard bosonic Josephson systems, we encounter chaos. By means of a mean-field approach, we identify the various regimes and corresponding phase diagram. At the short time scale, chaos is demonstrated to prevent regular self-trapping, while for longer times a dissipation-induced self-trapping effect is possible.

Larson, Jonas; Horsdal, Mats

2011-08-01

231

n Scroll chaos generators: a simple circuit model

Introduction: The use of chaotic signals in communications has recently received a great deal of interest. An important part in chaos-based analog /digital communications systems [1] is the choice of the chaotic oscillator. Chua's circuit [2] is probably the most well-known and commonly used chaotic oscillator in this field. Among the many generalizations of Chua's circuit, more complicated attractors have been proposed by Suykens & Vandewalle [3] by introducing additional breakpoints in the nonlinearity of Chua's circuit, leading to so-called n-double scroll attractors. A more complete family of n-scroll instead of n-double scroll attractors has been obtained from a generalized Chua's circuit reported in [4]. Experimental confirmations of 2-double scroll and 5-scroll attractors have been given in [5] and [6], respectively. The same generalization idea has been applied to n-scroll hyperchaotic attractors proposed by Yalcin, Suykens & Vandewalle [7]. The design of chaos generators has r

Yaln Zo Guz; M. E. Yaln; S. Zo Guz; J. A. K. Suykens

232

Organizing Chaos Via Constructing Almost Invariant Surfaces Dr. Stuart Hudson and Prof. R.L. Dewar

Organizing Chaos Via Constructing Almost Invariant Surfaces Dr. Stuart Hudson and Prof. R.L. Dewar 1st Dewar Symposium on (Equilibrium, ) Stability and Nonlinear dynamics of plasmas, 31 October 2009 are a natural extension of flux surfaces, defined for chaotic fields Dewar & Meiss, Physica D, 57, 476 (1992

Hudson, Stuart

233

Physics 326 Lab 9 11/13/04 THE ONSET OF CHAOS

in a nonlinear RLC circuit and to explore with MatLab the approach to chaos demonstrated by the Logistic Equation Review Letters 47 1349 (1981) "Mathematical methods for Scientists and Engineers", Peter Kahn, Chapter 16 and smaller increases in Vo. You will rapidly find, that no matter how good your apparatus, you cannot control

Glashausser, Charles

234

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

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

Cvitanovc', Predrag

235

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

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

236

On the synchronization of a class of electronic circuits that exhibit chaos

The synchronization of two nonlinear electronic circuits that exhibit chaos is numerically demonstrated using techniques from modern control theory. These circuits have been used to model a “jerk” equation and can either be identical or not identical. The technique is initially described using linear circuits.

Er-Wei Bai; Karl E. Lonngren; J. C. Sprott

2002-01-01

237

NASA Technical Reports Server (NTRS)

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

Hodges, D. H.

1976-01-01

238

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

239

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

NASA Astrophysics Data System (ADS)

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

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

2014-05-01

240

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

Can Feedback Traders Rock the Markets? A Logistic Tale of Persistence and Chaos Demosthenes N. Tambakis? Pembroke College, Cambridge and CERF March 24, 2006 Abstract This paper introduces a nonlinear feedback trading model at high frequency. All... hypothesis (EMH), ex- pected returns should be zero regardless of the trading frequency. The main objective of this paper is to investigate the key premise of EMH in a nonlinear (logistic) feedback trading model with no stochastic uncertainty. There are two...

Tambakis, Demosthenes N

241

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

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

242

NASA Astrophysics Data System (ADS)

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

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

2014-10-01

243

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

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

2014-10-01

244

Magnetospheric Dynamics and Chaos Theory

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

G. P. Pavlos

2012-03-26

245

NSDL National Science Digital Library

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

Osmond, Andrew.

246

Clustering and Uncertainty in Perfect Chaos Systems

The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An anomalous transport turned out to be natural property of this equation. A nonlinear dispersion of the considered motion allowed to find a principal consequence: a chaotic system with uniform dynamic properties tends to unstable clustering. Small fluctuations of particles density increase by time and form attractors and stochastic islands even if the initial transport properties have uniform distribution. It was shown that an instability of phase trajectories leads to the nonlinear dispersion law and consequently to a space instability. A fixed boundary system was considered, using a standard Fokker-Planck equation. We have derived that such a type of dynamic systems has a discrete diffusive and energy spectra. It was shown that phase space diffusion is the only parameter that defines a dynamic accuracy in this case. The uncertainty relations have been obtained for conjugate phase space variables with account of transport properties. Given results can be used in the area of chaotic systems modelling and turbulence investigation.

Sergey A. Kamenshchikov

2014-07-27

247

The information geometry of chaos

NASA Astrophysics Data System (ADS)

In this Thesis, we propose a new theoretical information-geometric framework (IGAC, Information Geometrodynamical Approach to Chaos) suitable to characterize chaotic dynamical behavior of arbitrary complex systems. First, the problem being investigated is defined; its motivation and relevance are discussed. The basic tools of information physics and the relevant mathematical tools employed in this work are introduced. The basic aspects of Entropic Dynamics (ED) are reviewed. ED is an information-constrained dynamics developed by Ariel Caticha to investigate the possibility that laws of physics---either classical or quantum---may emerge as macroscopic manifestations of underlying microscopic statistical structures. ED is of primary importance in our IGAC. The notion of chaos in classical and quantum physics is introduced. Special focus is devoted to the conventional Riemannian geometrodynamical approach to chaos (Jacobi geometrodynamics) and to the Zurek-Paz quantum chaos criterion of linear entropy growth. After presenting this background material, we show that the ED formalism is not purely an abstract mathematical framework, but is indeed a general theoretical scheme from which conventional Newtonian dynamics is obtained as a special limiting case. The major elements of our IGAC and the novel notion of information geometrodynamical entropy (IGE) are introduced by studying two "toy models". To illustrate the potential power of our IGAC, one application is presented. An information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth is suggested. Finally, concluding remarks emphasizing strengths and weak points of our approach are presented and possible further research directions are addressed. At this stage of its development, IGAC remains an ambitious unifying information-geometric theoretical construct for the study of chaotic dynamics with several unsolved problems. However, based on our recent findings, we believe it already provides an interesting, innovative and potentially powerful way to study and understand the very important and challenging problems of classical and quantum chaos.

Cafaro, Carlo

2008-10-01

248

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

NASA Astrophysics Data System (ADS)

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

Ataei, Mohammad; Kiyoumarsi, Arash; Ghorbani, Behzad

2010-09-01

249

Deterministic chaos in government debt dynamics with mechanistic primary balance rules

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

Lindgren, Jussi Ilmari

2011-01-01

250

An ultrawideband spin-wave medium-power chaos generator based on field-effect transistors

NASA Astrophysics Data System (ADS)

A prototype of an ultrawideband (UWB) microwave chaos generator based on a nonlinear spin-wave transmission line, a multistage transistor amplifier with an output amplifier based on GaAs field-effect transistors, and a microstrip bandpass filter was constructed. The possibility of autonomous generation of a UWB chaotic microwave signal with a central frequency of 3 GHz and a total power of about 4 W in a frequency band exceeding 30% was demonstrated. The proposed chaos generator is characterized by a fairly high efficiency of about 20%.

Grishin, S. V.; Grishin, V. S.; Romanenko, D. V.; Sharaevskii, Yu. P.

2014-10-01

251

Deterministic chaos in government debt dynamics with mechanistic primary balance rules

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

Jussi Ilmari Lindgren

2011-09-05

252

Route to Chaos in Optomechanics

NASA Astrophysics Data System (ADS)

We establish the emergence of chaotic motion in optomechanical systems. Chaos appears at negative detuning for experimentally accessible values of the pump power and other system parameters. We describe the sequence of period-doubling bifurcations that leads to chaos and state the experimentally observable signatures in the optical spectrum. In addition to the semiclassical dynamics, we analyze the possibility of chaotic motion in the quantum regime. We find that quantum mechanics protects the optomechanical system against irregular dynamics, such that simple periodic orbits reappear and replace the classically chaotic motion. In this way observation of the dynamical signatures makes it possible to pin down the crossover from quantum to classical mechanics.

Bakemeier, L.; Alvermann, A.; Fehske, H.

2015-01-01

253

Hyperbolic Chaos of Turing Patterns

NASA Astrophysics Data System (ADS)

We consider time evolution of Turing patterns in an extended system governed by an equation of the Swift-Hohenberg type, where due to an external periodic parameter modulation longwave and shortwave patterns with length scales related as 1?3 emerge in succession. We show theoretically and demonstrate numerically that the spatial phases of the patterns, being observed stroboscopically, are governed by an expanding circle map, so that the corresponding chaos of Turing patterns is hyperbolic, associated with a strange attractor of the Smale-Williams solenoid type. This chaos is shown to be robust with respect to variations of parameters and boundary conditions.

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

2012-05-01

254

Bistability and chaos at low levels of quanta

NASA Astrophysics Data System (ADS)

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

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

2013-08-01

255

Kneadings, Symbolic Dynamics and Painting Lorenz Chaos. A Tutorial

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

Roberto Barrio; Andrey Shilnikov; Leonid Shilnikov

2012-04-15

256

Controlling chaos in a thin circular yttrium iron garnet film

NASA Astrophysics Data System (ADS)

Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)] proposed that the chaotic oscillations of nonlinear dynamic systems could be stabilized onto periodic orbits by introducing weak perturbations upon an available parameter of the system. In the present work, stabilization and control of chaos are demonstrated for the first time in an rf-pumped magnetostatic-resonance instability experiment on a thin circular yttrium iron garnet film, using open-loop and closed-loop feedback methods to modulate the static magnetic field. Computer simulations using a standard model have yielded qualitative agreement with the experimental results.

Ye, M.; Jones, D. E.; Wigen, P. E.

1993-05-01

257

Observing chaos for quantum-dot microlasers with external feedback.

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

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

2011-01-01

258

Urban chaos and replacement dynamics in nature and society

NASA Astrophysics Data System (ADS)

Replacements resulting from competition are ubiquitous phenomena in both nature and society. The evolution of a self-organized system is always a physical process substituting one type of components for another type of components. A logistic model of replacement dynamics has been proposed in terms of technical innovation and urbanization, but it fails to arouse widespread attention in the academia. This paper is devoted to laying the foundations of general replacement principle by using analogy and induction. The empirical base of this study is urban replacement, including urbanization and urban growth. The sigmoid functions can be employed to model various processes of replacement. Many mathematical methods such as allometric scaling and head/tail breaks can be applied to analyzing the processes and patterns of replacement. Among varied sigmoid functions, the logistic function is the basic and the simplest model of replacement dynamics. A new finding is that replacement can be associated with chaos in a nonlinear system, e.g., urban chaos is just a part of replacement dynamics. The aim of developing replacement theory is at understanding complex interaction and conversion. This theory provides a new way of looking at urbanization, technological innovation and diffusion, Volterra-Lotka’s predator-prey interaction, man-land relation, and dynastic changes resulting from peasant uprising, and all that. Especially, the periodic oscillations and chaos of replacement dynamics can be used to explain and predict the catastrophic occurrences in the physical and human systems.

Chen, Yanguang

2014-11-01

259

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

260

ChaosBook.org |||||||||||||||||||||-version

wrote in the introduction to the announcement of Kepler's third law, Harmonice Mundi (Linz, 1619; Appendix A A brief history of chaos Laws of attribution 1. Arnol'd's Law: everything that is discov- ered is named after someone else (including Arnol'd's law) 2. Berry's Law: sometimes, the sequence of an

Lopes, Artur Oscar

261

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.

262

NASA Technical Reports Server (NTRS)

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

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

2001-01-01

263

Chaos Rules! Robert L. Devaney

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

Devaney, Robert L.

