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1

Some Nonlinear Equations with Double Solutions: Soliton and Chaos

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

Yi-Fang Chang

2007-12-03

2

Chaos Theory: Implications for Nonlinear Dynamics in Counseling.

ERIC Educational Resources Information Center

The purpose of this paper is to explore the implications of chaos theory for counseling. The scientific notion of chaos refers to the tendency of dynamical, nonlinear systems toward irregular, sometimes unpredictable, yet deterministic behavior. Therapists, especially those working from a brief approach, have noted the importance of the client's…

Stickel, Sue A.

3

Controlling spatiotemporal chaos in coupled nonlinear oscillators

NASA Astrophysics Data System (ADS)

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

Kocarev, Ljup?o.; Parlitz, Ulrich; Stojanovski, Toni; Janji?, Predrag

1997-07-01

4

Microcomputer Simulation of Nonlinear Systems: From Oscillations to Chaos.

ERIC Educational Resources Information Center

Presents two short microcomputer programs which illustrate features of nonlinear dynamics, including steady states, periodic oscillations, period doubling, and chaos. Logistic maps are explained, inclusion in undergraduate chemistry and physics courses to teach nonlinear equations is discussed, and applications in social and biological sciences…

Raw, Cecil J. G.; Stacey, Larry M.

1989-01-01

5

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

6

Chaos in a Series Circuit with Nonlinear Capacitor and Nonlinear Inductor

This paper proposes a nonlinear circuit that generates chaotic oscillations. The proposed nonlinear circuit includes a nonlinear capacitor and a nonlinear inductor by using Generalized Impedance Converters. Both computational experiments and experiments on the real circuits exhibit that the region for chaotic oscillation is very wide, which show that the proposed circuit is effective for a chaos generator.

Mitsugi Tokuyama; Hirokazu Ohtagaki

2003-01-01

7

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

8

Criteria of chaos in non-linear mechanics

Analytical criteria are derived for the geometrical interpretation (Zak, 1985) of the transition to chaos in nonlinear mechanical systems. The concept of orbital instability in configuration space is employed in the analysis, and the differences between chaotic instability and classical Liapunov instability are explored. The case of a symmetric rigid body rotating about its center of gravity is considered as

M. Zak

1986-01-01

9

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

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

Protopopescu, V.

1990-10-01

10

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.

11

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

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

Zausner, Tobi

2011-04-01

12

Two types of chaos in non-linear mechanics

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

M. Zak

1985-01-01

13

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

14

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

15

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

16

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

17

Nonlinear dynamics and chaos methods in neurodynamics and complex data analysis

In this paper, we review modern nonlinear dynamical methods used in neuroscience and complex data analysis. We start with\\u000a the general description of nonlinear dynamics, its geometrical (and topological) picture, as well as its extreme case, deterministic\\u000a chaos, including its most popular models and methods: Lorenz attractor, Lyapunov exponents, and Kolmogorov–Sinai entropy.\\u000a \\u000a Then we review the most important nonlinear models

Tijana Ivancevic; Lakhmi Jain; John Pattison; Alex Hariz

2009-01-01

18

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

19

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

20

NASA Astrophysics Data System (ADS)

A model of a nonlinear, damped kicked oscillator is discussed. For such a model intra-mode correlations described by mutual information parameter I[?] based on the Wehrl entropy are considered. Furthermore, the system's quantum evolution is compared to its classical counterpart. The mutual information parameter is discussed as a proposal for quantum chaos' witness.

Kalaga, J. K.; Leo?ski, W.; Kowalewska-Kud?aszyk, A.

2014-12-01

21

Chaos Synchronization of Fractional Order Unified Chaotic System via Nonlinear Control

NASA Astrophysics Data System (ADS)

Based on the stability theory of fractional order systems, an effective but theoretically rigorous nonlinear control method is proposed to synchronize the fractional order chaotic systems. Using this method, chaos synchronization between two identical fractional order unified systems is studied. Simulation results are shown to illustrate the effectiveness of this method.

Chen, Xiang Rong; Liu, Chong Xin

22

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

23

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

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

2013-11-13

24

NASA Astrophysics Data System (ADS)

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

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

2014-09-01

25

We consider Aharonov-Bohm oscillations in a mesoscopic semiconductor ring threaded by both a constant magnetic flux and a time-dependent, resonant magnetic field with one or two frequencies. Working in the ballistic regime, we establish that the theory of ``quantum nonlinear resonance'' applies, and thus that this system represents a possible solid-state realization of ``quantum nonlinear resonance'' and ``quantum chaos.'' In

Gennady P. Berman; Evgeny N. Bulgakov; David K. Campbell; Ilya V. Krive

1997-01-01

26

18.385 Nonlinear Dynamics and Chaos, Fall 2002

Nonlinear dynamics with applications. Intuitive approach with emphasis on geometric thinking, computational and analytical methods. Extensive use of demonstration software. Topics: Bifurcations. Phase plane. Nonlinear ...

Rosales, Rodolfo

27

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

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

di Bernardo, M; Stoten, D P

2006-09-15

28

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

29

We consider Aharonov-Bohm oscillations in a mesoscopic semiconductor ring threaded by both a constant magnetic flux and a time-dependent, resonant magnetic field with one or two frequencies. Working in the ballistic regime, we establish that the theory of {open_quotes}quantum nonlinear resonance{close_quotes} applies, and thus that this system represents a possible solid-state realization of {open_quotes}quantum nonlinear resonance{close_quotes} and {open_quotes}quantum chaos.{close_quotes} In

Gennady Berman; Evgeny Bulgakov; David Campbell; Ilya Krive

1997-01-01

30

We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup. PMID:19792231

Lavrov, Roman; Peil, Michael; Jacquot, Maxime; Larger, Laurent; Udaltsov, Vladimir; Dudley, John

2009-08-01

31

NASA Astrophysics Data System (ADS)

We demonstrate experimentally how nonlinear optical phase dynamics can be generated with an electro-optic delay oscillator. The presented architecture consists of a linear phase modulator, followed by a delay line, and a differential phase-shift keying demodulator (DPSK-d). The latter represents the nonlinear element of the oscillator effecting a nonlinear transformation. This nonlinearity is considered as nonlocal in time since it is ruled by an intrinsic differential delay, which is significantly greater than the typical phase variations. To study the effect of this specific nonlinearity, we characterize the dynamics in terms of the dependence of the relevant feedback gain parameter. Our results reveal the occurrence of regular GHz oscillations (approximately half of the DPSK-d free spectral range), as well as a pronounced broadband phase-chaotic dynamics. Beyond this, the observed dynamical phenomena offer potential for applications in the field of microwave photonics and, in particular, for the realization of novel chaos communication systems. High quality and broadband phase-chaos synchronization is also reported with an emitter-receiver pair of the setup.

Lavrov, Roman; Peil, Michael; Jacquot, Maxime; Larger, Laurent; Udaltsov, Vladimir; Dudley, John

2009-08-01

32

Nonlinear elasticity of cross-linked networks

NASA Astrophysics Data System (ADS)

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

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

2013-04-01

33

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

34

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

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

2011-07-15

35

Chaos in fractional-order autonomous nonlinear systems

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

Wajdi M. Ahmad; J. C. Sprott

2003-01-01

36

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

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

Imada, M.

1985-01-01

37

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

38

Mutation and Chaos in Nonlinear Models of Heredity

In this short communication, 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. A numerical simulation assists us to get some clear picture about chaotic behaviors of such models.

Nasir Ganikhodjaev; Mansoor Saburov; Ashraf Mohamed Nawi

2013-04-21

39

Homoclinic orbits and chaos in a pair of parametrically-driven coupled nonlinear resonators

We study the dynamics of a pair of parametrically-driven coupled nonlinear mechanical resonators of the kind that is typically encountered in applications involving microelectromechanical and nanoelectromechanical systems (MEMS & NEMS). We take advantage of the weak damping that characterizes these systems to perform a multiple-scales analysis and obtain amplitude equations, describing the slow dynamics of the system. This picture allows us to expose the existence of homoclinic orbits in the dynamics of the integrable part of the slow equations of motion. Using a version of the high-dimensional Melnikov approach, developed by Kovacic and Wiggins [Physica D, 57, 185 (1992)], we are able to obtain explicit parameter values for which these orbits persist in the full system, consisting of both Hamiltonian and non-Hamiltonian perturbations, to form so-called Shilnikov orbits, indicating a loss of integrability and the existence of chaos. Our analytical calculations of Shilnikov orbits are confirmed numerically.