264

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

NASA Astrophysics Data System (ADS)

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

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

2010-12-01

265

NASA Astrophysics Data System (ADS)

Based on the polarization-resolved chaos synchronization between twin 1550 nm vertical-cavity surface-emitting lasers (VCSELs), a novel long-haul dual-channel bidirectional chaos communication system is proposed. In this system, a time delay signature (TDS)-suppressed chaotic signal, generated by a driving VCSEL (D-VCSEL) under double external cavity feedbacks (DECFs), simultaneously injects into twin VCSELs by variable-polarization optical injection (VPOI) to synchronize them and enhance the chaos output bandwidth of the two VCSELs. The simulated results show that, under proper injection parameters, high-quality polarization-resolved chaos synchronization between the twin VCSELs can be achieved; meanwhile the bandwidths of chaotic signals output from the twin VCSELs have been enhanced in comparison with that of the driven chaotic signal. Based on the high-quality polarization-resolved chaos synchronization, after adopting polarization-division-multiplexing (PDM) and chaos masking (CM) techniques, four 10 Gb/s messages hidden respectively in four chaotic carriers can be decrypted effectively after propagating 15 km in single-mode fiber (SMF) links. After adopting dispersion-shifted fibers (DSFs) as fiber links, the dual-channel bidirectional chaos communication distance can be extended to 140 km.

Wang, Ling; Wu, Zheng-Mao; Wu, Jia-Gui; Xia, Guang-Qiong

2015-01-01

266

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

267

On the nonlinear properties analysis of multipath fading channel

In this paper, a nonlinear dynamical model for multipath fading channel is established on the basis of the study on the nonlinear dynamical properties of wireless mobile communication channel by using chaos and fractal theory. The phase space of the multipath fading time serials is reconstructed and the correlation dimension is analyzed, which indicate that the dynamical system has finite

Chong Fu; Fang-fang Zhang

2007-01-01

268

Nonlinear dynamics, fractals, cardiac physiology and sudden death

NASA Technical Reports Server (NTRS)

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

Goldberger, Ary L.

1987-01-01

269

NASA Astrophysics Data System (ADS)

Transient spatiotemporal chaos was reported in models for chemical reactions and in experiments for turbulence in shear flow. This study shows that transient spatiotemporal chaos also exists in a diffusively coupled Morris-Lecar (ML) neuronal network, with a collapse to either a global rest state or to a state of pulse propagation. Adding synaptic coupling to this network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strengths and almost all numbers of synapses. For large coupling strengths, close to the threshold of excitation, the average lifetime increases beyond the value for only diffusive coupling, and the collapse to the rest state dominates over the collapse to a traveling pulse state. The regime of spatiotemporal chaos is characterized by a slightly increasing Lyapunov exponent and degree of phase coherence as the number of synaptic links increases. In contrast to the diffusive network, the pulse solution must not be asymptotic in the presence of synapses. The fact that chaos could be transient in higher dimensional systems, such as the one being explored in this study, point to its presence in every day life. Transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provide a possibility for switching between metastable states observed in information processing and brain function. Such transient dynamics have been observed experimentally by Mazor, when stimulating projection neurons in the locust antennal lobe with different odors.

Lafranceschina, Jacopo

270

NASA Technical Reports Server (NTRS)

[figure removed for brevity, see original site]

The THEMIS VIS camera is capable of capturing color images of the Martian surface using five different color filters. In this mode of operation, the spatial resolution and coverage of the image must be reduced to accommodate the additional data volume produced from using multiple filters. To make a color image, three of the five filter images (each in grayscale) are selected. Each is contrast enhanced and then converted to a red, green, or blue intensity image. These three images are then combined to produce a full color, single image. Because the THEMIS color filters don't span the full range of colors seen by the human eye, a color THEMIS image does not represent true color. Also, because each single-filter image is contrast enhanced before inclusion in the three-color image, the apparent color variation of the scene is exaggerated. Nevertheless, the color variation that does appear is representative of some change in color, however subtle, in the actual scene. Note that the long edges of THEMIS color images typically contain color artifacts that do not represent surface variation.

This false color image is located in a different part of Aureum Chaos. Compare the surface textures with yesterday's image. This image was collected during the Southern Fall season.

Image information: VIS instrument. Latitude -4.1, Longitude 333.9 East (26.1 West). 35 meter/pixel resolution.

Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time.

NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

2005-01-01

271

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

272

Chaos Induced by Snap-back Repellers and Its Applications to Anti-control of Chaos

Chaos Induced by Snap-back Repellers and Its Applications to Anti-control of Chaos Yuming Shi Pei@pyu1.apmaths.uwo.ca Abstract Â This paper surveys some recent results about chaos induced by snap induced by snap-back re- pellers in finite and infinite dimensional dynamical sys- tems are introduced

Yu, Pei

273

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

274

Characteristic Spaces Emerging from Primitive Chaos

NASA Astrophysics Data System (ADS)

This paper describes the emergence of two characteristic notions, nondegenerate Peano continuum and Cantor set, by the exploration of the essence of the existence of primitive chaos from a topological viewpoint. The primitive chaos is closely related to vital problems in physics itself and leads to chaotic features under natural conditions. The nondegenerate Peano continuum represents an ordinarily observed space, and the existence of a single nondegenerate Peano continuum guarantees the existence of infinite varieties of the primitive chaos leading to the chaos. This result provides an explanation of the reason why we are surrounded by diverse chaotic behaviors. Also, the Cantor set is a general or universal notion different from the special set, the Cantor middle-third set, and the existence of a single Cantor set guarantees infinite varieties of the primitive chaos leading to the chaos. This analogy implies the potential of the Cantor set for the method of new recognizing physical phenomena.

Ogasawara, Yoshihito; Oishi, Shin'ichi

2014-01-01

275

Nonlinear dynamics in cardiac conduction

NASA Technical Reports Server (NTRS)

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

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

1988-01-01

276

Robust chaos in smooth unimodal maps

NASA Astrophysics Data System (ADS)

Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhood of the parameter space. It has been conjectured that robust chaos cannot occur in smooth systems [E. Barreto, B. Hunt, and C. Grebogi, Phys. Rev. Lett. 78, 4561 (1997); 80, 3049 (1998)]. Contrary to this conjecture, we describe a general procedure for generating robust chaos in smooth unimodal maps.

Andrecut, M.; Ali, M. K.

2001-08-01

277

Robust chaos in smooth unimodal maps.

Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhood of the parameter space. It has been conjectured that robust chaos cannot occur in smooth systems [E. Barreto, B. Hunt, and C. Grebogi, Phys. Rev. Lett. 78, 4561 (1997); 80, 3049 (1998)]. Contrary to this conjecture, we describe a general procedure for generating robust chaos in smooth unimodal maps. PMID:11497642

Andrecut, M; Ali, M K

2001-08-01

278

Subharmonics, Chaos, and Beyond

NASA Technical Reports Server (NTRS)

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

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

2011-01-01

279

The Dynamics of Deterministic Chaos in Numerical Weather Prediction Models

Atmospheric weather systems are coherent structures consisting of discrete cloud cells forming patterns of rows/streets, mesoscale clusters and spiral bands which maintain their identity for the duration of their appreciable life times in the turbulent shear flow of the planetary Atmospheric Boundary Layer. The existence of coherent structures (seemingly systematic motion) in turbulent flows has been well established during the last 20 years of research in turbulence. Numerical weather prediction models based on the inherently non-linear Navier-Stokes equations do not give realistic forecasts because of the following inherent limitations: (1) the non-linear governing equations for atmospheric flows do not have exact analytic solutions and being sensitive to initial conditions give chaotic solutions characteristic of deterministic chaos (2) the governing equations do not incorporate the dynamical interactions and co-existence of the complete spectrum of turbulent fluctuations which form an integral part of the large coherent weather systems (3) limitations of available computer capacity necessitates severe truncation of the governing equations, thereby generating errors of approximations (4) the computer precision related roundoff errors magnify the earlier mentioned uncertainties exponentially with time and the model predictions become unrealistic. The accurate modelling of weather phenomena therefore requires alternative concepts and computational techniques. In this paper a universal theory of deterministic chaos applicable to the formation of coherent weather structures in the ABL is presented.

A. Mary Selvam

2003-10-07

280

Polynomial Chaos Using Transformed Sparse Grids

NASA Astrophysics Data System (ADS)

The topic of general polynomial chaos has received significant attention in the last few years as a means to efficiently estimate model outcomes based on known stochastic processes. The method requires numerical integrations in order to evaluate the expectation integrals that are the coefficients of the stochastic polynomial. The key concern is that these numerical integrations are very time consuming when applied to demanding computational problems such as flow simulation. Therefore, methods which can perform this integration with a minimum number of integration points are highly desirable. An obvious choice is a sparse-grid method based on a 1D Gauss-quadrature rule, because this allows highly accurate integration rules to be designed for arbitrary PDFs in the expectation integral. Unfortunately, Gauss quadrature is a very poor choice for sparse-grid integration, because the corresponding integration rules are weakly nested, and thus do not allow reuse of integration points from one sparse-grid level to the next. Alternatively, Clenshaw-Curtis integration produces very strongly nested quadrature rules, but these are designed for uniform distributions and are inefficient for many PDFs, e.g., Gaussians. In this work, we present a nonlinear transformation of Fejer type 2 quadrature rules that realizes the benefits of having both a high degree of sparsity and being tailored to specific PDFs. We demonstrate that this method has the potential to integrate arbitrary functions in high stochastic dimensions (>8) with orders of magnitude fewer integration points than are required for similar Gauss-quadrature rules.

Tompkins, M. J.; Prange, M.

2011-12-01

281

Sedimentary Rocks of Aram Chaos

NASA Technical Reports Server (NTRS)

10 May 2004 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows outcroppings of light-toned, layered, sedimentary rock within Aram Chaos, an ancient, partly-filled impact crater located near 3.2oN, 19.9oW. This 1.5 meters (5 feet) per pixel picture is illuminated by sunlight from the left and covers an area about 3 km (1.9 mi) across.

2004-01-01

282

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.

283

Experimental techniques for exploiting chaos

NASA Astrophysics Data System (ADS)

We describe the implementation of the Ott-Grebogi-Yorke method of controlling chaos in a physical system. This method requires only small time dependent perturbations of one system parameter and does not demand the use of model equations to describe the dynamics of the system. One advantage of the OGY method is that, between these perturbations, the system remains on chaotic trajectories. One can thus use the sensitivity of the chaotic system to switch between different orbits at will.

Ditto, William L.; Spano, Mark L.

1993-01-01

284

Temperature chaos and quenched heterogeneities

NASA Astrophysics Data System (ADS)

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

Barucca, Paolo; Parisi, Giorgio; Rizzo, Tommaso

2014-03-01

285

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

286

Chaos in Geophysical Fluids I. General Introduction

NASA Astrophysics Data System (ADS)

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

Hide, Raymond

1994-09-01

287

Dynamic Equilibrium, Self-Organizing Systems, and Chaos Theory

NSDL National Science Digital Library

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

Enright, Rachel

288

NASA Astrophysics Data System (ADS)

We present an inverse modeling procedure for the estimation of model parameters of sedimentary basins subject to compaction driven by mechanical and geochemical processes. We consider a sandstone basin whose dynamics are governed by a set of unknown key quantities. These include geophysical and geochemical system attributes as well as pressure and temperature boundary conditions. We derive a reduced (or surrogate) model of the system behavior based on generalized Polynomial Chaos Expansion (gPCE) approximations, which are directly linked to the variance-based Sobol indices associated with the selected uncertain model parameters. Parameter estimation is then performed within a Maximum Likelihood (ML) framework. We then study the way the ML inversion procedure can benefit from the adoption of anisotropic polynomial approximations (a-gPCE) in which the surrogate model is refined only with respect to selected parameters according to an analysis of the nonlinearity of the input-output mapping, as quantified through the Sobol sensitivity indices. Results are illustrated for a one-dimensional setting involving quartz cementation and mechanical compaction in sandstones. The reliability of gPCE and a-gPCE approximations in the context of the inverse modeling framework is assessed. The effects of (a) the strategy employed to build the surrogate model, leading either to a gPCE or a-gPCE representation, and (b) the type and quality of calibration data on the goodness of the parameter estimates is then explored.

Porta, G.; Tamellini, L.; Lever, V.; Riva, M.

2014-12-01

289

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

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

290

Chaos in Bird Vocalizations A Senior Project submitted to

Chaos in Bird Vocalizations A Senior Project submitted to The Division of Science, Mathematics;Abstract Chaos is studied in terms of bird vocalizations. Zebra Finch song is analyzed for chaos using and are thus not chaotic. A model of the syrinx, the bird's sound production organ, is then analyzed for chaos

Landweber, Gregory D.

291

Short-term load forecasting with chaos time series analysis

This paper presents a new approach to short-term load forecasting in power systems. The proposed method makes use of chaos time series analysis that is based on deterministic chaos to capture characteristics of complicated load behaviour. Deterministic chaos allows us to reconstruct a time series and determine the number of input variables. This paper describes chaos time series analysis of

Hiroyuki Mori; Shouichi Urano

1996-01-01

292

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

NASA Astrophysics Data System (ADS)

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

Mackey, Peter Francis

1995-01-01

293

Blind Multi-User Detection of a Chaos-Based CDMA System Using Support Vector Machine

This paper presents the algorithms and the results of multi-user detectors (MUD) on a synchronous chaos-based code division multiple access system (CDMA), which uses chaotic sequences as the spreading codes. Popular linear and non-linear MUD algorithms such as the decorrelator detector, minimum mean square error (MMSE) detector and parallel interference cancellation (PIC) detector are all considered in this paper. These

Johnny W. H. Kao; Stevan M. Berber; Vojislav Kecman

2008-01-01

294

Chaos and rectification of electromagnetic wave in a lateral semiconductor superlattice

We find the conditions for a rectification of electromagnetic wave in a lateral semiconductor superlattice with a high mobility of electrons. The rectification is assisted by a transition to a dissipative chaos at a very high mobility. We show that mechanism responsible for the rectification is a creation of warm electrons in the superlattice miniband caused by an interplay of the effects of nonlinearity and finite band width.

Kirill N. Alekseev; Pekka Pietilainen; Alexander A. Zharov; Feodor V. Kusmartsev

2002-09-11

295

We demonstrate an optical transmission system based on a 53.5-Gb\\/s differential 6-ary phase-shift-keying (D6PSK) signal with copropagating 10.7-Gb\\/s nonreturn-to-zero (NRZ) on–off keying (OOK) channels over either 320-km-long single-mode fiber link with in-line dispersion compensation or 320-km-long dispersion-shifted fiber link, and compare its performances with that of a classical polarization-division-multiplexing differential quadrature phase-shift-keying (DQPSK)-based system. The results show that the nonlinear

Hyeon Yeong Choi; Itsuro Morita

2012-01-01

296

Transitions to chaos in squeeze-film dampers

NASA Astrophysics Data System (ADS)

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

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

2006-09-01

297

Monohydrated Sulfates in Aurorae Chaos

NASA Technical Reports Server (NTRS)

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

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

The top panel in the montage above shows the location of the CRISM image on a mosaic taken by the Mars Odyssey spacecraft's Thermal Emission Imaging System (THEMIS). The CRISM data covers an area featuring several knobs of erosion-resistant material at one end of what appears to be a large teardrop shaped plateau. Similar plateaus occur throughout the interior of Valles Marineris, and they are formed of younger, typically layered rocks that post-date formation of the canyon system. Many of the deposits contain sulfate-rich layers, hinting at ancient saltwater.

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

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

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

2008-01-01

298

Sedimentary Rocks of Aram Chaos

NASA Technical Reports Server (NTRS)

4 February 2004 Aram Chaos is a large meteor impact crater that was nearly filled with sediment. Over time, this sediment was hardened to form sedimentary rock. Today, much of the eastern half of the crater has exposures of light-toned sedimentary rock, such as the outcrops shown in this Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image. The picture is located near 2.0oN, 20.3oW, and covers an area 3 km (1.9 mi) wide. Sunlight illuminates the scene from the left.

2004-01-01

299

Decoherence, determinism and chaos revisited

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

Noyes, H.P.

1994-11-15

300

Quantum Chaos and Effective Thermalization

NASA Astrophysics Data System (ADS)

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

Altland, Alexander; Haake, Fritz

2012-02-01

301

Robust chaos in a model of the electroencephalogram: Implications for brain dynamics

NASA Astrophysics Data System (ADS)

Various techniques designed to extract nonlinear characteristics from experimental time series have provided no clear evidence as to whether the electroencephalogram (EEG) is chaotic. Compounding the lack of firm experimental evidence is the paucity of physiologically plausible theories of EEG that are capable of supporting nonlinear and chaotic dynamics. Here we provide evidence for the existence of chaotic dynamics in a neurophysiologically plausible continuum theory of electrocortical activity and show that the set of parameter values supporting chaos within parameter space has positive measure and exhibits fat fractal scaling.

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

2001-09-01

302

Titration of chaos with added noise

Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple “litmus test” for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems. PMID:11416195

Poon, Chi-Sang; Barahona, Mauricio

2001-01-01

303

Nonlinear lattice waves in heterogeneous media

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

304

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

NASA Astrophysics Data System (ADS)

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

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

2013-06-01

305

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

The occurrence of so-called four dimensional chaos in dynamical systems represented by coupled, nonlinear, ordinary differential equations is rarely reported in the literature. In this paper, we present evidence that Liley's mesoscopic theory of the electroencephalogram (EEG), which has been used to describe brain activity in a variety of clinically relevant contexts, possesses a chaotic attractor with a Kaplan-Yorke dimension significantly larger than three. This accounts for simple, high order chaos for a physiologically admissible parameter set. Whilst the Lyapunov spectrum of the attractor has only one positive exponent, the contracting dimensions are such that the integer part of the Kaplan-Yorke dimension is three, thus giving rise to four dimensional chaos. A one-parameter bifurcation analysis with respect to the parameter corresponding to extracortical input is conducted, with results indicating that the origin of chaos is due to an inverse period doubling cascade. Hence, in the vicinity of the high order, strange attractor, the model is shown to display intermittent behavior, with random alternations between oscillatory and chaotic regimes. This phenomenon represents a possible dynamical justification of some of the typical features of clinically established EEG traces, which can arise in the case of burst suppression in anesthesia and epileptic encephalopathies in early infancy. PMID:23822476

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

2013-06-01

306

Time and Chaos in General Relativity

The study of dynamics in general relativity has been hampered by a lack of coordinate independent measures of chaos. Here we present a variety of invariant measures for quantifying chaotic dynamics in relativity by exploiting the coordinate independence of fractal dimensions. We discuss how preferred choices of time naturally arise in chaotic systems and how the existence of invariant signals of chaos allow us to reinstate standard coordinate dependent measures. As an application, we study the Mixmaster universes and find it to exhibit transient soft chaos.

Neil J. Cornish

1996-02-27

307

Edge of chaos and genesis of turbulence

NASA Astrophysics Data System (ADS)

The edge of chaos is analyzed in a spatially extended system, modeled by the regularized long-wave equation, prior to the transition to permanent spatiotemporal chaos. In the presence of coexisting attractors, a chaotic saddle is born at the basin boundary due to a smooth-fractal metamorphosis. As a control parameter is varied, the chaotic transient evolves to well-developed transient turbulence via a cascade of fractal-fractal metamorphoses. The edge state responsible for the edge of chaos and the genesis of turbulence is an unstable traveling wave in the laboratory frame, corresponding to a saddle point lying at the basin boundary in the Fourier space.

Chian, Abraham C.-L.; Muñoz, Pablo R.; Rempel, Erico L.

2013-11-01

308

NASA Astrophysics Data System (ADS)

It has been reported that the minimal spatially extended phytoplankton-zooplankton system exhibits both temporal regular/chaotic behaviour, and spatiotemporal chaos in a patchy environment. As a further investigation by means of computer simulations and theoretical analysis, in this paper we observe that the spiral waves may exist and the spatiotemporal chaos emerge when the parameters are within the mixed Turing-Hopf bifurcation region, which arises from the far-field breakup of the spiral waves over a large range of diffusion coefficients of phytoplankton and zooplankton. Moreover, the spatiotemporal chaos arising from the far-field breakup of spiral waves does not gradually invade the whole space of that region. Our results are confirmed by nonlinear bifurcation of wave trains. We also discuss ecological implications of these spatially structured patterns.

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

2009-02-01

309

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

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

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

2011-04-15

310

Chaos Control in the Wake of an Oscillating Cylinder

NASA Astrophysics Data System (ADS)

The nonlinear dynamics of vortex shedding behind circular cylinders are investigated using a previously developed spatial-temporal map lattice. The map studied consists of a series of circle map oscillators placed along the cylinder span coupled with a simple diffusion model. Chaotic states associated with disordered vortex shedding patterns are observed when forcing the cylinder outside the classical lock-on region. These are controlled through application of a small-amplitude periodic perturbation of a system parameter, as proposed by Ott, Grebogi, and Yorke. Periodic lace-like structures and parallel shedding patterns are realized by driving the chaotic system to the desired target state. A wide range of forcing frequency-amplitude combinations are studied along with manipulation of vortex lock-on region extents. Preliminary extensions of these chaos control techniques to a two-dimensional wake flow using finite element techniques are also discussed.

Balasubramanian, Ganapathi R.; Olinger, David J.

1997-11-01

311

Periodic-orbit theory of universality in quantum chaos

NASA Astrophysics Data System (ADS)

We argue semiclassically, on the basis of Gutzwiller’s periodic-orbit theory, that full classical chaos is paralleled by quantum energy spectra with universal spectral statistics, in agreement with random-matrix theory. For dynamics from all three Wigner-Dyson symmetry classes, we calculate the small-time spectral form factor K(?) as power series in the time ? . Each term ?n of that series is provided by specific families of pairs of periodic orbits. The contributing pairs are classified in terms of close self-encounters in phase space. The frequency of occurrence of self-encounters is calculated by invoking ergodicity. Combinatorial rules for building pairs involve nontrivial properties of permutations. We show our series to be equivalent to perturbative implementations of the nonlinear ? models for the Wigner-Dyson ensembles of random matrices and for disordered systems; our families of orbit pairs have a one-to-one relationship with Feynman diagrams known from the ? model.

Müller, Sebastian; Heusler, Stefan; Braun, Petr; Haake, Fritz; Altland, Alexander

2005-10-01

312

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

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

Resnicow, Kenneth; Page, Scott E

2008-08-01

313

Relation of Origins of Primitive Chaos

A new concept, primitive chaos, was proposed, as a concept closely related to the fundamental problems of sciences themselves such as determinism, causality, free will, predictability, and time asymmetry [{\\em J. Phys. Soc. Jpn.} {\\bf 2014}, {\\em 83}, 1401]. This concept is literally a primitive chaos in such a sense that it leads to the characteristic properties of the conventional chaos under natural conditions. Then, two contrast concepts, nondegenerate Peano continuum and Cantor set, are known as the origins of the primitive chaos. In this study, the relation of these origins is investigated with the aid of a mathematical method, topology. Then, we can see the emergence of interesting concepts such as the relation of whole and part, and coarse graining, which imply the essence of our intrinsic recognition for phenomena.

Yoshihito Ogasawara

2014-10-29

314

Order and chaos : articulating support, housing transformation

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

Boehm, William Hollister

1990-01-01

315

The control of chaos: theory and applications

NASA Astrophysics Data System (ADS)

Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott-Grebogi-Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos control, such as the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions, and point out applications for controlling fractal basin boundaries. In short, we describe procedures for stabilizing desired chaotic orbits embedded in a chaotic attractor and discuss the issues of communicating with chaos by controlling symbolic sequences and of synchronizing chaotic systems. Finally, we give a review of relevant experimental applications of these ideas and techniques.

Boccaletti, S.; Grebogi, C.; Lai, Y.-C.; Mancini, H.; Maza, D.

2000-05-01

316

Wave chaos in rapidly rotating stars

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

F. Lignieres; B. Georgeot

2008-05-12

317

NASA Astrophysics Data System (ADS)

In the celebratory dinner honouring Celso Grebogi's 60th birthday, a number of scientists in the area of chaos were asked by James Yorke to tell the tale about how they got involved in the field. Since all the participants have played crucial roles in the development of the subject, their stories give unique insights into the historical development of dynamical systems and chaos. We have transcribed their tales here.

Thiel, Marco; Kurths, Jürgen; Romano, M. Carmen; Moura, Alessandro; Károlyi, György

318

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

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

Kot, M.

1990-07-01

319

Time-Reversal Invariance and the Relation between Wave Chaos and Classical Chaos

Time-Reversal Invariance and the Relation between Wave Chaos and Classical Chaos Roel Snieder for imaging are invariant for time reversal. The physical reason for this is that in imaging one propagates the recorded waves backward in time to the place and time when the waves interacted with the medium

Snieder, Roel

320

NASA Technical Reports Server (NTRS)

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

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

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

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

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

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

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

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

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

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

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

2008-01-01

321

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

322

Transient chaos in optical metamaterials.