Eyal Kenig; Yuriy A. Tsarin; Ron Lifshitz

2010-07-22

40

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

41

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

Sorin Vlad; Paul Pascu; Nicolae Morariu

2010-01-20

42

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

43

Chaos and bifurcation in Power Electronics Medical Instruments Implications

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

Gajic, Zoran

44

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

45

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

46

Nonlinear resonance and dynamical chaos in a diatomic molecule driven by a resonant ir field

We consider the transition from regular motion to dynamical chaos in a classical model of a diatomic molecule which is driven by a circularly polarized resonant ir field. Under the conditions of a nearly two-dimensional case, the Hamiltonian reduces to that for the nonintegrable motion of a charged particle in an electromagnetic wave [A. J. Lichtenberg and M. A. Lieberman,

Gennady P. Berman; Evgeny N. Bulgakov; Darryl D. Holm

1995-01-01

47

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

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

2006-01-01

48

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

49

NASA Astrophysics Data System (ADS)

A numerical exploration of a gain-loss nonlinear Schrödinger equation was carried out utilizing over 180?000 core hours to conduct more than 10?000 unique simulations in an effort to characterize the model's six dimensional parameter space. The study treated the problem in full generality, spanning a minimum of eight orders of magnitude for each of three linear and nonlinear gain terms and five orders of magnitude for higher order nonlinearities. The gain-loss nonlinear Schrödinger equation is of interest as a model for spin wave envelopes in magnetic thin film active feedback rings and analogous driven damped nonlinear physical systems. Bright soliton trains were spontaneously driven out of equilibrium and behaviors stable for tens of thousands of round trip times were numerically identified. Nine distinct complex dynamical behaviors with lifetimes on the order of ms were isolated as part of six identified solution classes. Numerically located dynamical behaviors include: (i) low dimensional chaotic modulations of bright soliton trains; (ii) spatially symmetric/asymmetric interactions of solitary wave peaks; (iii) dynamical pattern formation and recurrence; (iv) steady state solutions; and (v) intermittency. Simulations exhibiting chaotically modulating bright soliton trains were found to qualitatively match previous experimental observations. Ten new dynamical behaviors, eight demonstrating long lifetimes, are predicted to be observable in future experiments.

Anderson, Justin Q.; Ryan, Rachel A.; Wu, Mingzhong; Carr, Lincoln D.

2014-02-01

50

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

), limited by energy conservation, When the resonance is "detuned," the equilibrium becomes stable to small dissipation of the negative energy modes, or nonlinearly via resonant wave-wave coupling, leading to explosive initially nonresonant systems to reach resonance by diffusion in phase space. In this and a companion paper

Morrison, Philip J.,

51

LOCAL FIELDS' LOCALIZATION AND CHAOS AND NONLINEAR-OPTICAL ENHANCEMENT IN COMPOSITES

in some metallic (especially silver, gold, or platinum) colloidal clusters, metal #12;2 nanocomposites of disordered clusters and nanocomposites. Linear and nonlinear optical polarizabilities of large disordered clusters, fractal clusters in particular, and susceptibilities of nanocomposites are found and calculated

Stockman, Mark I.

52

Spatiotemporal chaos in mixed linear-nonlinear coupled logistic map lattice

NASA Astrophysics Data System (ADS)

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

Zhang, Ying-Qian; Wang, Xing-Yuan

2014-05-01

53

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

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

2006-01-01

54

NASA Astrophysics Data System (ADS)

In this paper, sliding mode control is utilized for stabilization of a particular class of nonlinear polytopic differential inclusion systems with fractional-order-0 < q < 1. This class of fractional order differential inclusion systems is used to model physical chaotic fractional order Chen and Lu systems. By defining a sliding surface with fractional integral formula, exploiting the concept of the state space norm, and obtaining sufficient conditions for stability of the sliding surface, a special feedback law is presented which enables the system states to reach the sliding surface and consequently creates a sliding mode control. Finally, simulation results are used to illustrate the effectiveness of the proposed method.

Balochian, Saeed; Sedigh, Ali Khaki

2012-03-01

55

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

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

2006-01-01

56

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

57

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

58

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

59

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

60

Chaos and chaotic dynamics in economics.

Proponents of chaos theory attempted to articulate a new, more realistic, scientific world-view contradictory to the fundamental notions of the Newtonian view of science. Nonlinearity and chaos give the opportunity of a reconciliation of economics with a more realistic representation of its phenomena. Chaos theory represents a means for enhancing both the methodological and theoretical foundations for exploring the complexity of economic phenomena. This paper offers an overview of the applications of chaos theory in economics highlighting that recognizing the existence of deterministic chaos in economics is important from both a theoretical and practical point of view. PMID:19527622

Faggini, Marisa

2009-07-01

61

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

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

62

Chaos in driven Alfven systems

NASA Technical Reports Server (NTRS)

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

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

1990-01-01

63

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

NASA Astrophysics Data System (ADS)

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

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

2011-08-01

64

Chaos Theory and the Problem of Change in Family Systems

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

Matthijs Koopmans

1998-01-01

65

Terminal chaos for information processing in neurodynamics

New nonlinear phenomenon — terminal chaos caused by failure of the Lipschitz condition at equilibrium points of dynamical systems is introduced. It is shown that terminal chaos has a well organized probabilistic structure which can be predicted and controlled. This gives an opportunity to exploit this phenomenon for information processing. It appears that chaotic states of neurons activity are associated

M. Zak

1991-01-01

66

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

Zhao, Haiquan; Zhang, Jiashu

2009-04-01

67

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

68

The dynamics of flexible rotors associated with fluid film bearings have been studied since the 1950s. Most of the literature has assumed rigid, undamped bearing support with linear elastic restoring force. For a more precise description of fluid film bearing-rotor systems, a non-linearly supported model is proposed in this paper, where a linear damping force and a non-linear elastic restoring

Chieh-Li Chen; Her-Terng Yau

1998-01-01

69

The dynamic analysis of the rotor-bearing system is studied in this paper and is supported by oil film journal bearings. An observation of a nonlinearly supported model and the rub-impact between rotor and stator is needed for more precise analysis of rotor-bearing systems. Inclusive of the analysis methods of the dynamic trajectory, the power spectra, the Poincaré maps, the bifurcation

Cai-Wan Chang-Jian; Chao-Kuang Chen

2007-01-01

70

We observe deterministic chaos in a simple network of electronic logic gates that are not regulated by a clocking signal. The resulting power spectrum is ultra-wide-band, extending from dc to beyond 2 GHz. The observed behavior is reproduced qualitatively using an autonomously updating Boolean model with signal propagation times that depend on the recent history of the gates and filtering of pulses of short duration, whose presence is confirmed experimentally. Electronic Boolean chaos may find application as an ultra-wide-band source of radio waves

Rui Zhang; Hugo L. D. de S. Cavalcante; Zheng Gao; Daniel J. Gauthier; Joshua E. S. Socolar; Matthew M. Adams; Daniel P. Lathrop

2009-09-11

71

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.

72

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

Rey Juan Carlos, Universidad

73

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

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

2013-02-11

74

NASA Astrophysics Data System (ADS)

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

Ishizaki, Ryuji; Hata, Hiroki; Shoji, Tatsuo

2011-04-01

75

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

76

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

77

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

78

An LPV framework for chaos synchronization in communication

NASA Astrophysics Data System (ADS)

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

Halimi, M.; Millérioux, G.

2014-06-01

79

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

80

Quantitative Assessment of UVA-Riboflavin Corneal Cross-Linking Using Nonlinear Optical Microscopy

Purpose. Corneal collagen cross-linking (CXL) by the use of riboflavin and ultraviolet-A light (UVA) is a promising and novel treatment for keratoconus and other ectatic disorders. Since CXL results in enhanced corneal stiffness, this study tested the hypothesis that CXL-induced stiffening would be proportional to the collagen autofluorescence intensity measured with nonlinear optical (NLO) microscopy. Methods. Rabbit eyes (n = 50) were separated into five groups including: (1) epithelium intact; (2) epithelium removed; (3) epithelium removed and soaked in riboflavin, (4) epithelium removed and soaked in riboflavin, with 15 minutes of UVA exposure; and (5) epithelium removed and soaked in riboflavin, with 30 minutes of UVA exposure. Corneal stiffness was quantified by measuring the force required to displace the cornea 500 ?m. Corneas were then fixed in paraformaldehyde and sectioned, and the collagen autofluorescence over the 400- to 450-nm spectrum was recorded. Results. There was no significant difference in corneal stiffness among the three control groups. Corneal stiffness was significantly and dose dependently increased after UVA (P < 0.0005). Autofluorescence was detected only within the anterior stroma of the UVA-treated groups, with no significant difference in the depth of autofluorescence between different UVA exposure levels. The signal intensity was also significantly increased with longer UVA exposure (P < 0.001). Comparing corneal stiffness with autofluorescence intensity revealed a significant correlation between these values (R2 = 0.654; P < 0.0001). Conclusions. The results of this study indicate a significant correlation between corneal stiffening and the intensity of collagen autofluorescence after CXL. This finding suggests that the efficacy of CXL in patients could be monitored by assessing collagen autofluorescence. PMID:21508101

Chai, Dongyul; Gaster, Ronald N.; Roizenblatt, Roberto; Juhasz, Tibor; Brown, Donald J.

2011-01-01

81

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

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

Fulai, Wang

2012-12-01

82

Modeling and Performance Evaluation of Nonlinear Satellite Links-A Volterra Series Approach

An analytical solution to the problem of modeling bandpass nonlinear channels and evaluating the performance of digital communication systems operating on them is presented. A method based on a Volterra series representation of the overall channel is first proposed, which allows one to extend to nonlinearities with memory the well-known concepts of complex envelope of bandpass signals and low-pass equivalent

S. Benedetto; E. Biglieri; R. Daffara

1979-01-01

83

Dissipative Chaos in Semiconductor Superlattices

We consider the motion of ballistic electrons in a miniband of a semiconductor superlattice (SSL) under the influence of an external, time-periodic electric field. We use the semi-classical balance-equation approach which incorporates elastic and inelastic scattering (as dissipation) and the self-consistent field generated by the electron motion. The coupling of electrons in the miniband to the self-consistent field produces a cooperative nonlinear oscillatory mode which, when interacting with the oscillatory external field and the intrinsic Bloch-type oscillatory mode, can lead to complicated dynamics, including dissipative chaos. For a range of values of the dissipation parameters we determine the regions in the amplitude-frequency plane of the external field in which chaos can occur. Our results suggest that for terahertz external fields of the amplitudes achieved by present-day free electron lasers, chaos may be observable in SSLs. We clarify the nature of this novel nonlinear dynamics in the superlattice-external field system by exploring analogies to the Dicke model of an ensemble of two-level atoms coupled with a resonant cavity field and to Josephson junctions.

Kirill N. Alekseev; Gennady P. Berman; David K. Campbell; Ethan H. Cannon; Matthew C. Cargo

1996-04-29

84

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

85

ERIC Educational Resources Information Center

Presented is an educational game called "The Chaos Game" which produces complicated fractal images. Two basic computer programs are included. The production of fractal images by the Sierpinski gasket and the Chaos Game programs is discussed. (CW)

Barton, Ray

1990-01-01

86

Magnetic field induced dynamical chaos

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

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

2013-12-15

87

Chaos in a fractional order Chua's system

This brief studies the effects of fractional dynamics in chaotic systems. In particular, Chua's system is modified to include fractional order elements. By varying the total system order incrementally from 3.6 to 3.7, it is demonstrated that systems of “order” less than three can exhibit chaos as well as other nonlinear behavior. This effectively forces a clarification of the definition

Tom T. Hartley; Carl F. Lorenzo; Helen Killory Qammer

1995-01-01

88

Stochastic representation of chaos using terminal attractors

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

Michail Zak

2005-01-01

89

ERIC Educational Resources Information Center

Outlines a course on fractal geometry and chaos theory. Discusses how chaos theory and fractal geometry have begun to appear as separate units in the mathematics curriculum and offers an eight unit course by pulling together units related to chaos theory and fractal geometry. Contains 25 references. (ASK)

Bedford, Crayton W.

1998-01-01

90

Coherence and chaos in extended dynamical systems

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

Bishop, A.R.

1994-12-31

91

Tracking Quasiclassical Chaos in Ultracold Boson Gases

We study the dynamics of an ultracold boson gas in a lattice submitted to a constant force. We track the route of the system towards chaos created by the many-body-induced nonlinearity and show that relevant information can be extracted from an experimentally accessible quantity, the gas mean position. The threshold nonlinearity for the appearance of chaotic behavior is deduced from Kolmogorov-Arnold-Moser arguments and agrees with the value obtained by calculating the associated Lyapunov exponent.

Lepers, Maxence; Zehnle, Veronique; Garreau, Jean Claude [Laboratoire de Physique des Lasers, Atomes et Molecules, Universite des Sciences et Technologies de Lille, CNRS, F-59655 Villeneuve d'Ascq Cedex (France)

2008-10-03

92

Lab 8: The onset of chaos Background of chaos

not approximately determine the future. -Edwards Lorenz Chaos Random #12;Chaos theory Chaos theory studies a Tornado in Texas? - Edward Lorentz, AAAS, (1972) Edward Norton Lorenz #12;Applications of Chaos theory. Is there any universal behavior in chaos phenomena? #12;Logistic equation Run LabView program ( ) ( ) ( )1 1x n

Glashausser, Charles

93

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

94

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

95

We propose the following model equation, u(t) + 1/2(u(2)-uu(s))x = f(x,u(s)) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x = 0 for any t ? 0. Here, u(s)(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations. PMID:23521260

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

2013-03-01

96

NASA Astrophysics Data System (ADS)

We present a novel method of preparing highly efficient and stable second-order nonlinear optical (NLO) polymers via chemical cross-linking induced vitrification under electric field. In this method a soluble prepolymer is first prepared that contains cross-linking sites attached to the NLO-active groups. Upon preparing samples of desired thicknesses, the prepolymer is heated (precured) to enable some chemical cross-linking and thus to increase the glass transition temperature (Tg) to an optimum for poling. The precured polymer is then heated above its Tg and subjected to a high electric field to obtain the desired alignment of NLO moieties. Subsequent chemical cross-linking (curing) under electric field continues to advance the Tg and hence leads to in situ vitrification of the polymer that stabilizes the electric-field-induced orientation of the NLO moieties. Detailed results of thermal, linear optical, poling kinetics, and NLO properties are described for the polymer system prepared from tetrafunctional 4-nitro 1,2-phenylenediamine and bifunctional Bisphenol-A diglycidylether as the starting monomers. The polymer which has been cured finally at 140 °C under a very high corona field exhibits d33?14 and d31?3 pm/V, determined from the Maker-fringe experiments. Most significant, however, is the fact that this polymer shows no detectable decay in second harmonic generation for over 500 h under ambient conditions and no tendency of relaxation even at 85 °C.

Eich, Manfred; Reck, Bernd; Yoon, Do Y.; Willson, C. Grant; Bjorklund, Gary C.

1989-10-01

97

Nonlinear Distortion in a Silicon Microring-Based Electro-Optic Modulator for Analog Optical Links

We analyze silicon microring modulators for analog signal generation, in terms of harmonic and intermodulation distortions. Free carrier plasma dispersion effect in silicon, Lorentzian-shaped resonance profile, and cavity photon lifetime are identified as the sources of modulation nonlinearity. Simulations show that the silicon microring modulators exhibit good modulation index and carrier-to-distortion ratio (CDR). For the generation of 10-GHz suboctave analog

Muping Song; Lin Zhang; Raymond G. Beausoleil; Alan E. Willner

2010-01-01

98

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

99

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

100

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

101

Linking Nonlinear Tactile Elements by Cell-Bridge System Takayuki Hoshi and Hiroyuki Shinoda

]-[11]. Almost all of them are arrays of sensor elements that measure only one parameter, averages of pressure], and that sensitivity to the sharpness is a high priority for a human-like sensor skin. Because the sensing theory various touch feelings, and is soft and stretchable. We are developing a tactile sensor array by linking

Shinoda, Hiroyuki

102

Physical white chaos generation

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

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

2014-01-26

103

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

104

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

105

Invoking the muse: Dada's chaos.

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

Rosen, Diane

2014-07-01

106

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

107

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

NASA Astrophysics Data System (ADS)

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.

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

2013-11-01

108

NELSEVIER Physica D 131 (1999) 78-89 Quantum chaos with cesium atoms: pushing the boundaries

of experiments with sodium atoms we observed dynamical localization, a quantum suppression of chaotic diffusion: Quantum chaos; Dynamical localization: Atom optics 1. Introduction The interface between nonlinear localization and quantum chaos with cold sodium atoms, establishing atom optics as a new experimental testing

Texas at Austin. University of

109

Synchronization and generation of chaos in a driven TWT amplifier with delayed feedback

Summary form only given. The application of chaos in communications and radars offer new and interesting possibilities. We report further investigations on the use of traveling wave tube (TWT) amplifiers as sources of chaotic radiation. Chaos can be generated in a TWT amplifier when it is made to operate in a highly nonlinear regime by recirculating a fraction of the

C. Marchewka; P. Larsen; S. Bhattacharjee; N. M. Ryskin; J. H. Booske; V. N. Titov

2004-01-01

110

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

111

Chaos control of parametric driven Duffing oscillators

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

Jin, Leisheng; Mei, Jie; Li, Lijie, E-mail: L.Li@swansea.ac.uk [College of Engineering, Swansea University, Swansea SA2 8PP (United Kingdom)

2014-03-31

112

scientific models derived from nonlinear thought into interpretive approaches within their disciplines. Helen in their efforts at integration that theyprovoked the vitriolic assault of Paul Gross and Norman Levitt a very important stage in contemporary thought. Over a decade has past since Gross and Levitt staged

Sprott, Julien Clinton

113

NASA Astrophysics Data System (ADS)

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

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

2014-06-01

114

Quantum chaos in Aharonov-Bohm oscillations

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

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

1995-10-01

115

Quantum weak chaos in a degenerate system

Quantum weak chaos is studied in a perturbed degenerate system --- a charged particle interacting with a monochromatic wave in a transverse magnetic field. The evolution operator for an arbitrary number of periods of the external field is built and its structure is explored in terms of the QE (quasienergy eigenstates) under resonance condition (wave frequency $=$ cyclotron frequency) in the regime of weak classical chaos. The new phenomenon of diffusion via the quantum separatrices and the influence of chaos on diffusion are investigated and, in the quasi classical limit, compared with its classical dynamics. We determine the crossover from purely quantum diffusion to a diffusion which is the quantum manifestation of classical diffusion along the stochastic web. This crossover results from the non-monotonic dependence of the characteristic localization length of the QE states on the wave amplitude. The width of the quantum separatrices was computed and compared with the width of the classical stochastic web. We give the physical parameters which can be realized experimentally to show the manifestation of quantum chaos in nonlinear acoustic resonance.