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. PMID:21974651

Ni, Xuan; Lai, Ying-Cheng

2011-09-01

323

Control of collective network chaos.

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

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

2014-06-01

324

General method of controlling chaos

NASA Astrophysics Data System (ADS)

We present a mathematical framework for describing the allowable forms of perturbations of a control parameter for the purpose of controlling chaos. The present paper extends the method initially proposed by Ott, Grebogi, and Yorke [Phys. Rev. Lett. 64, 1196 (1990)] and later extended by Romeiras et al. [Physica D 58, 165 (1992)], allowing for a more general choice of feedback forms. Among the allowable feedback forms, those that do not include the coordinates of the desired control object explicitly provide a natural way to go about tracking, especially when the parameter changes are involuntary. Another benefit of the method is that the control can be implemented by the use of earlier states of the system as the feedback information. The generalized method can be conveniently used to deal with an experimental system in the absence of an a priori mathematical system model where the delay coordinates are used. These are illustrated by numerical examples in the paper.

Zhao Hong; Yan Jie; Wang Jiao; Wang Yinghai

1996-01-01

325

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

326

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

327

Control mechanisms for a nonlinear model of international relations

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

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

1997-07-15

328

Topological horseshoes in travelling waves of discretized nonlinear wave equations

Applying the concept of anti-integrable limit to coupled map lattices originated from space-time discretized nonlinear wave equations, we show that there exist topological horseshoes in the phase space formed by the initial states of travelling wave solutions. In particular, the coupled map lattices display spatio-temporal chaos on the horseshoes.

Chen, Yi-Chiuan, E-mail: YCChen@math.sinica.edu.tw [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China)] [Institute of Mathematics, Academia Sinica, Taipei 10617, Taiwan (China); Chen, Shyan-Shiou, E-mail: sschen@ntnu.edu.tw [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China)] [Department of Mathematics, National Taiwan Normal University, Taipei 11677, Taiwan (China); Yuan, Juan-Ming, E-mail: jmyuan@pu.edu.tw [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)] [Department of Financial and Computational Mathematics, Providence University, Shalu, Taichung 43301, Taiwan (China)

2014-04-15

329

Apply modified projective synchronization to nonlinear vibration isolation system

One method was proposed which realize the modified projective synchronization between two degree nonlinear vibration isolation system and four dimension chaos system based on active control, in order to solve the conflict between the linear spectra reduction based on chaotifiy vibration responses and the capability of vibration isolation. The effectiveness of the proposed scheme was validated by the numerical simulation,

Zhang Xing; Zhu Shijian; Zeng Qianghong

2010-01-01

330

Edge of chaos as critical local symmetry breaking in dissipative nonautonomous systems

The fully nonlinear notion of resonance -$\\textit{geometrical resonance}$- in the general context of dissipative systems subjected to $\\textit{nonsteady}$ potentials is discussed. It is demonstrated that there is an exact local invariant associated with each geometrical resonance solution which reduces to the system's energy when the potential is steady. The geometrical resonance solutions represent a \\textit{local symmetry} whose critical breaking leads to a new analytical criterion for the order-chaos threshold. This physical criterion is deduced in the co-moving frame from the local energy conservation over the shortest significant timescale. Remarkably, the new criterion for the onset of chaos is shown to be valid over large regions of parameter space, thus being useful beyond the perturbative regime and the scope of current mathematical techniques.

Ricardo Chacón

2015-04-08

331

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

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

2012-09-01

332

Controlling Chaos Via Knowledge of Initial Condition for a Curved Structure

NASA Technical Reports Server (NTRS)

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

Maestrello, L.

2000-01-01

333

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

NASA Technical Reports Server (NTRS)

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

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

1992-01-01

334

Determinisme, Chaos en Toeval Instituut voor Wiskunde en Informatica

deterministisch systeem stabiel en voorspelbaar? Chaos p.3 #12;Leibniz en Voltaire Gottfried Wilhelm Leibniz Groningen Chaos p.1 #12;Helden - Newton en Laplace - Leibniz en Voltaire - Poincaré en Kolmogorov - Lorenz

Broer, H.W.

335

Chaos and Order in Weakly Coupled Systems of Nonlinear Oscillators

NASA Astrophysics Data System (ADS)

We consider in this paper perturbations of two degree of freedom Hamiltonian systems which contain periodic and heteroclinic orbits. The Melnikov-Keener condition is used to proof the existence of horseshoes in the dynamics. The same condition is applied to prove a high degree of order in the motion of the swinging Atwood's machine. For some selected parameter values the theoretical predictions are checked by numerical calculations.

Bruhn, B.

1987-01-01

336

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

, West Virginia UniVersity, Morgantown, West Virginia 26506-6045 ReceiVed: NoVember 30, 1995; In Final. I. Introduction If one were to show a freshman chemistry class two beakers of solution and suggest

Showalter, Kenneth

337

Nonlinear Oscillations and Chaos in Chemical Cardiorespiratory Control

We report progress made on an analytic investigation of low-frequency cardiorespiratory variability in humans. The work is based on an existing physiological model of chemically-mediated blood-gas control via the central and peripheral chemoreceptors, that of Grodins, Buell & Bart (1967). Scaling and simplification of the Grodins model yields a rich variety of dynamical subsets; the thesis focusses on the dynamics obtained under the normoxic assumption (i.e., when oxygen is decoupled from the system). In general, the method of asymptotic reduction yields submodels that validate or invalidate numerous (and more heuristic) extant efforts in the literature. Some of the physiologically-relevant behaviour obtained here has therefore been reported before, but a large number of features are reported for the first time. A particular novelty is the explicit demonstration of cardiorespiratory coupling via chemosensory control. The physiology and literature reviewed in Chapters 1 and 2 set the stage for the investigation. Chapter 3 scales and simplifies the Grodins model; Chapters 4, 5, 6 consider carbon dioxide dynamics at the central chemoreceptor. Chapter 7 begins analysis

Giridhar Padmanabhan Kalamangalam

1995-01-01

338

Lagrangian chaos in an ABC-forced nonlinear dynamo

NASA Astrophysics Data System (ADS)

The Lagrangian properties of the velocity field in a magnetized fluid are studied using three-dimensional simulations of a helical magnetohydrodynamic dynamo. We compute the attracting and repelling Lagrangian coherent structures (LCS), which are dynamic lines and surfaces in the velocity field that delineate particle transport in flows with chaotic streamlines and act as transport barriers. Two dynamo regimes are explored, one with a robust coherent mean magnetic field and the other with intermittent bursts of magnetic energy. The LCS and the statistics of the finite-time Lyapunov exponents indicate that the stirring/mixing properties of the velocity field decay as a linear function of magnetic energy. The relevance of this study to the solar dynamo problem is also discussed.

Rempel, Erico L.; C-L Chian, Abraham; Brandenburg, Axel

2012-07-01

339

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

Boyer, Edmond

340

Broad spectrum period adding chaos in a transistor circuit

Period adding chaos, in which a driven system makes transitions such as period 2-chaos-period 3-chaos-period 4, is well known. In most cases, however, the frequency of the chaotic signal is close to the frequencies of the periodic signals. I have done expriments with a simple circuit in which the chaos has a very broad power spectrum, covering 6 orders of

Thomas Carroll

2006-01-01

341

An image blocks encryption algorithm based on spatiotemporal chaos

In this paper, the CML-based spatiotemporal chaos system is used for image blocks encryption, which gets higher security.\\u000a The basic idea is to divide the image into blocks, and then use the block numbers as the spatial parameter of CML to iterate\\u000a the chaos system. Each lattice generates a chaos sequence, and the number of chaos sequence values is equal

Xingyuan Wang; Lin Teng

342

Book Reviews Chaos and Coarse Graining in Statistical Mechanics.

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

Boehning, Dankmar

343

Chaos of the logistic equation with piecewise constant argument

We consider the logistic equation with different types of the piecewise constant argument. It is proved that the equation generates chaos and intermittency. Li-Yorke chaos is obtained as well as the chaos through period-doubling route. Basic plots are presented to show the complexity of the behavior.

Marat Akhmet; Derya Altintan; Tanil Ergenc

2010-06-24

344

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

345

A lowmemory parallel version of Matsuo, Chao and Tsujii's algorithm

A lowÂmemory parallel version of Matsuo, Chao and Tsujii's algorithm Pierrick Gaudry 1 and â?? Eric to the algorithm of Matsuo, Chao and Tsujii. This algorithm computes the group order of the JaÂ cobian of a genus 2, the time necessary to compute the Jacobian order varies like 1/ # m. In 2002, Matsuo, Chao and Tsujii [14

Gaudry, Pierrick

346

Change in Chaos: Seven Lessons Learned from Katrina

nderstanding change is a lifetime's work. And for most of us, its intricacies remain elusive. One way to try to understand change is through the lens of chaos. What happens in chaos, and after chaos when changes are sincerely sought? What can we learn about future efforts at change based on the chaotic events of the past? And what, if

Alison A. Carr-Chellman; Brian Beabout; Khaled A. Alkandari; Luis C. Almeida; Husra T. Gursoy; Ziyan Ma; Rucha S. Modak; Raymond S. Pastore

347

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

348

Nonlinear analysis and prediction of pulsatile hormone secretion

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

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

1996-06-01

349

The Capabilities of Chaos and Complexity

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

Abel, David L.

2009-01-01

350

Nonlinear Dynamics of a Diffusing Interface

NASA Technical Reports Server (NTRS)

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

Duval, Walter M. B.

2001-01-01

351

Order, chaos and nuclear dynamics

NASA Astrophysics Data System (ADS)

The relation between the order-to-chaos transition in the dynamics of independent classical particles in a container, and the transition from an elastic to a dissipative response of the container to shape changes, is studied by means of computer simulations. The validity of the wall formula for energy dissipation is confirmed in the case of containers whose surfaces are rippled according to Legendre polynomials P3, P4, P5, P6, in which case the particle trajectories are largely chaotic, as revealed by Poincaré sections in phase space. The opposite limit of an elastic response is illustrated by means of spheroidal containers of various eccentricities, for which the particle trajectories are integrable and the phase space is foliated by tori. Fission-like deformations are also considered, for which the response of the container changes from elastic to dissipative with increasing deformation. Idealized giant-dipole oscillations of the gas are studied for spherical as well as deformed containers. A generalization of the wall formula valid for long times (i.e., for arbitrarily large excitations of the gas) is constructed. The principal lesson of these studies is that a gas of independent particles in a time-dependent container does not behave at all like a gas.

Blocki, J.; Shi, J.-J.; Swiatecki, W. J.

1993-03-01

352

Chaos Lab: An Orderly Pursuit of Disorder

NSDL National Science Digital Library

Chaos Lab is a great piece of software that teaches users about fractals and chaos theory. The menu-driven interface is extremely easy to use; however, a significant drawback of the software is its poor documentation. This can make experimenting with the settings more fun, but it would be helpful to have better explanations of the more obscure functions. What Chaos Lab lacks in documentation, it makes up for in the remarkable visual representations of famous fractals. The Mandelbrot and Julia sets can be explored with simple zooming tools, equation definitions, and brilliant color selections. Many more options are available, making the program a powerful educational tool in a small package. It is a free download.

1969-12-31

353

Towards CHAOS-5 - How can Swarm contribute?

NASA Astrophysics Data System (ADS)

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

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

2014-05-01

354

Controlling chaos in semiconductor laser devices

NASA Astrophysics Data System (ADS)

In most encounters, chaos is considered a nuisance, if not a down right detriment to system performance, especially in laser devices. However, the presence of chaos in a system can act as a rich source of complex frequencies if one only had a way of accessing them. In this work we present a discussion of the recent work of Ott, Grebogi and Yorke on controlling chaos as applied to a semiconductor diode laser subject to optical feedback via an external mirror. In the regime in which the laser is chaotic, stabilization can be achieved by sampling the output intensity and feeding back minuscule amounts of a correcting signal on the pumping current at the appropriate time interval. We present the results of our numerical investigations.

Gavrielides, Athanasios; Kovanis, Vassilios; Alsing, Paul M.