V. Ya. Demikhovskii; D. I. Kamenev; G. A. Luna-Acosta

1998-09-27

116

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

117

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

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

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

118

NSDL National Science Digital Library

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

2007-07-18

119

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

120

Chaos in the Classroom: An Application of Chaos Theory.

ERIC Educational Resources Information Center

A review of studies on chaos theory suggests that some elements of the theory (systems, fractals, initial effects, and bifurcations) may be applied to classroom learning. Chaos theory considers learning holistic, constructive, and dynamic. Some researchers suggest that applying chaos theory to the classroom enhances learning by reinforcing…

Trygestad, JoAnn

121

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

122

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

123

Simple Process Equations, Fixed-Point Methods, and Chaos

's method exhibit all of the rich structure of chaos (period doubling, aperiodicity, fractal basin Engineering Clarkson University Potsdarn, NY 13699 Introduction Process simulation has been an important part tripling, fractal basin boundaries, Julia sets, and related properties) on even the simplest nonlinear

Lucia, Angelo

124

Tracking quasi-classical chaos in ultracold boson gases

We study the dynamics of a ultra-cold boson gas in a lattice submitted to a constant force. We track the route of the system towards chaos created by the many-body-induced nonlinearity and show that relevant information can be extracted from an experimentally accessible quantity, the gas mean position. The threshold nonlinearity for the appearance of chaotic behavior is deduced from KAM arguments and agrees with the value obtained by calculating the associated Lyapunov exponent.

Maxence Lepers; Véronique Zehnlé; Jean Claude Garreau

2008-08-05

125

Averages and Critical Exponents in Type-III Intermittent Chaos

The natural measure in a map with type-III intermittent chaos is used to define critical exponents for the average of a variable from a dynamical system near bifurcation. Numerical experiments were done with maps and verify the analytical predictions. Physical experiments to test the usefulness of such exponents to characterize the nonlinearity at bifurcations were done in a driven electronic circuit with diode as nonlinear element. Two critical exponents were measured: $\

Hugo L. D. de S. Cavalcante; J. R. Rios Leite

2003-03-21

126

Application of Chaos Theory to Psychological Models

NASA Astrophysics Data System (ADS)

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

Blackerby, Rae Fortunato

127

Speculations on Nonlinear Speculative Bubbles

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

J. Barkley Rosser

1997-01-01

128

Networked control systems: a perspective from chaos

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

Guofeng Zhang; Tongwen Chen

2014-05-10

129

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

130

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.

131

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

132

Experimental observation of quantum chaos in a beam of light.

The manner in which unpredictable chaotic dynamics manifests itself in quantum mechanics is a key question in the field of quantum chaos. Indeed, very distinct quantum features can appear due to underlying classical nonlinear dynamics. Here we observe signatures of quantum nonlinear dynamics through the direct measurement of the time-evolved Wigner function of the quantum-kicked harmonic oscillator, implemented in the spatial degrees of freedom of light. Our setup is decoherence-free and we can continuously tune the semiclassical and chaos parameters, so as to explore the transition from regular to essentially chaotic dynamics. Owing to its robustness and versatility, our scheme can be used to experimentally investigate a variety of nonlinear quantum phenomena. As an example, we couple this system to a quantum bit and experimentally investigate the decoherence produced by regular or chaotic dynamics. PMID:23169052

Lemos, Gabriela B; Gomes, Rafael M; Walborn, Stephen P; Souto Ribeiro, Paulo H; Toscano, Fabricio

2012-01-01

133

Formation and manipulation of optomechanical chaos via a bichromatic driving

NASA Astrophysics Data System (ADS)

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

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

2014-10-01

134

NASA Astrophysics Data System (ADS)

The characteristics of chaos regions on Europa suggest they may be sites of melt-through from below. They are wide ranging in size, location, and age. The largest are hundreds of kilometers across. Most are similar to Conamara with a matrix reminiscent of frozen slush and often rafts of preexisting crust. Edges are of two types: ramps, perhaps the tapering of crustal thickness to zero, or cliffs, where rafts appear to have broken clear from the shore. The small features called lenticulae generally appear to be small chaoses with textured matrix and occasional rafts, and many domes may be small chaoses raised by isostatic compensation following refreezing of the crust. The extent of chaoses often appears to be limited by ridge systems with the coastline parallel and set back by a distance comparable to the width of the ridge system. Preexisting ridges often survive as causeways or chains of rafts. Boundaries of chaoses are apparently not controlled by preexisting cracks, consistent with formation by a thermal, rather than mechanical, process. Ridges may thicken the crust such that melt-through is more likely (but not always) between ridge systems. Subsequent cracks and ridges form across preexisting chaoses, ranging from fresh cases with few cracks or ridges across them (with paths somewhat jagged as they meander among rafts) to heavily dissected examples. Isolated tilted raft-like blocks surrounded by densely ridged terrain may be relics of former chaotic terrain. Thus two fundamental resurfacing processes have alternated over Europa's geological history: melt-through (at various places and times) forming chaos terrain, and tectonic cracking and dilation building densely ridged and banded terrain. Mapping of chaos features based on morphology at 200 m shows that they correlate, albeit imperfectly, with dark regions in global (2-km resolution) mosaics (except dark regions due to ridge margins or craters). Extrapolating from our mapping of the 5% of Europa covered by appropriate images, at least 18% of the surface of Europa is fresh appearing chaos, an additional 4% is slightly modified chaos, and much more older chaotic terrain has been overprinted by tectonic structures. Considerable area has been available globally to accommodate the expansion of crust that occurs along extensional ridges and bands. Chaos ubiquity suggests that europan geology has been dominated by the effects of having liquid water under a very thin ice shell, with chaos regions being widespread indicators of occasional zero shell thickness.

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

1999-10-01

135

Domain chaos in Rayleigh-Benard convection

NASA Astrophysics Data System (ADS)

Due to the Kuppers-Lortz instability, Rayleigh-Benard convection-patterns exhibit spatio-temporal chaos at the onset of convection when the sample rotates fast enough about a vertical axis. Previous work showed that the scaling of the correlation length xi and frequency f determined from the experimental chaotic patterns disagreed with the prediction from a Ginzburg-Landau weakly-nonlinear model [34]. Commonly the power spectrum of the pattern images (the structure factor) is used to extract xi from the half-width of its peak and f from angle-time correlation functions obtained from the structure factor. Past experiments and simulations used standard Fourier techniques to calculate the power spectrum. On the basis of simulations using the Swift-Hohenberg equation, we show that those results are influenced strongly by the finite image-size available from experiment. In the case of xi, the disagreement between experiment and theory was resolved by using the maximum-entropy method to calculate the power spectra. The maximum-entropy method is not as sensitive to the finite image-size effect. By utilizing this method, we found agreement between experiment and the prediction. In the case of f it was found that the centrifugal force, which is commonly neglected in models of domain chaos, is responsible for the discrepancy between experiment and theory. Furthermore, we discovered a hybrid state consisting of domain chaos in the interior of the sample surrounded by an annulus of radial rolls with gliding defects, which is caused by the centrifugal force. We utilized local wave-director analysis techniques in order to characterize the hybrid state as well as to study local properties of regular domain chaos.

Becker, Nathan

136

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

NASA Astrophysics Data System (ADS)

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

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

2014-06-01

137

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

138

A chaos model of meandering rivers

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

Stoelum, H.H.

1991-03-01

139

Tunneling Mechanism due to Chaos in a Complex Phase Space

We have revealed that the barrier-tunneling process in non-integrable systems is strongly linked to chaos in complex phase space by investigating a simple scattering map model. The semiclassical wavefunction reproduces complicated features of tunneling perfectly and it enables us to solve all the reasons why those features appear in spite of absence of chaos on the real plane. Multi-generation structure of manifolds, which is the manifestation of complex-domain homoclinic entanglement created by complexified classical dynamics, allows a symbolic coding and it is used as a guiding principle to extract dominant complex trajectories from all the semiclassical candidates.

T. Onishi; A. Shudo; K. S. Ikeda; K. Takahashi

2001-05-30

140

NASA Astrophysics Data System (ADS)

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

Bick, Christian; Kolodziejski, Christoph; Timme, Marc

2014-09-01

141

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

142

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

143

-evolving maps Brajendra K. Singh a,b,*, Manoj Gambhir a , Chin-Kun Hu b,c,* a Department of Infectious Disease.1016/j.chaos.2008.02.024 * Corresponding authors. Address: Department of Infectious Disease Epidemiology;to the presence of well-known chaos-generating factors (such as non-linearity), if the process

144

Chaos and Complexity in Psychology, Psyc 198 & 896 Fall, 2007 M W 1:00-2:15 PM Cudahy Hall 131

of the behavior of many virtual decision makers that act according to their own decision rules, but produce-mail: Stephen.guastello@marquette.edu WHAT IS CHAOS THEORY? "Chaos Theory is an alternative name for "nonlinear dynamical systems theory." The latter is an umbrella term for the study of phenomena such as attractors

Sanders, Matthew

145

ON DEVANEY'S DEFINITION OF CHAOS

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

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

1992-01-01

146

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

147

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

148

Chaos Theory and Post Modernism

ERIC Educational Resources Information Center

Chaos theory is often associated with post modernism. However, one may make the point that both terms are misunderstood. The point of this article is to define both terms and indicate their relationship. Description: Chaos theory is associated with a definition of a theory dealing with variables (butterflies) that are not directly related to a…

Snell, Joel

2009-01-01

149

Modeling of nonlinear metamaterials

NASA Astrophysics Data System (ADS)

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

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

2011-10-01

150

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

151

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

152

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

153

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

154

Chaos in hydrodynamic BL Herculis models

NASA Astrophysics Data System (ADS)

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

Smolec, R.; Moskalik, P.

2014-06-01

155

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

156

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

157

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

158

Parametrization of Chaos in the Beam-Wave Interactions

NASA Astrophysics Data System (ADS)

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

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

1997-11-01

159

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

160

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

161

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

162

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

Voolich, Johanna; Devaney, Robert L.

2003-01-01

163

The mathematical structure of Sudoku puzzles is akin to hard constraint satisfaction problems lying at the basis of many applications, including protein folding and the ground-state problem of glassy spin systems. Via an exact mapping of Sudoku into a deterministic, continuous-time dynamical system, here we show that the difficulty of Sudoku translates into transient chaotic behavior exhibited by this system. We also show that the escape rate ?, an invariant of transient chaos, provides a scalar measure of the puzzle's hardness that correlates well with human difficulty ratings. Accordingly, ? = ?log10 ? can be used to define a “Richter”-type scale for puzzle hardness, with easy puzzles having 0 < ? ? 1, medium ones 1 < ? ? 2, hard with 2 < ? ? 3 and ultra-hard with ? > 3. To our best knowledge, there are no known puzzles with ? > 4. PMID:23061008

Ercsey-Ravasz, Mária; Toroczkai, Zoltán

2012-01-01

164

In this paper we report investigations of driven TWT oscillators with delayed feedback as potential sources of wideband, high power, chaotic radiation. We present observations and characterization of chaos when the TWT oscillator is made to operate in a highly nonlinear regime at overdriven feedback. Experimental results on time series as a function of feedback attenuation, phase plots, FFT spectra

S. Hattacharjee; C. Marchewka; J. H. Booske; J. E. Scharer

2003-01-01

165

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

of a linear system. You also may have done or studied an analogous experiment on a resonant series RLC circuit. In this experiment you will study a series resonant RLC circuit, but with one crucial change. In place of using in a nonlinear RLC circuit and to explore with MatLab the approach to chaos demonstrated by the Logistic Equation

Glashausser, Charles

166

Continuous control of ionization wave chaos by spatially derived feedback signals

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

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

1997-01-01

167

Continuous control of ionization wave chaos by spatially derived feedback signals

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

A. Piel; A. Atipo; G. Bonhomme

168

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

ERIC Educational Resources Information Center

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

Wong, Marina

2013-01-01

169

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

LITAK Department of Applied Mechanics, Lublin University of Technology, Nadbystrzycka 36, PL-20 to suspension of vehicles, among others. Keywords: Nonlinear oscillations, Melnikov criterion, Chaos, Non in practical situations as in the suspension of vehicles [Verros et al., 2000; Von Wagner, 2004], among others

Rey Juan Carlos, Universidad

170

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

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

Wajdi M. Ahmad; Ahmad M. Harb

2003-01-01

171

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

172

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS--I: FUNDAMENTAL THEORY AND APPLICATIONS, VOL. 44, NO. 10, OCTOBER 1997 1027 REFERENCES [1] M. J. Ogorzalek, "Taming chaos--Part II: Control," IEEE Trans. Circuits and methodolo- gies in controlling chaotic nonlinear dynamical systems," Int. J. Bifurc. Chaos, vol. 3, pp. 1363

Collins, James J.

173

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

174

NASA Astrophysics Data System (ADS)

The hybrid mid-link spectral inversion (H-MLSI) and digital signal processing techniques to compensate for the optical Kerr effects in 224 Gbit/s DP-16QAM transmission over 640 km of single-mode fiber are numerically evaluated. Digital signal processing methods, i.e., electronic dispersion compensation (EDC) and digital backward propagation (DBP) techniques, are implemented. The system is evaluated for diverse signal input launch powers for both single-channel and multichannel transmission in which five channels are multiplexed with a channel spacing of 100 GHz with central wavelength at 1550 nm. The system performance is enumerated by monitoring the bit error ratio. From the results, it is clear that the nonlinear threshold point is improved by 2 and 3 dBm signal power by using H-MLSI and DBP, respectively, with 20 steps per fiber span as compared to EDC. Furthermore, we have also evaluated the DBP complexity as compared to H-MLSI and the resultant impact on maximum transmission distance. Moreover, the performance penalty coming from the span-offset of H-MLSI can be reduced by employing DBP to compensate for the residual Kerr effects.

Asif, Rameez; Shabbir, Ghulam; Akram, Adeel

2013-09-01

175

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.

176

Global Superdiffusion of Weak Chaos

A class of kicked rotors is introduced, exhibiting accelerator-mode islands (AIs) and {\\em global} superdiffusion for {\\em arbitrarily weak} chaos. The corresponding standard maps are shown to be exactly related to generalized web maps taken modulo an ``oblique cylinder''. Then, in a case that the web-map orbit structure is periodic in the phase plane, the AIs are essentially {\\em normal} web islands folded back into the cylinder. As a consequence, chaotic orbits sticking around the AI boundary are accelerated {\\em only} when they traverse tiny {\\em ``acceleration spots''}. This leads to chaotic flights having a quasiregular {\\em steplike} structure. The global weak-chaos superdiffusion is thus basically different in nature from the strong-chaos one in the usual standard and web maps.

Itzhack Dana

2003-10-20

177

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

178

NASA Astrophysics Data System (ADS)

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

Wang, Shihong; Li, Da; Zhou, Hu

2012-02-01

179

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

180

Scaling invariance for dissipative chaos

NASA Astrophysics Data System (ADS)

It is known that dissipative chaos might satisfy scaling invariance. We discuss this statement from point of view of quantum-classical transition for a model of anharmonic driven dissipative oscillator with time-modulated parameters. We apply the scaling ideology to study the ranges of chaos in quantum and semiclassical dynamics. Chaotic dynamics is analyzed numerically within framework of both the Poincaré section in classical description and the Poincaré section of a single trajectory in quantum description. We concentrate on analysis of nontrivial regimes for which the system has chaotic behavior in quantum treatment, while the dynamics is not chaotic in classical description.

Gevorgyan, T. V.; Manvelyan, S. B.; Shahinyan, A. R.; Kryuchkyan, G. Yu.

2011-09-01

181

Exploration of Order in Chaos with Replica Exchange Monte Carlo

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

Tatsuo Yanagita; Yukito Iba

2008-11-18

182

More memory under evolutionary learning may lead to chaos

NASA Astrophysics Data System (ADS)

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

Diks, Cees; Hommes, Cars; Zeppini, Paolo

2013-02-01

183

Chaos in the library environment

Describes the impact of chaos theory in social systems and the phenomena that result from it, drawing attention to related phenomena in the state of the library today. It then considers the factors that lead library systems to exhibit chaotic behaviour. These factors are the plethora of technological tools and the variety of software and interfaces, the dependence of resource

Anthi Katsirikou; Christos H. Skiadas

2001-01-01

184

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

185

Chaos Theory and James Joyce's

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

Peter Francis Mackey

1995-01-01

186

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.

187

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-period'' 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 10^{12} 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 10^9 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!

M. Lecar; F. Franklin; M. Holman; N. Murray

2001-11-30

188

NASA Technical Reports Server (NTRS)

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

Smyrlis, Yiorgos S.; Papageorgiou, Demetrios T.

1991-01-01

189

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

190

Practical implementation of nonlinear time series methods: The TISEAN package

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

Rainer Hegger; Holger Kantz; Thomas Schreiber

1999-01-01

191

NASA Astrophysics Data System (ADS)

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

192

Does chaos assist localization or delocalization?

NASA Astrophysics Data System (ADS)

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

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

2014-12-01

193

After general considerations about limits of theories and models, where small changes may imply large effects, we discuss three cases in galactic astrophysics illustrating how galactic dynamics models may become insufficient when previously neglected effects are taken into account: 1) Like in 3D hydrodynamics, the non-linearity of the Poisson-Boltzmann system may imply dissipation through the growth of discontinuous solutions. 2) The relationship between the microscopic exponential sensitivity of N-body systems and the stability of mean field galaxy models. 3) The role of quantum physics in the dynamics of structure formation, considering that cosmological neutrinos are massive and semi-degenerate fermions.