1993-12-01

355

Prospects for chaos control of machine tool chatter

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

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

1998-06-01

356

Topological approximation of the nonlinear Anderson model

NASA Astrophysics Data System (ADS)

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

Milovanov, Alexander V.; Iomin, Alexander

2014-06-01

357

The uncertainty principle and quantum chaos

NASA Technical Reports Server (NTRS)

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

Chirikov, Boris V.

1993-01-01

358

Wave chaos in rapidly rotating stars.

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

2008-07-01

359

Relaxation of isolated quantum systems beyond chaos

In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is -- to say the least -- fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many body quantum systems that can be parametrically tuned from regular to chaotic. We show that a universal relation between relaxation and delocalization of the initial state in the perturbed basis can be established regardless of the chaotic nature of system.

Ignacio García-Mata; Augusto J. Roncaglia; Diego A. Wisniacki

2015-01-23

360

Robust chaos generation by a perceptron

The properties of time series generated by a perceptron with monotonic and non-monotonic transfer function, where the next input vector is determined from past output values, are examined. Analysis of the parameter space reveals the following main finding: a perceptron with a monotonic function can produce fragile chaos only whereas a non-monotonic function can generate robust chaos as well. For non-monotonic functions, the dimension of the attractor can be controlled monotonically by tuning a natural parameter in the model.

A. Priel; I. Kanter

2000-07-05

361

Relaxation of isolated quantum systems beyond chaos.

In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is-to say the least-fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many-body quantum systems that can be parametrically tuned from regular to chaotic. We show that a universal relation between relaxation and delocalization of the initial state in the perturbed basis can be established regardless of the chaotic nature of system. PMID:25679559

García-Mata, Ignacio; Roncaglia, Augusto J; Wisniacki, Diego A

2015-01-01

362

Relaxation of isolated quantum systems beyond chaos

NASA Astrophysics Data System (ADS)

In classical statistical mechanics there is a clear correlation between relaxation to equilibrium and chaos. In contrast, for isolated quantum systems this relation is—to say the least—fuzzy. In this work we try to unveil the intricate relation between the relaxation process and the transition from integrability to chaos. We study the approach to equilibrium in two different many-body quantum systems that can be parametrically tuned from regular to chaotic. We show that a universal relation between relaxation and delocalization of the initial state in the perturbed basis can be established regardless of the chaotic nature of system.

García-Mata, Ignacio; Roncaglia, Augusto J.; Wisniacki, Diego A.

2015-01-01

363

Controlling chaos in the Pierce diode

NASA Astrophysics Data System (ADS)

The chaotic state of the classical Pierce diode is studied using a particle-in-cell computer simulation. The dynamics of the chaotic state is analyzed by estimating ergodic measures of the reconstructed attractor that refine and extend previously reported results [Matsumoto et al., Phys. Plasmas 3 (1996) 177]. The chaos control algorithm suggested by Ott, Grebogi, and Yorke is systematically applied to stabilize periodic orbits up to periodicity four. This demonstrates successful chaos control in a plasma, i.e., a many particle system with long range collective Coulomb interaction.

Krahnstöver, N.; Klinger, T.; Greiner, F.; Piel, A.

1998-02-01

364

Exploring Chaos: A Case Study.

ERIC Educational Resources Information Center

Describes software, hardware, and devices that were designed to provide students with an environment to experiment with basic ideas of mechanics, including nonlinear dynamics. Examines the behavior of a Lorenzian water wheel by comparing experimental data with theoretical results obtained from computer-based sensors. (MDH)

Nemirovsky, Ricardo; Tinker, Robert

1993-01-01

365

Chaos and complexity in astrophysics

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

Oded Regev

2007-05-16

366

From Ikeda ring cavity to optoelectronic setups dedicated to chaos-based secure communications

NASA Astrophysics Data System (ADS)

Nonlinear delayed dynamics was first proposed in Optics by Kensuke Ikeda in 1979. Since then, many different setups based on similar dynamical principles were carried out experimentally, first to explore the numerous and various behaviours, and then to use the high complexity chaotic regimes for optical data encryption. After a brief review of the different setups and principles, we will report on 4 different optoelectronics realizations developed in our group, emphasizing on the characteric properties of each setup, and their implementation in chaos--based secure communication systems.

Larger, Laurent; Goedgebuer, Jean-Pierre; Udaltsov, Vladimir; Lee, Min Won; Genin, Eric; Gastaud, Nicolas

2004-09-01

367

Transition to chaos of a vertical collapsible tube conveying air flow

NASA Astrophysics Data System (ADS)

"Sky dancers", the large collapsible tubes used as advertising, are studied in this work through a simple experimental device. Our study is devoted to the nonlinear dynamics of this system and to its transition to chaos. Firstly, we have shown that after a collapse occurs, the air fills the tube at a different speed rate from the flow velocity. Secondly, the temporal intermittency is studied as the flow rate is increased. A statistical analysis shows that the chaotic times maintain roughly the same value by increasing air speed. On the other hand, laminar times become shorter, until the system reaches a completely chaotic state.

Castillo Flores, F.; Cros, A.

2009-05-01

368

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

369

Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation

NASA Astrophysics Data System (ADS)

The motion of a randomly driven quantum nonlinear pendulum is considered. Utilizing a one-step Poincaré map, we demonstrate that the classical phase space corresponding to a single realization of the random perturbation can involve domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study the influence of finite-time stability on quantum dynamics. It is shown that domains of finite-time stability give rise to ordered patterns in distributions of FTEO eigenfunctions. The transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.

Makarov, D. V.; Kon’kov, L. E.

2015-03-01

370

Electronic circuits manifesting hyperbolic chaos and their simulation with software package Multisim

We consider several electronic circuits, which represent dynamical systems with hyperbolic chaotic attractors of Smale-Williams type, and demonstrate results of their simulation using the software package NI Multisim 10. The developed approach is useful as an intermediate step of constructing real electronic devices manifesting structurally stable hyperbolic chaos applicable e.g. in systems of secure communication, noise radar, for cryptographic systems and random number generators. This is also of methodological interest for training students who specialize in radio-physics and nonlinear dynamics in the design and analysis of systems with complex dynamics using examples close to practical applications.

Sergey P. Kuznetsov

2011-11-24

371

Order-Chaos-Order Transitions in Electrosprays: The Electrified Dripping Faucet

NASA Astrophysics Data System (ADS)

Electrosprays have diverse applications including protein analysis, electrospinning, and nanoencapsulation for drug delivery. We show that a variety of electrospray regimes exhibit fundamental analogy with the nonlinear dynamics of a dripping faucet. The applied voltage in electrosprays results in additional period doublings and temporal order-chaos-order transitions. Attractors in the return maps show logarithmic self-similarity in time, suggesting self-similar capillary waves on the meniscus. The bifurcations in ejection time can be explained by phase variations between capillary waves and pinch-off conditions and by ejection mode changes due to contact angle variations.

Marginean, Ioan; Nemes, Peter; Vertes, Akos

2006-08-01

372

Order-to-chaos transition in the model of a quantum pendulum subjected to noisy perturbation

Motion of randomly-driven quantum nonlinear pendulum is considered. Utilizing one-step Poincar\\'e map, we demonstrate that classical phase space corresponding to a single realization of the random perturbation involves domains of finite-time stability. Statistical analysis of the finite-time evolution operator (FTEO) is carried out in order to study influence of finite-time stability on quantum dynamics. It is shown that domains of finite-time stability give rise to ordered patterns in distributions of FTEO eigenfunctions. Transition to global chaos is accompanied by smearing of these patterns; however, some of their traces survive on relatively long timescales.

Denis Makarov; Leonid Kon'kov

2015-02-06

373

We examine the Melnikov criterion for a global homoclinic bifurcation and a possible transition to chaos in case of a single degree of freedom nonlinear oscillator with a symmetric double well nonlinear potential. The system was subjected simultaneously to parametric periodic forcing and self excitation via negative damping term. Detailed numerical studies confirm the analytical predictions and show that transitions from regular to chaotic types of motion are often associated with increasing the energy of an oscillator and its escape from a single well.

Grzegorz Litak; Marek Borowiec; Arkadiusz Syta; Kazimierz Szabelski

2006-01-14

374

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

375

Traveling wave solutions of the nonlinear acoustic wave equation are obtained for the fundamental and second harmonic resonances of a fluid-filled cavity. The solutions lead to the development of a non-autonomous toy model for cavity oscillations. Application of the Melnikov method to the model equation predicts homoclinic bifurcation of the Smale horseshoe type leading to a cascade of period doublings with increasing drive displacement amplitude culminating in chaos. The threshold value of the drive displacement amplitude at tangency is obtained in terms of the acoustic drive frequency and fluid attenuation coefficient. The model prediction of subharmonic generation leading to chaos is validated from acousto-optic diffraction measurements in a water-filled cavity using a 5?MHz acoustic drive frequency and from the measured frequency spectrum in the bifurcation cascade regime. The calculated resonant threshold amplitude of 0.2?nm for tangency is consistent with values estimated for the experimental set-up. Experimental evidence for the appearance of a stable subharmonic beyond chaos is reported. PMID:25725651

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

2015-02-01

376

NASA Astrophysics Data System (ADS)

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

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

2015-02-01

377

Nonlinear problems in flight dynamics

NASA Technical Reports Server (NTRS)

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

Chapman, G. T.; Tobak, M.

1984-01-01

378

Automotive 2020 Clarity beyond the chaos

Automotive 2020 Clarity beyond the chaos Automotive IBM Institute for Business Value IBM Global@us.ibm.com for more information. #12;1 The automotive ecosystem is in the midst of significant change, with increasing for information, environmental responsibility and safety. Automotive companies are racing to develop new business

379

H. Jonathan Chao ECE Dept Head

wireless and high-speed networks) Â· Computer engineering (medical implant devices, multiprocessors on chip Implant Device (Artan, Chao) Â· Implant devices with brain-computer interface for epilepsy and other Battery Charger Microcontroller 16 Implant Circuits Developed at NYU-Poly Test setup

Aronov, Boris

380

Chaos-based cryptography: a brief overview

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

Ljupco Kocarev

2001-01-01

381

Dimensie en Dispersie het `meten' van chaos

. . . Een manier om dit te begrijpen gaat als volgt. Neem eenheidsinterval [0, 1] Hoeveel intervalletjes ter III De Sierpinski driehoek Sp. Neem zijde van lengte 1. Overdekking met driehoekjes met zijde Direct (1857-1918) (1941-) Chaos Â p.11 #12;Dispersie exponent I Neem de Bakkers transformatie B : x [0, 1] 2

Broer, H.W.

382

Chaos, Collaboration, and Curriculum: A Deliberative Process.

ERIC Educational Resources Information Center

Presents curriculum as a complex social process. Explores chaos theory as a metaphor for understanding curriculum and a framework for viewing the curriculum-development process. Provides examples of collaborative leadership (described by David Chrislip and Carl Larson) and shows how they might answer Joseph Schwab's call for a deliberative…

Goff, Katherine E.

1998-01-01

383

Tachyons, Quanta and Chaos Mark Davidson

1 Tachyons, Quanta and Chaos By Mark Davidson February 15, 2001 Spectel Research Corporation 807 that classical charged tachyons have several features normally thought to be unique to quantum mechanics. Spin-like self-orbiting helical motions are shown to exist at discrete values for the velocity of the tachyon

384

Chaos theory, informational needs, and natural disasters

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

385

Chaos in three species food chains

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

386

How to Generate Chaos at Home.

ERIC Educational Resources Information Center

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

Smith, Douglas

1992-01-01

387

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.

David Paddy

2005-01-01

388

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

389

Chaos in a computer-animated pendulum

NASA Astrophysics Data System (ADS)

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

Kautz, R. L.

1993-05-01

390

Order, chaos and nuclear dynamics: An introduction

This is an introductory lecture illustrating by simple examples the anticipated effect on collective nuclear dynamics of a transition from order to chaos in the motions of nucleons inside an idealized nucleus. The destruction of order is paralleled by a transition from a rubber-like to a honey-like behaviour of the independent-particle nuclear model. 10 refs., 6 figs.

Swiatecki, W.J.