Daniel Pfenniger

2008-02-22

194

Chaos and Statistical Mechanics in the Hamiltonian Mean Field Model

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

Vito Latora; Andrea Rapisarda; Stefano Ruffo

1998-03-13

195

Understanding of Arab Spring with Chaos Theory - Uprising or Revolution

NASA Astrophysics Data System (ADS)

`Arab Spring' can be considered as one of the most remarkable events in the history of world politics. On December 18, 2010, a Tunisian young protestor burned himself in a public square of the city. This event triggered probably one of the most chaotic and long term uprisings in the Middle East. From the day of its initiation until the present, `Arab Spring' in the Middle East created unstable political situation and several uprisings. In this chapter, we will first give general information about chaos theory, and then we will examine the `butterfly effect' created by the Tunisian young protestor and process of Arab Spring in the Middle East regarding its extend and form in those countries within the framework of chaos theory. For the first part of this chapter, the spark created by the Tunisian young protestor and its effects can be analyzed under `butterfly effect' perspective within chaos theory, arguing whether the events followed each other consecutively or randomly. The question is whether the incidents following each other have reasonable links of causality to one another, or the events defining the phenomena known as `Arab Spring' have no predictable reasons and outcomes regardless of the regional, social and political differences. The events caused the collapse of the regimes in Tunisia, Egypt and Libya; they had very serious outcomes.

Aç?kal?n, ?uay Nilhan; Bölücek, Cemal Alpgiray

196

Controlling Fast Chaos in Delay Dynamical Systems

We introduce a novel approach for controlling fast chaos in time-delay dynamical systems and use it to control a chaotic photonic device with a characteristic time scale of ~12 ns. Our approach is a prescription for how to implement existing chaos control algorithms in a way that exploits the system's inherent time-delay and allows control even in the presence of substantial control-loop latency (the finite time it takes signals to propagate through the components in the controller). This research paves the way for applications exploiting fast control of chaos, such as chaos-based communication schemes and stabilizing the behavior of ultrafast lasers.

J. N. Blakely; L. Illing; D. J. Gauthier

2004-04-27

197

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

198

Parameter Uncertainties on the Predictability of Periodicity and Chaos

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

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

2014-03-07

199

Haotic, Fractal, and Nonlinear Signal Processing. Proceedings

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

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

1996-10-01

200

Route to chaos in optomechanics.

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. PMID:25615468

Bakemeier, L; Alvermann, A; Fehske, H

2015-01-01

201

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

Boris Chirikov

2005-03-09

202

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

203

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

204

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

205

The quantum to classical crossover for a weak link capacitor

We consider a model weak link, an ultra-small capacitor subject to tunnelling, to ohmic dissipation and fed with an external displacement current. The framework we employ is the new approach of quantum state diffusion, which treats individual open quantum systems as well as being able to generate the conventional ensemble averages. We show how evidence, for archetypal quantum behaviour (coherent oscillations) and archetypal classical behaviour (chaos) arises, for weak links whose parameters are related by a rather modest scaling. Interestingly, the quantum behaviour can arise for a weak link with intrinsic parameter values such that it could exhibit chaos, if it were a purely classical device.

Spiller, T.P.; Clark, T.D.; Prance, H.; Prance, R.J. [Univ. of Sussex (United Kingdom)

1995-12-01

206

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

207

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.

208

The control of chaos: theory and applications

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

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

2000-01-01

209

Chaos in the Quantum Measurement Record

We investigate measures of chaos in the measurement record of a quantum system which is being observed. Such measures are attractive because they can be directly connected to experiment. Two measures of chaos in the measurement record are defined and investigated numerically for the case of a quantum kicked top. A smooth transition between chaotic and regular behavior is found.

M. A. Nielsen

1995-12-09

210

Advising Undecided Students: Lessons from Chaos Theory.

ERIC Educational Resources Information Center

Uses chaos theory as a metaphor for advising undecided college students. Applies chaos theory concepts of dependence on initial conditions, strange attractors, emergent behavior in complex systems, and fractals to the advising relationship. Suggests the paradigm reinforces the basics of advising, such as the importance of accepting the student's…

Beck, Amy

1999-01-01

211

Continuous control of ionization wave chaos by spatially derived feedback signals

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

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

1997-01-27

212

Discretization chaos - Feedback control and transition to chaos

NASA Technical Reports Server (NTRS)

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

Grantham, Walter J.; Athalye, Amit M.

1990-01-01

213

Hydaspis Chaos in Nighttime Infrared

NASA Technical Reports Server (NTRS)

This nighttime infrared image, taken by the thermal emission imaging system, captures a massively disrupted region on Mars called Hydaspis Chaos, which is located near the equator at two degrees north, 29 degrees west. The total vertical difference from the lowest to highest points in this region is about five kilometers (three miles.)

The steep slopes leading down into the canyon of Hydaspsis Chaos are strewn with rocks, while the plateaus and mesas above are covered in dust. This pattern indicates that processes are at work to prevent the dust from completely covering the surface of these slopes, even over the very long period since these canyons were formed.

The slopes and floor of these canyons show remarkable variability in the distribution of rocks and fine-grained material. Chaotic terrain may have been formed when subsurface ground water or ice was removed, and the overlying ground collapsed. The release of this water or ice (or both)formed the outflow channel Tiu Valles, which flowed across the Mars Pathfinder landing site.

This image captures a region of chaotic terrain about 106 kilometers (65 miles) long and 32 kilometers (20 miles) wide. The channel that feeds into the chaos at the bottom of the image is about 7 kilometers (4.3 miles)wide and 280 meters (930 feet) deep. The image was acquired on February 19, 2002. North is to the right of the image.

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 was provided by Arizona State University, Tempe. Lockheed Martin Astronautics, Denver, is the prime contractor for the 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.

2002-01-01

214

The route to chaos for the Kuramoto-Sivashinsky equation

NASA Technical Reports Server (NTRS)

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

Papageorgiou, Demetrios T.; Smyrlis, Yiorgos

1990-01-01

215

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

216

Decoherence, determinism and chaos revisited

NASA Astrophysics Data System (ADS)

We suggest that the derivation of the free space Maxwell Equations for classical electromagnetism, using a discrete ordered calculus developed by L.H. Kauffman and T. Etter, necessarily pushes the discussion of determinism in natural science down to the level of relativistic quantum mechanics and hence renders the mathematical phenomena studied in deterministic chaos research irrelevant to the question of whether the world investigated by physics is deterministic. We believe that this argument reinforces Suppes' contention that the issue of determinism versus indeterminism should be viewed as a Kantian antinomy incapable of investigation using currently available scientific tools.

Noyes, H. P.

217

Markov transitions and the propagation of chaos

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

Gottlieb, A.

1998-12-01

218

Common prescriptions for psychology derived from dialectical materialism and chaos theory.

During the entire Soviet period (1917-1991), Russian psychologists labored to create a psychology which would be consonant with Marxist-Leninist assumptions derived from dialectical materialism. Some of their early prescriptions, in particular those put forward by Konstantin N. Kornilov in the 1920s and early 1930s, are identical to strategies being advanced by contemporary American psychologists who propose that chaos theory and nonlinear meta-modeling techniques in general, given advances in computer and television technologies, can be designed for research capable of dealing with the complexities, nonlinearities, self-organizational processes, and abrupt transformations characteristic of human psychological functioning. PMID:10840901

Gilgen, A R

2000-04-01

219

Chaos detection in the space debris population.

NASA Astrophysics Data System (ADS)

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

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

220

Urban chaos and replacement dynamics in nature and society

Many growing phenomena in both nature and society can be predicted with sigmoid function. The growth curve of the level of urbanization is a typical S-shaped one, and can be described by using logistic function. The logistic model implies a replacement process, and the logistic substitution suggests non-linear dynamical behaviors such as bifurcation and chaos. Using mathematical transform and numerical computation, we can demonstrate that the 1-dimensional map comes from a 2-dimensional two-group interaction map. By analogy with urbanization, a general theory of replacement dynamics is presented in this paper, and the replacement process can be simulated with the 2-dimansional map. If the rate of replacement is too high, periodic oscillations and chaos will arise, and the system maybe breaks down. The replacement theory can be used to interpret various complex interaction and conversion in physical and human systems. The replacement dynamics provides a new way of looking at Volterra-Lotka's predator-prey inte...

Chen, Yanguang

2011-01-01

221

Adapted polynomial chaos expansion for failure detection

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

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

2007-09-10

222

Chaos and Fractals in Human Physiology.

ERIC Educational Resources Information Center

Discusses the irregularity and unpredictability of the human body. Presented are pictures showing the fractallike structures and research findings on the mechanism for chaos in the human body. Lists four further reading materials. (YP)

Goldberger, Ary L.; And Others

1990-01-01

223

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

224

Chaos control in traffic flow models

Chaos control in some of the one- and two-dimensional traffic flow dynamical models in the mean field theory is studied.One dimensional model is investigated taking into account the effect of random delay. Two dimensional model takes into account the effects of overpasses, symmetric distribution of cars and blockages of cars moving in the same direction. Chaos synchronization is performed within both replica and nonreplica approaches, and using parameter perturbation method.