1990-08-01

391

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

392

The Chemical Imaging Initiative Dr. Chao Yang

Berkeley National Laboratory "Computational Approaches to Largescale Xray Image Electron Analysis The Chemical Imaging Initiative Presents Dr. Chao Yang Computational Research Division Lawrence" May 20, 2011 EMSL 1077 11:00 am The latest advances in Xray and electron light source

393

Chaos Based Secure IP Communications over Satellite DVB

NASA Astrophysics Data System (ADS)

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

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

2010-06-01

394

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

Arzeno, Natalia M. (Natalia María Arzeno Soltero)

2007-01-01

395

A novel 2D wavelength-time chaos code in optical CDMA system

NASA Astrophysics Data System (ADS)

Two-dimensional wavelength-time chaos code is proposed and constructed for a synchronous optical code division multiple access system. The access performance is compared between one-dimensional chaos code, WDM/chaos code and the proposed code. Comparison shows that two-dimensional wavelength-time chaos code possesses larger capacity, better spectral efficiency and bit-error ratio than WDM/chaos combinations and one-dimensional chaos code.

Zhang, Qi; Xin, Xiangjun; Wang, Yongjun; Zhang, Lijia; Yu, Chongxiu; Meng, Nan; Wang, Houtian

2012-11-01

396

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

397

Nonlinear Lattice Waves in Random Potentials

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transition, quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field. We will discuss recent advances in the dynamics of nonlinear lattice waves in random potentials. In the absence of nonlinear terms in the wave equations, Anderson localization is leading to a halt of wave packet spreading. Nonlinearity couples localized eigenstates and, potentially, enables spreading and destruction of Anderson localization due to nonintegrability, chaos and decoherence. The spreading process is characterized by universal subdiffusive laws due to nonlinear diffusion. We review extensive computational studies for one- and two-dimensional systems with tunable nonlinearity power. We also briefly discuss extensions to other cases where the linear wave equation features localization: Aubry-Andre localization with quasiperiodic potentials, Wannier-Stark localization with dc fields, and dynamical localization in momentum space with kicked rotors.

Sergej Flach

2014-09-10

398

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

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

Schmeer, Kammi K.; Taylor, Miles

2013-01-01

399

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

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

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

2013-10-01

400

Nonlinear Control of Heart Rate Variability in Human Infants

NASA Astrophysics Data System (ADS)

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

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

1996-03-01

401

Ergodic chaos-based communication schemes.

Recent studies have shown the applicability of synchronized chaotic systems to the area of communications in different ways. At the same time synchronization based signal recovery and estimation of parameters severely suffer due to the presence of channel noise. By exploiting the ergodic properties of chaotic signals effectively, a simple technique called the mean-value method is introduced. This method is shown to be capable of estimating chaos system parameters from the transmitted chaotic signal efficiently for a low signal-to-noise ratio. A suitable demodulator has been designed for ergodic chaotic parameter modulation scheme for digital signal communication. Further, the mean-value technique incorporates a noncoherent receiver to recover analog information signal from the chaos masked signal efficiently. It is found that the proposed chaotic masking scheme is robust even in the presence of strong noise. In addition, this scheme has the potential advantage of a very simple hardware realization, which promises enhanced signal recovery performances. PMID:12366220

Leung, H; Yu, H; Murali, K

2002-09-01

402

Role of parametric resonances in global chaos

NASA Astrophysics Data System (ADS)

The quasi-isochronous (QI) dynamical system, in the presence of synchrotron radiation damping and rf phase modulation, exhibits a sequence of period-2 bifurcations en route towards global chaos (instability) in a region of modulation tune. The critical modulation amplitude for the onset of the global chaos shows a cusp as a function of the modulation tune. This cusp is shown to arise from the transition from the 2:1 to the 1:1 parametric resonances. We have also studied the effect of the rf voltage modulation on the QI dynamical system and found that the tolerance of the rf voltage modulation is much larger than that of the rf phase modulation.

Jeon, D.; Bai, M.; Chu, C. M.; Kang, X.; Lee, S. Y.; Riabko, A.; Zhao, X.

1996-10-01

403

Chaos in a Hydraulic Control Valve

NASA Astrophysics Data System (ADS)

In this paper we have studied the instability and chaos occurring in a pilot-type poppet valve circuit. The system consists of a poppet valve, an upstream plenum chamber, a supply pipeline and an orifice inserted between the pelnum and the pipeline. Although the poppet valve rests on the seat stably for a supply pressure lower than the cracking pressure, the circuit becomes unstable for an initial disturbance beyond a critical value and develops a self-excited vibration. In this unstable region, chaotic vibration appears at the period-doubling bifurcation. We have investigated the stability of the circuit and the chaotic phenomenon numerically, and elucidated it by power spectra, a bifurcation diagram and Lyapunov exponent calculations, showing that the phenomenon follows the Feigenbaum route to chaos.Copyright 1997 Academic Press Limited

Hayashi, S.; Hayase, T.; Kurahashi, T.

1997-08-01

404

Input-dependent Suppression of Chaos in Recurrent Neural Networks

NASA Astrophysics Data System (ADS)

Neuronal responses arise from an interaction between spontaneous activity and responses driven by external inputs. Experiments studying cortical circuits reveal a striking similarity between the magnitude and complexity of intrinsic and input-generated activity. How does a network generating complex activity remain sensitive to external inputs? This seems unlikely for a network in which input-driven responses add linearly to ongoing activity generated by stochastic noise generators. We developed a mean-field theory and used recurrent network models to distinguish between this type of external noise and chaotic background generated by strong coupling within the circuit. As a result of a highly nonlinear relationship between input- and internally generated activity, we show that intrinsic noise is sensitive to the amplitude and the spatiotemporal structure of the input. We find that input not only drives responses, it also actively suppresses spontaneous activity, leading to a phase transition in which the chaotic background is absent. Although the power spectrum of the spontaneous activity falls exponentially from zero, the phase transition reveals a resonant frequency at which relatively a weak input suppresses chaos. As long as the input drives the system across the phase transition, a spontaneously active network can work with coupling strong enough to allow large signal amplification and selectivity without the complex background interfering with sensory processing.

Rajan, K.; Abbott, L. F.; Sompolinsky, H.

2010-03-01

405

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

406

The CHAOS-4 geomagnetic field model

NASA Astrophysics Data System (ADS)

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

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

2014-05-01

407

Chaos in free electron laser oscillators

The chaotic nature of a storage-ring Free Electron Laser (FEL) is investigated. The derivation of a low embedding dimension for the dynamics allows the low-dimensionality of this complex system to be observed, whereas its unpredictability is demonstrated, in some ranges of parameters, by a positive Lyapounov exponent. The route to chaos is then explored by tuning a single control parameter, and a period-doubling cascade is evidenced, as well as intermittence.

C. Bruni; R. Bachelard; D. Garzella; G. L. Orlandi; M. E. Couprie

2009-09-04

408

Chaos: Understanding and Controlling Laser Instability

NASA Technical Reports Server (NTRS)

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

Blass, William E.

1997-01-01

409

Detecting chaos in irregularly sampled time series.

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

Kulp, C W

2013-09-01

410

From chaos to space-time chaos in subcritical systems. The case of plane Couette flow.

NASA Astrophysics Data System (ADS)

Using a recently derived Swift--Hohenberg-like model of plane Couette flow,(P.M., ``Modeling transitional plane Couette flow,'' in Advances in turbulence VIII), C. Dopazo et al. (Eds.) CIMNE, Barcelona, 2000. we study the effects of in-plane size (periodic b.c.) on the statistics of the transition to chaos in a typically subcritical extended system. Quenching and annealing methodologies are compared as to the threshold Reynolds number below which chaos gets finite life-time with probability one.

Manneville, Paul

2001-03-01

411

Nonlinear Dynamics, Magnitude-Period Formula and Forecasts on Earthquake

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

Chang, Yi-Fang

2008-01-01

412

Influence of Mixture Quality on Nonlinear Combustion Process of Natural Gas Engine

Combustion characteristic in a spark ignition natural gas engine was studied under different conditions of mixture quality based on chaos theory, in order to estimate nonlinear dynamic level in combustion system, we reconstructed attractor of combustion system using Indicated Mean Effective Pressure (IMEP), computed correlation dimensions and largest Lyapunov exponent (LLE) of the attractors, results show that there are low-dimensions

Yang Li-ping; Ma Xiu-zhen; Song En-zhe

2010-01-01

413

Detecting non-linearities in neuro-electrical signals: A study of synchronous local field potentials

The question of the presence and detection of non-linear dynamics and possibly low-dimensional chaos in the brain is still an open question, with recent results indicating that initial claims for low dimensionality were faulted by incomplete statistical testing. To make some progress on this question, our approach was to use stringent data analysis of precisely controlled and behaviorally significant neuroelectric

Johannes Müller-Gerking; Jacques Martinerie; Sergio Neuenschwander; Laurent Pezard; Bernard Renault; Francisco J. Varela

1996-01-01

414

Nonlinear Analysis of Neural Activity of Prefrontal Cortex of the Rat Injected Methamphetamine

We analyzed neural activity of the prefrontal cortex of rats injected a psychotic drug metham- phetamine by using nonlinear dynamics and chaos theory. Although correlation dimensions of the attractors generated by using interspike intervals (ISI) of the observed neural spikes showed little dif- ference before and after drug injection, the ISI distribution revealed a noticeable dierence. Before and after drug

Youngtae Kim

2004-01-01

415

The Origin of Chaos in the Outer Solar System

The Origin of Chaos in the Outer Solar System N. Murray1 and M. Holman2 Classical analytic theories. This disagreement is resolved by a new analytic theory. The theory shows that the chaos among the jovian planets 10Â 43 , most planetary systems, in the sense of measure theory, are stable and un- dergo

Murray, Norman

416

Analysis of decision-making in economic chaos control

In some economic chaotic systems, players are concerned about whether their performance is improved besides taking some methods to control chaos. In the face of chaos occurring in competition, whether one player takes controlling measures or not affects not only their own earning but also other opponents’ income. An output duopoly competing evolution model with bounded rationality is introduced in

Jian-guo Du; Tingwen Huang; Zhaohan Sheng

2009-01-01

417

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

. I Maxwell on Chaos Brian R. Hunt and James A. Yorke* James Clerk Maxwell (1831-1879) is perhaps. They can be reached by eleclronic mail aliwIII@ipSI.umd.edu. James Clerk'Maxwell. Courtesy of American Articles in this issue... Scientific Article Maxwell on Chaos Brian R. Hunt and James A. Yorke Feature

Yorke, James

418

Entrainment and Chaos in the Hodgkin-Huxley Oscillator

Entrainment and Chaos in the Hodgkin-Huxley Oscillator Kevin K. Lin http that the Hodgkin-Huxley neuron model, driven by a periodic impulse train, can exhibit entrainment, transient chaos, rigorous perturbation theory of kicked oscillators (Qiudong Wang & Lai-Sang Young). 2. Hodgkin

Lin, Kevin K.

419

Order and Chaos in Spiral Galaxies Seen through their Morphology

Summary. It is clear from dynamical considerations and N-body models that both order and chaos are important for spiral galaxies. To study the relative importance of order and chaos in real galaxies, one needs accurate kinematic information for the stellar population. Unfortunately, such data are still very difficult to obtain outside the very central parts of spiral galaxies due to

P. Grosbøl; Karl-Schwarzschild Strasse

2009-01-01

420

Comment on "Ruling out chaos in compact binary systems"

In a recent Letter, Schnittman and Rasio argue that they have ruled out chaos in compact binary systems since they find no positive Lyapunov exponents. In stark constrast, we find that the chaos discovered in the original paper under discussion, J.Levin, PRL, 84 3515 (2000), is confirmed by the presence of positive Lyapunov exponents.