Elman Mohammed Shahverdiev; Shin-ichi Tadaki

1998-11-30

225

Dimensie en Dispersie het `meten' van chaos

.L.P. Cantor Felix Hausdorf (1845-1918) (1868-1942) Chaos Â p.3 #12;Lebesgue en Brouwer Henri Lebesgue L: broer@math.rug.nl URL: http://www.math.rug.nl/~broer Chaos Â p.2 #12;Cantor en Hausdorff Georg F derden Cantor verzameling ln(2) ln(3) bedraagt. En, hoe zit het met de kustlijn van het Koch eiland

Broer, H.W.

226

NASA Astrophysics Data System (ADS)

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

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

2013-12-01

227

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

228

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

229

There is an increasing awareness of the potentials of nonlinear modeling in regional science. This can be explained partly by the recognition of the limitations of conventional equilibrium models in complex situations, and also by the easy availability and accessibility of sophisticated computational techniques. Among the class of nonlinear models, dynamic variants based on, for example, chaos theory stand out

Thomas de Graaff; Raymond J. C. M. Florax; Peter Nijkamp; Aura Reggiani

2001-01-01

230

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

ERIC Educational Resources Information Center

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

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

2008-01-01

231

Study of the non-linear dynamic response of a rotor system with faults and uncertainties

Study of the non-linear dynamic response of a rotor system with faults and uncertainties JÃ©rÃ´me of the non-linear re- sponse in rotor systems with multi-faults (such as unbalance, asymmetric shaft, bow linear problem, it is proposed to use the Harmonic Balance Method (HBM) with a Polynomial Chaos Expansion

Paris-Sud XI, UniversitÃ© de

232

Control of collective network chaos

NASA Astrophysics Data System (ADS)

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

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

2014-06-01

233

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

234

Defect Statistics in Undulation Chaos

NASA Astrophysics Data System (ADS)

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

Daniels, Karen E.; Bodenschatz, Eberhard

2000-03-01

235

Dynamics of monthly rainfall-runoff process at the Gota basin: A search for chaos

NASA Astrophysics Data System (ADS)

Sivakumar et al. (2000a), by employing the correlation dimension method, provided preliminary evidence of the existence of chaos in the monthly rainfall-runoff process at the Gota basin in Sweden. The present study verifies and supports the earlier results and strengthens such evidence. The study analyses the monthly rainfall, runoff and runoff coefficient series using the nonlinear prediction method, and the presence of chaos is investigated through an inverse approach, i.e. identifying chaos from the results of the prediction. The presence of an optimal embedding dimension (the embedding dimension with the best prediction accuracy) for each of the three series indicates the existence of chaos in the rainfall-runoff process, providing additional support to the results obtained using the correlation dimension method. The reasonably good predictions achieved, particularly for the runoff series, suggest that the dynamics of the rainfall-runoff process could be understood from a chaotic perspective. The predictions are also consistent with the correlation dimension results obtained in the earlier study, i.e. higher prediction accuracy for series with a lower dimension and vice-versa, so that the correlation dimension method can indeed be used as a preliminary indicator of chaos. However, the optimal embedding dimensions obtained from the prediction method are considerably less than the minimum dimensions essential to embed the attractor, as obtained by the correlation dimension method. A possible explanation for this could be the presence of noise in the series, since the effects of noise at higher embedding dimensions could be significantly greater than that at lower embedding dimensions.

Sivakumar, B.; Berndtsson, R.; Olsson, J.; Jinno, K.; Kawamura, A.

236

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

237

Outer Solar System on the Edge of Chaos

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

Wayne B. Hayes

2006-01-01

238

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

239

Probability density of the empirical wavelet coefficients of a noisy chaos

NASA Astrophysics Data System (ADS)

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

Garcin, Matthieu; Guégan, Dominique

2014-05-01

240

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

241

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

242

Transition probability from matter-wave soliton to chaos

For a Bose-Einstein condensate loaded into a weak traveling optical superlattice, it is demonstrated that under a stochastic initial set and in a given parameter region, the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically and different chaotic regions associated with different chaos probabilities are found. The results suggest a method for weakening or strengthening chaos by modulating the moving superlattice.

Zhu Qianquan; Hai Wenhua; 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)

2009-07-15

243

Controlling transition probability from matter-wave soliton to chaos

For a Bose-Einstein condensate loaded into a weak traveling optical superlattice it is demonstrated that under a stochastic initial set and in a given parameter region the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically, and different chaotic regions associated with different chaos probabilities are found. The results suggest a feasible method for eliminating or strengthening chaos by modulating the moving superlattice experimentally.

Qianquan Zhu; Wenhua Hai; Shiguang Rong

2008-04-06

244

Chaos Theory as a Model for Managing Issues and Crises.

ERIC Educational Resources Information Center

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

Murphy, Priscilla

1996-01-01

245

REGULAR ARTICLES Food chain chaos due to Shilnikov's orbit

REGULAR ARTICLES Food chain chaos due to Shilnikov's orbit Bo Denga) and Gwendolen Hinesb of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption not be properly understood without understanding the role chaos plays in food chains. Yet chaos generating

Logan, David

246

Chaos in the fractional order Chen system and its control

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

Chunguang Li; Guanrong Chen

2004-01-01

247

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

248

PREDICTION OF CHAOS USING STABILIZATION F'RINCIPLE

In this paper several comments concerning chaos from the viewpoint of theory of stability are made. Special attention is paid to dependence of orbital instability (leading to chaos) upon frames of reference, metrics of configuration space, and class of functions selected for mathematical models of physical phenomena. New representation of chaos is discussed. The theory is illustrated by examples.

Michail Zak; Ronald Meyers

249

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

250

Chaos theory in hydrology: important issues and interpretations

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

B. Sivakumar

2000-01-01

251

Enhancing supply chain solutions with the application of chaos theory

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

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

2006-01-01

252

Emergence of nonlinear behavior in the dynamics of ultracold bosons

We study the evolution of a system of interacting ultracold bosons, which presents nonlinear, chaotic, behaviors in the limit of very large number of particles. Using the spectral entropy as an indicator of chaos and three different numerical approaches : Exact diagonalization, truncated Husimi method and mean-field (Gross-Pitaevskii) approximation, we put into evidence the destructive impact of quantum noise on the emergence of the nonlinear dynamics.

Benoit Vermersch; Jean Claude Garreau

2015-01-28

253

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

254

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

255

Feigenbaum Graphs: A Complex Network Perspective of Chaos

The recently formulated theory of horizontal visibility graphs transforms time series into graphs and allows the possibility of studying dynamical systems through the characterization of their associated networks. This method leads to a natural graph-theoretical description of nonlinear systems with qualities in the spirit of symbolic dynamics. We support our claim via the case study of the period-doubling and band-splitting attractor cascades that characterize unimodal maps. We provide a universal analytical description of this classic scenario in terms of the horizontal visibility graphs associated with the dynamics within the attractors, that we call Feigenbaum graphs, independent of map nonlinearity or other particulars. We derive exact results for their degree distribution and related quantities, recast them in the context of the renormalization group and find that its fixed points coincide with those of network entropy optimization. Furthermore, we show that the network entropy mimics the Lyapunov exponent of the map independently of its sign, hinting at a Pesin-like relation equally valid out of chaos. PMID:21915254

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

2011-01-01

256

Bifurcations and chaos in register transitions of excised larynx experiments

NASA Astrophysics Data System (ADS)

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

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

2008-03-01

257

Controlling chaos in an economic model

NASA Astrophysics Data System (ADS)

A Cournot duopoly, with a bounded inverse demand function and different constant marginal production costs, can be modeled as a discrete-time dynamical system, which exhibits complex bifurcating and chaotic behaviors. Based on some essential features of the model, we show how bifurcation and chaos can be controlled via the delayed feedback control method. We then propose and evaluate an adaptive parameter-tuning algorithm for control. In addition, we discuss possible economic implications of the chaos control strategies described in the paper.

Chen, Liang; Chen, Guanrong

2007-01-01

258

Chaos prediction and control in MEMS resonators

NASA Astrophysics Data System (ADS)

The chaotic dynamics of a micro mechanical resonator with electrostatic forces on both sides is investigated. Using the Melnikov function, an analytical criterion for homoclinic chaos in the form of an inequality is written in terms of the system parameters. Detailed numerical studies including phase portrait, Poincare map and bifurcation diagram confirm the analytical prediction and reveal the effect of excitation amplitude on the system transition to chaos. Moreover a robust adaptive fuzzy control algorithm previously proposed by the authors is applied for controlling the chaotic motion. Additional numerical simulations show the effectiveness of the proposed control approach.

Haghighi, Hossein S.; Markazi, Amir H. D.