Neil J. Cornish; Janna Levin

2002-10-17

421

Chaos and cryptography: block encryption ciphers based on chaotic maps

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

Goce Jakimoski; Ljupco Kocarev

2001-01-01

422

Developing Quality Preschool Movement Programs: CHAOS and KinderPlay

ERIC Educational Resources Information Center

This article presents two models for creating new developmentally appropriate preschool movement programs: CHAOS (Children Helping Adults Open Senses) at Eastern Connecticut State University and "KinderPlay" at Florida International University. CHAOS and KinderPlay utilize skill themes and movement concepts as their focus and incorporate parents…

Robert, Darren L.; Yongue, Bill

2004-01-01

423

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

424

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

425

Gain-controlled wave chaos in a chaotic optical fibre

Gain-controlled wave chaos in a chaotic optical fibre C. Michel, S. Tascu, V. Doya, O. Legrand, F of a multimode chaotic optical fibre. More precisely, we introduce Ytterbium in the optical fibre as a gain of a chaotic optical fibre as a device to visualise quantum chaos, we describe the amplification process

Paris-Sud XI, UniversitÃ© de

426

Adaptive chaos: Mild disorder may help contain major disease

of adaptive chaos for sleep diseases, e.g., enuresis, and other potentially life threatening disorders be examples of how a disorder can treat a disease. Sleep medicine offers multiple examples of sleep disordersAdaptive chaos: Mild disorder may help contain major disease Alexander Golbin a , Alexander

Umantsev, Alexander

427

Chaos in a rotor system supported by ball bearings

to observing chaos in rotor systems. Further, there has been little work carried out in the area of chaos control, of which only a small portion has been applied to rotor systems. Originally, the goal of the research described in this paper was to control...

Fisher, James Robert, 1979-

2013-02-22

428

Communication using Synchronization of Chaos in Semiconductor Lasers with optoelectronic

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

Illing, Lucas

429

Intermittency and solitons in the driven dissipative nonlinear Schroedinger equation

NASA Technical Reports Server (NTRS)

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

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

1984-01-01

430

Black bears on the 6000-ha Huntington Wildlife Forest, in the central Adirondack region of upper New York State, were modeled using the stella II simulation software. The purposes were to (1)express black-bear biology as a population system inseparably derived from its ecosystem; (2)demonstrate how chaos, with origins in nonlinearity, and sustainability, related to linearity, can be incorporated into dynamical models,

Bernard C Patten

1997-01-01

431

Amplitude death in coupled robust-chaos oscillators

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

M. J. Palazzi; M. G. Cosenza

2014-04-08

432

Nonlinear dynamic analysis of an unbalanced rotor supported by roller bearing

In this paper, the non-linear dynamic analysis of an unbalanced rotor supported by roller bearings has been made. The non-linearity in the rotor bearing system is due to Hertzian contact, unbalanced rotor effect and radial internal clearance. The system can excite bi-periodically by the varying compliance frequency and the rotational frequency. The results show the appearance of instability and chaos

S. P. Harsha

2005-01-01

433

NASA Astrophysics Data System (ADS)

In sharp contrast to the early positivist view of the nature of science and scientific knowledge, Kuhn argues that the scientific enterprise involves states of continuous, gradual development punctuated by comparatively rare instances of turmoil and change, which ultimately brings about a new stability and a qualitatively changed knowledge base. Although this discontinuous or nonlinear view of scientific knowledge is shared by a number of philosophers of science and science educators currently, Kuhn's description of how progress in science occurs has never been formally modeled from a nonlinear mathematical perspective. In this article, we represent aspects of Kuhn's main thesis and ideas as stated in his classic work The Structure of Scientific Revolutions using catastrophe theory, which is a particular instantiation of chaos theory capable of describing discontinuous phenomenon. Through this catastrophe theory representation we attempt to depict and develop a formal nonlinear model of scientific change. The pedagogical implications of the model developed and presented are discussed.

Perla, Rocco J.; Carifio, James

434

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

A unit of study for gifted 4th and 5th graders is described on the subject of mathematical periodicity and chaos and the underlying physical processes which produce these phenomena. A variety of hands-on experiments and the use of various data analysis tools and computer aids provide students with powerful raw material for their analysis, interpretation, and understanding. The concepts of

Helen M. Adams; John C. Russ

1992-01-01

435

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

436

Technology Transfer Automated Retrieval System (TEKTRAN)

A review of the literature reveals conflicting results regarding the existence and inherent nature of chaos in hydrological processes such as precipitation and streamflow,i.e. whether they are low dimensional chaotic or stochastic.This issue is examined further in this paper, particularly the effect...

437

The connections between the frustrated chaos and the intermittency chaos in small Hopfield networks

In a previous paper we introduced the notion of frustrated chaos occurring in Hopfield networks [Neural Networks 11 (1998) 1017]. It is a dynamical regime which appears in a network when the global structure is such that local connectivity patterns responsible for stable oscillatory behaviors are intertwined, leading to mutually competing attractors and unpredictable itinerancy among brief appearance of these

Hugues Bersini; Pierre Sener

2002-01-01

438

Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe

Bloembergen, Nicolaas

1996-01-01

439

Method of controlling chaos in laser equations

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, M. (Physics Department, Lawrence Livermore National Laboratory, University of California, Livermore, California 94550 (United States))

1993-01-01

440

The CHAOS-4 Geomagnetic Field Model

NASA Astrophysics Data System (ADS)

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

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

2013-12-01

441

Classical and Quantum Chaos in Atom Optics

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

Farhan Saif

2006-04-10

442

Enlightening complexity: making energy with chaos

We study the energy harvesting of photons undergoing chaotic dynamics with different complexity degrees. Our theory employs a multiscale analysis, which combines Hamiltonian billiards, time-dependent coupled mode theory and ab-initio simulations. In analogy to classical thermodynamics, where the presence of microscopic chaos leads to a single direction for time and entropy, an increased complexity in the motion of photons yields to a monotonic accumulation of energy, which dramatically grows thanks to a constructive mechanism of energy buildup. This result could lead to the realization of novel complexity-driven, energy harvesting architectures.

Molinari, D

2011-01-01

443

Many intriguing properties of driven nonlinear resonators, including the appearance of chaos, are very important for understanding the universal features of nonlinear dynamical systems and can have great practical significance. We consider a cylindrical cavity resonator driven by an alternating voltage and filled with a nonlinear nondispersive medium. It is assumed that the medium lacks a center of inversion and the dependence of the electric displacement on the electric field can be approximated by an exponential function. We show that the Maxwell equations are integrated exactly in this case and the field components in the cavity are represented in terms of implicit functions of special form. The driven electromagnetic oscillations in the cavity are found to display very interesting temporal behavior and their Fourier spectra contain singular continuous components. This is a demonstration of the existence of a singular continuous (fractal) spectrum in an exactly integrable system. PMID:23004812

Petrov, E Yu; Kudrin, A V

2012-05-01

444

NASA Astrophysics Data System (ADS)

The permanent-magnet synchronous motor (PMSM) system, which is a nonlinear dynamic system, will demonstrate a variety of chaotic phenomena when its parameters or external inputs fall into a certain area, which will lead to a deterioration of its performance. Thus, chaos should be suppressed or eliminated. In this paper, the property of equilibrium points is analyzed, and the condition for the occurrence of a Hopf bifurcation in a PMSM system is given based on a mathematical model of the PMSM system with a bifurcation diagram, a Lyapunov exponent map and phase plane diagrams given. After the drawbacks of the existing control methods have been analyzed, a robust nonlinear feedback controller is designed to control the chaos in the PMSM system with a load torque disturbance. The object is to eliminate the chaos and to drive the system speed to a desired value, Numerical simulation proves the validity of this control method.

Hu, Jian; Liu, Long; Ma, Da-wei

2014-12-01

445

NASA Technical Reports Server (NTRS)

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

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

1983-01-01

446

Theory of the nucleus as applied to quantum chaos

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a quantum signature of chaos in classical mechanics is given. It is proposed to specify a regular versus a chaotic behavior on the basis of symmetries of the system being considered and global integrals of motion that are associated with these symmetries in accordance with the Liouville-Arnold theorem rather than on the basis of the concept of Lyapunov’s instability of trajectories. Numerical criteria of quantum chaos that follow from the proposed concept are analyzed.

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University, Petersburg Nuclear Physics Institute, National Research Center Kurchatov Institute (Russian Federation)

2014-12-15

447

Quantum Chaos in Physical Systems: from Super Conductors to Quarks

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

Elmar Bittner; Harald Markum; Rainer Pullirsch

2001-10-31

448

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

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

Kot, M.

1992-10-01

449

Chaos and scaling in daily river flow

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

M. De Domenico; M. Ali Ghorbani

2011-04-07

450

Noise, chaos, and (?, ?)-entropy per unit time

NASA Astrophysics Data System (ADS)

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

Gaspard, Pierre; Wang, Xiao-Jing

1993-12-01

451

Chaos and structure of level densities

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

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

2008-01-01

452

Morphogenesis by diffusive chaos in epidemiological systems

NASA Astrophysics Data System (ADS)

This paper deals with a discrete mathematical model of epidemiological systems based on the SIRS model. A population of susceptible individuals can be infected by contact to infective individuals which recover. The first part of this paper deals with temporal discrete models. Three threshold values of a control parameter depending on the transmission rate and the total population share the behaviour of the epidemic in four zones: no infection, increase of infection, bifurcation and then chaos. It is shown that for the same transmission rate, a critical total population shares the dynamics of the infection: for low population, infection disappears and for high population, the infection increases but the number of susceptible individuals remains at a positive constant value. In the second part of this paper, the SIRS model is generalised in taking into account the spatial diffusion of the populations. Classically space-time models are based on the reaction-diffusion equation. There is a problem with such a parabolic equation because this predicts an infinite speed of propagation for the population disturbances. To avoid this biologically incorrect feature, a non-stationary term is introduced. Numerical simulations show the propagation of the infection with chaotic spatial heterogeneities, called morphogenesis by diffusive chaos. In spatial region with low population, no infection propagates.

Dubois, Daniel M.; Sabatier, Philippe

1998-07-01

453

RAPID DYNAMICAL CHAOS IN AN EXOPLANETARY SYSTEM

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

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

2012-08-10

454

Generalized spectral decomposition for stochastic nonlinear problems

We present an extension of the generalized spectral decomposition method for the resolution of nonlinear stochastic problems. The method consists in the construction of a reduced basis approximation of the Galerkin solution and is independent of the stochastic discretization selected (polynomial chaos, stochastic multi-element or multi-wavelets). Two algorithms are proposed for the sequential construction of the successive generalized spectral modes. They involve decoupled resolutions of a series of deterministic and low-dimensional stochastic problems. Compared to the classical Galerkin method, the algorithms allow for significant computational savings and require minor adaptations of the deterministic codes. The methodology is detailed and tested on two model problems, the one-dimensional steady viscous Burgers equation and a two-dimensional nonlinear diffusion problem. These examples demonstrate the effectiveness of the proposed algorithms which exhibit convergence rates with the number of modes essentially dependent on the spectrum of the stochastic solution but independent of the dimension of the stochastic approximation space.

Nouy, Anthony [Research Institute in Civil Engineering and Mechanics (GeM), Nantes Atlantic University, Ecole Centrale Nantes, UMR CNRS 6183, 2 rue de la Houssiniere, B.P. 92208, 44322 Nantes Cedex 3 (France)], E-mail: anthony.nouy@univ-nantes.fr; Le Maitre, Olivier P. [LIMSI-CNRS, BP133, F-91403 Orsay (France); DEN/DM2S/SFME, Centre d'Etudes Nucleaires, Saclay (France)], E-mail: olm@limsi.fr

2009-01-10

455

Zeeman catastrophe machines as a toolkit for teaching chaos

NASA Astrophysics Data System (ADS)

The investigation of chaotic motions and cooperative systems offers a magnificent opportunity to involve modern physics in the basic course of mechanics taught to engineering students. In this paper, it will be demonstrated that the Zeeman machine can be a versatile and motivating tool for students to acquire introductory knowledge about chaotic motion via interactive simulations. The Zeeman catastrophe machine is a typical example of a quasi-static system with hysteresis. It works in a relatively simple way and its properties can be understood very easily. Since the machine can be built easily and the simulation of its movement is also simple, the experimental investigation and the theoretical description can be connected intuitively. Although the Zeeman machine is known mainly for its quasi-static and catastrophic behaviour, its dynamic properties are also of interest with its typical chaotic features. By means of a periodically driven Zeeman machine, a wide range of chaotic properties of the simple systems can be demonstrated, such as bifurcation diagrams, chaotic attractors, transient chaos, Lyapunov exponents and so on. This paper is organically linked to our website (http://csodafizika.hu/zeeman) where the discussed simulation programs can be downloaded. In a second paper, the novel construction of a network of Zeeman machines will be presented to study the properties of cooperative systems.

Nagy, Péter; Tasnádi, Péter

2014-01-01

456

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

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

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

2014-07-29

457

A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes

We study the convergence properties of the recently developed Dynamically Orthogonal (DO) field equations [1] in comparison with the Polynomial Chaos (PC) method. To this end, we consider a series of one-dimensional prototype SPDEs, whose solution can be expressed analytically, and which are associated with both linear (advection equation) and nonlinear (Burgers equation) problems with excitations that lead to unimodal and strongly bi-modal distributions. We also propose a hybrid approach to tackle the singular limit of the DO equations for the case of deterministic initial conditions. The results reveal that the DO method converges exponentially fast with respect to the number of modes (for the problems considered) giving same levels of computational accuracy comparable with the PC method but (in many cases) with substantially smaller computational cost compared to stochastic collocation, especially when the involved parametric space is high-dimensional.

Choi, Minseok [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)] [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States); Sapsis, Themistoklis P. [Courant Institute of Mathematical Sciences, New York University, NY 10012 (United States)] [Courant Institute of Mathematical Sciences, New York University, NY 10012 (United States); Karniadakis, George Em, E-mail: george_karniadakis@brown.edu [Division of Applied Mathematics, Brown University, Providence, RI 02912 (United States)

2013-07-15

458

A convergence study for SPDEs using combined Polynomial Chaos and Dynamically-Orthogonal schemes

NASA Astrophysics Data System (ADS)

We study the convergence properties of the recently developed Dynamically Orthogonal (DO) field equations [1] in comparison with the Polynomial Chaos (PC) method. To this end, we consider a series of one-dimensional prototype SPDEs, whose solution can be expressed analytically, and which are associated with both linear (advection equation) and nonlinear (Burgers equation) problems with excitations that lead to unimodal and strongly bi-modal distributions. We also propose a hybrid approach to tackle the singular limit of the DO equations for the case of deterministic initial conditions. The results reveal that the DO method converges exponentially fast with respect to the number of modes (for the problems considered) giving same levels of computational accuracy comparable with the PC method but (in many cases) with substantially smaller computational cost compared to stochastic collocation, especially when the involved parametric space is high-dimensional.

Choi, Minseok; Sapsis, Themistoklis P.; Karniadakis, George Em

2013-07-01

459

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

In this paper a unified approach is presented for controlling chaos in nonlinear partial differential systems by a fuzzy control design. First almost all known chaotic partial differential equation systems are represented by Takagi-Sugeno fuzzy model. For investigating design procedure, Kuramoto-Sivashinsky (K-S) equation is selected. Then, all linear subsystems of K-S equation are transformed to ordinary differential equation (ODE) systems by truncated Fourier series of sine-cosine functions. By solving Riccati equation for each ODE systems, parallel stabilizing feedback controllers are determined. Finally, a distributed fuzzy feedback for K-S equation is designed. Numerical simulations are given to show that the distributed fuzzy controller is very easy to design, efficient, and capable to extend. PMID:24387539

Vasegh, Nastaran; Khellat, Farhad

2013-12-01

460

Hamiltonian Hopf bifurcations and chaos of NLS/GP standing-wave modes

We examine the dynamics of solutions to nonlinear Schrodinger/Gross-Pitaevskii equations that arise due to Hamiltonian Hopf (HH) bifurcations--the collision of pairs of eigenvalues on the imaginary axis. To this end, we use inverse scattering to construct localized potentials for this model which lead to HH bifurcations in a predictable manner. We perform a formal reduction from the partial differential equations (PDE) to a small system of ordinary differential equations (ODE). We show numerically that the behavior of the PDE is well-approximated by that of the ODE and that both display Hamiltonian chaos. We analyze the ODE to derive conditions for the HH bifurcation and use averaging to explain certain features of the dynamics that we observe numerically.

Roy H. Goodman

2011-01-31

461

Quantitative uniform in time chaos propagation for Boltzmann collision processes

This paper is devoted to the study of mean-field limit for systems of indistinguables particles undergoing collision processes. As formulated by Kac \\cite{Kac1956} this limit is based on the {\\em chaos propagation}, and we (1) prove and quantify this property for Boltzmann collision processes with unbounded collision rates (hard spheres or long-range interactions), (2) prove and quantify this property \\emph{uniformly in time}. This yields the first chaos propagation result for the spatially homogeneous Boltzmann equation for true (without cut-off) Maxwell molecules whose "Master equation" shares similarities with the one of a L\\'evy process and the first {\\em quantitative} chaos propagation result for the spatially homogeneous Boltzmann equation for hard spheres (improvement of the %non-contructive convergence result of Sznitman \\cite{S1}). Moreover our chaos propagation results are the first uniform in time ones for Boltzmann collision processes (to our knowledge), which partly answers the important question...

Mischler, Stéphane

2010-01-01

462

Parameter Mismatches, Chaos Synchronization and Fast Dynamic Logic Gates

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

E. M. Shahverdiev

2009-07-02

463

Windows and chaos in double-plasma devices

Chaotic behaviors are investigated numerically in a double-plasma device. Windows in cascading bifurcations and chaos have been observed in the calculations of frequency spectra, phase space trajectories and Lyapunov exponents.

T. Okada; T. Okabe; N. Honda

2000-01-01

464

The New Science of Chaos Prof. Clint Sprott

in Brazil can cause a tornado in Texas a few weeks later. Such "chaos" has now been observed in simple almost random. Tiny changes in the initial conditions cause enormous changes at a later time, making

Saffman, Mark

465

Low-temperature physics: Chaos in the cold

NASA Astrophysics Data System (ADS)

A marriage between theory and experiment has shown that ultracold erbium atoms trapped with laser light and subjected to a magnetic field undergo collisions that are characterized by quantum chaos. See Letter p.475

Julienne, Paul S.

2014-03-01

466

Filtering with Marked Point Process Observations via Poisson Chaos Expansion

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

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

2013-06-15

467

Numerical Chaos in a Fractional Order Logistic Map

In this paper we investigate a fractional order logistic map and its discrete time dynamics. We show some basic properties of the fractional logistic map and numerically study its period-doubling route to chaos.

Joakim Munkhammar

2010-11-10

468

Numerical and experimental exploration of phase control of chaos.

A well-known method to suppress chaos in a periodically forced chaotic system is to add a harmonic perturbation. The phase control of chaos scheme uses the phase difference between a small added harmonic perturbation and the main driving to suppress chaos, leading the system to different periodic orbits. Using the Duffing oscillator as a paradigm, we present here an in-depth study of this technique. A thorough numerical exploration has been made focused in the important role played by the phase, from which new interesting patterns in parameter space have appeared. On the other hand, our novel experimental implementation of phase control in an electronic circuit confirms both the well-known features of this method and the new ones detected numerically. All this may help in future implementations of phase control of chaos, which is globally confirmed here to be robust and easy to implement experimentally. PMID:16599742

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

2006-03-01

469

Route to, and control of chaos in multidimensional systems

are studied through the variation of this parameter. It was found that the route to chaos always begins, in the pendulum system, with a secondary Hopf Bifurcation followed by consecutive torus doubling bifurcations, ending with torus breaking. A comparison...

Zaki, Karim Shafik

1999-01-01

470

Dynamical and Wave Chaos in the Bose-Einstein Condensate

NASA Astrophysics Data System (ADS)

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

Reinhardt, William P.; McKinney, Sarah B.

471

Dynamical and Wave Chaos in the Bose-Einstein Condensate

NASA Astrophysics Data System (ADS)

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

Reinhardt, William P.; McKinney, Sarah B.

2001-10-01

472

New chaos indicators for systems with extremely small Lyapunov exponents

We propose new chaos indicators for systems with extremely small positive Lyapunov exponents. These chaos indicators can firstly detect a sharp transition between the Arnold diffusion regime and the Chirikov diffusion regime of the Froeschl\\'e map and secondly detect chaoticity in systems with zero Lyapunov exponent such as the Boole transformation and the Symmetric R\\'enyi (Saito) map to characterize sub-exponential diffusions.

Ken-ichi Okubo; Ken Umeno

2015-01-13

473

From classical chaos to decoherence in Robertson-Walker cosmology

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

Fernando C. Lombardo; Mario Castagnino; Luca Bombelli

1999-03-23

474

Suppression of quantum chaos in a quantum computer hardware

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

J. Lages; D. L. Shepelyansky

2005-10-14

475

Different routes from a matter wavepacket to spatiotemporal chaos

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.

Rong Shiguang [Department of Physics and Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081 (China); Department of Physics, Hunan University of Science and Technology, Xiangtan 411201 (China); Hai Wenhua; Xie Qiongtao; Zhong Honghua [Department of Physics and Key Laboratory of Low-dimensional Quantum Structures and Quantum Control of Ministry of Education, Hunan Normal University, Changsha 410081 (China)

2012-09-15

476

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

477

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

NASA Astrophysics Data System (ADS)

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

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

2014-07-01

478

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

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

479

Main principles of the complex nonlinear thinking which are based on the notions of the modern theory of evolution and self-organization of complex systems called also synergetics are under discussion in this article. The principles are transdisciplinary, holistic, and oriented to a human being. The notions of system complexity, nonlinearity of evolution, creative chaos, space-time definiteness of structure-attractors of evolution,

HELENA KNYAZEVA

2004-01-01

480

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

NASA Technical Reports Server (NTRS)

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

Ray, William J.

1994-01-01

481

Rocks Exposed on Slope in Aram Chaos

NASA Technical Reports Server (NTRS)

MGS MOC Release No. MOC2-550, 20 November 2003

This spectacular vista of sedimentary rocks outcropping on a slope in Aram Chaos was acquired by the Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) on 14 November 2003. Dark piles of coarse talus have come down the slopes as these materials continue to erode over time. Note that there are no small meteor impact craters in this image, indicating that erosion of these outcrops has been recent, if not on-going. This area is located near 2.8oS, 20.5oW. The 200 meter scale bar is about 656 feet across. Sunlight illuminates the scene from the lower right.

2003-01-01

482

ADDENDUM: Chaos in Bohmian quantum mechanics

NASA Astrophysics Data System (ADS)

In our recently published paper 'Chaos in Bohmian quantum mechanics' we criticized a paper by Parmenter and Valentine (1995 Phys. Lett. A 201 1), because the authors made an incorrect calculation of the Lyapunov exponent in the case of Bohmian orbits in a quantum system of two uncoupled harmonic oscillators. After our paper was published, we became aware of an erratum published by the same authors (Parmenter and Valentine 1996 Phys. Lett. A 213 319) that recognized the error made in their previous calculations. The authors realized that, when correctly calculated, 'aperiodic trajectories with well defined boundaries...have vanishing Lyapunov exponents', i.e., they are not chaotic. We want to supplement our paper with a reference to this erratum. The generic calculation of Lyapunov exponents in Bohmian quantum systems remains an original contribution of our paper (section 2).

Efthymiopoulos, C.; Contopoulos, G.

2006-06-01

483

Route to chaos in generalized logistic map

Motivated by a possibility to optimize modelling of the population evolution we postulate a generalization of the well-know logistic map. Generalized difference equation reads: \\begin{equation} x_{n+1}=rx^p_n(1-x^q_n), \\end{equation} $x\\in[0,1],\\;(p,q)>0,\\;n=0,1,2,...$, where the two new parameters $p$ and $q$ may assume any positive values. The standard logistic map thus corresponds to the case $p=q=1$. For such a generalized equation we illustrate the character of the transition from regularity to chaos as a function of $r$ for the whole spectrum of $p$ and $q$ parameters. As an example we consider the case for $p=1$ and $q=2$ both in the periodic and chaotic regime. We focus on the character of the corresponding bifurcation sequence and on the quantitative nature of the resulting attractor as well as its universal attribute (Feigenbaum constant).

Rafa? Rak; Ewa Rak

2015-02-01

484

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

485

The chaos anti-control and synchronization of a two-degrees-of-freedom loudspeaker system are studied in this paper. Anti-control term is added to change state from regular to chaos. The anti-control methods such as addition of a constant force, of a periodic square wave, of a periodic saw tooth wave, of a periodic triangle wave, of a periodic rectified sinusoidal wave and of

Z.-M. Ge; W.-Y. Leu

2004-01-01

486

The peculiarities of the effective cubic nonlinearity are analysed upon second harmonic generation in a medium with a quadratic nonlinearity. It is shown that in this case, the polarisation state of the pump wave changes during its propagation due to additional effective photoinduced anisotropy of propagatio