2010-10-01

259

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

260

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

261

Low-dimensional chaos in turbulence

NASA Technical Reports Server (NTRS)

Direct numerical simulations are being performed on two different fluid flows in an attempt to discover the mechanism underlying the transition to turbulence in each. The first system is Taylor-Couette flow; the second, two-dimensional flow over an airfoil. Both flows exhibit a gradual transition to high-dimensional turbulence through low-dimensional chaos. The hope is that the instabilities leading to chaos will be easier to relate to physical processes in this case, and that the understanding of these mechanisms can then be applied to a wider array of turbulent systems.

Vastano, John A.

1989-01-01

262

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

263

Transient Hamiltonian chaos in the cavity electrodynamics

We consider the chaotic dynamics of the interaction between an ensemble of two-level atoms in a high-Q Fabry-Perot cavity with a single mode of self-consistent field and with an external amplitude-modulated field. It is shown that in the case of an exact atom-field resonance and at the initial population of the atomic ground state, the Hamiltonian chaos in the system is always transient. The differences in the chaotic dynamics for the Fabry-Perot and ring cavity geometries are considered. The conditions for the experimental observation of the transient Hamiltonian chaos are discussed.

Kirill N. Alekseev; Gennady P. Berman

1998-07-30

264

Topological approximation of the nonlinear Anderson model.

We study the phenomena of Anderson localization in the presence of nonlinear interaction on a lattice. A class of nonlinear 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. PMID:25019865

Milovanov, Alexander V; Iomin, Alexander

2014-06-01

265

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

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

2011-04-11

266

Controlling spatiotemporal chaos and spiral turbulence in excitable media: A review

Excitable media are a generic class of models used to simulate a wide variety of natural systems including cardiac tissue. Propagation of excitation waves in this medium results in the formation of characteristic patterns such as rotating spiral waves. Instabilities in these structures may lead to spatiotemporal chaos through spiral turbulence, which has been linked to clinically diagnosed conditions such as cardiac fibrillation. Usual methods for controlling such phenomena involve very large amplitude perturbations and have several drawbacks. There have been several recent attempts to develop low-amplitude control procedures for spatiotemporal chaos in excitable media which are reviewed in this paper. The control schemes have been broadly classified by us into three types: (i) global, (ii) non-global spatially-extended and (iii) local, depending on the way the control signal is applied, and we discuss the merits and drawbacks for each.

Sitabhra Sinha; S. Sridhar

2007-10-11

267

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

268

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

269

Information encryption and retrieval in mid-RF range using acousto-optic chaos

NASA Astrophysics Data System (ADS)

In recent work, low-frequency AC signal encryption, decryption and retrieval using system-parameter based keys at the receiver stage of an acousto-optic (A-O) Bragg cell under first-order feedback have been demonstrated [1,2]. The corresponding nonlinear dynamics have also been investigated using the Lyapunov exponent and the so-called bifurcation maps [3]. The results were essentially restricted to A-O chaos around 10 KHz, and (baseband) signal bandwidths in the 1-4 KHz range. The results have generally been satisfactory, and parameter tolerances (prior to severe signal distortion at the output) in the +/-5% - +/-10% range have been obtained. Periodic AC waveforms, and a short audio clip have been examined in this series of investigations. Obviously, a main drawback in the above series of simulations has been the low and impractical signal bandwidths used. The effort to increase the bandwidth involves designing a feedback system with much higher chaos frequency that would then be amenable to higher BW information. In this paper, we re-visit the problem for the case where the feedback delay time is reduced considerably, and the system parameters in the transmitter adjusted in order to drive the system with a DC driver bias into chaos. Reducing the feedback time delay to less than 1 ?s, an average chaos frequency of about 10 MHz was achieved after a few trials. For the AC application, a chaos region was chosen that would allow a large enough dynamic range for the width of the available passband. Based on these dynamic choices, periodic AC signals with 1 MHz (fundamental) bandwidth were used for the RF bias driver (along with a DC bias). A triangular wave and a rectangular pulse train were chosen as examples. Results for these cases are presented here, along with comments on the system performance, and the possibility of including (static) images for signal encryption. Overall, the results are encouraging, and affirm the possibility of using A-O chaos for securely transmitting and retrieving information in the mid-RF range (a few 10s of MHz).

Chatterjee, Monish R.; Kundur, Abhinay

2012-06-01

270

In this article we consider singularly perturbed systems of ordinary differential equations having one swift and one n (n = 3) slow variable. Conditions for the existence of attractors of hard turbulence type and of on-off intermittency are formulated. It is shown that any finite-dimensional system with chaos can be complemented so that it will have one dimension more and

A. Yu. Kolesov; N. Kh. Rozov; V. A. Sadovnichiy

2004-01-01

271

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

272

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

R. Newcomb; S. Sathyan

1983-01-01

273

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

274

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

275

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

276

Deterministic representation of chaos in classical dynamics

Chaos in an Anosov-type mechanical system is eliminated by referring the governing equations to a specially selected rapidly oscillating (non-inertial) frame of reference in which the stabilization effect is caused by inertia forces. The result is generalized to any orbitally unstable mechanical system.

M. Zak

1985-01-01

277

Improved particle swarm optimization combined with chaos

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

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

2005-01-01

278

Spatio-Temporal Chaos in Thermal Convection

NASA Astrophysics Data System (ADS)

In this talk I will report on experimental and theoretical results on the pattern-formation processes occuring in Rayleigh-Benard convection (RBC). After an introduction to pattern-formation in extended systems I will introduce RBC and discuss recent andvances in the understanding of spatio-temporal chaos. more details can be found at http://milou.msc.cornell.edu/stc.html

Bodenschatz, Eberhard

1999-11-01

279

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

280

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

281

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

282

Control of chaos in a three-well duffing system

Analytical and numerical results concerning control of chaos in a three-well duffing system with two external excitations are given by using the Melnikov methods proposed by Chacón et al. [Chacón R. General results on chaos suppression for biharmonically driven dissipative systems. Phys Lett A 1999;257:293–300, Chacón R, Palmero F, Balibrea F. Taming chaos in a driven Josephson Junction. Int J

Jianping Yang; Zhujun Jing

2009-01-01

283

Entrainment by Spatiotemporal Chaos in Glow Discharge-Semiconductor Systems

Entrainment of limit cycles by chaos [1] is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach [2], it is verified that the phenomenon is not a chaos synchronization. Simulations demonstrate various aspects of the chaos appearance in both drive and response systems. Chaotic control is through the external circuit equation and governs the electrical potential on the boundary. The expandability of the theory to collectives of glow discharge systems is discussed, and this increases the potential of applications of the results. Moreover, the research completes the previous discussion of the chaos appearance in a glow discharge-semiconductor system [3].

Marat Akhmet; Ismail Rafatov; Mehmet Onur Fen

2014-06-15

284

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

285

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

286

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

287

Stabilization of stochastic cycles and control of noise-induced chaos

NASA Astrophysics Data System (ADS)

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

Bashkirtseva, Irina

2014-04-01

288

Implications of chaos, scale-invariance, and fractal statistics in geology

NASA Technical Reports Server (NTRS)

A set of three nonlinear total differential equations (Lorenz equations) exhibiting deterministic chaos is considered, and it is shown that these equations demonstrate that deterministic equations with deterministic initial conditions can yield stocastic solutions with fractal statistics. The logistic map, fractal distributions, and fragmentation are discussed. It is pointed out that well-defined fractal distributions of earthquakes are found both regionally and globally, and that the general applicability of the fractal relation for seismicity can provide the basis for a quantitative seismic hazard assessment. It is suggested that the governing physics of erosional topography is nonlinear and may be related to a fractal distribution of storms and floods that generate and renew erosional feature such as gullies and drainage systems.

Turcotte, D. L.

1990-01-01

289

Nonlinear control of heart rate variability in human infants.

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 greater than or equal to 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 > or = to 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. PMID:8637921

Sugihara, G; Allan, W; Sobel, D; Allan, K D

1996-01-01

290

Are earthquakes an example of deterministic chaos?

NASA Technical Reports Server (NTRS)

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

Huang, Jie; Turcotte, Donald L.

1990-01-01

291

Noise suppressions in synchronized chaos lidars.

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

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

2010-12-01

292

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

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

Pezard, L; Nandrino, J L

2001-01-01

293

Forecasting Confined Spatiotemporal Chaos with Genetic Algorithms

NASA Astrophysics Data System (ADS)

A technique to forecast spatiotemporal time series is presented. It uses a proper orthogonal or Karhunen-Loève decomposition to encode large spatiotemporal data sets in a few time series, and genetic algorithms to efficiently extract dynamical rules from the data. The method works very well for confined systems displaying spatiotemporal chaos, as exemplified here by forecasting the evolution of the one-dimensional complex Ginzburg-Landau equation in a finite domain.

López, Cristóbal; Álvarez, Alberto; Hernández-García, Emilio

2000-09-01

294

Forecasting confined spatiotemporal chaos with genetic algorithms.

A technique to forecast spatiotemporal time series is presented. It uses a proper orthogonal or Karhunen-Loève decomposition to encode large spatiotemporal data sets in a few time series, and genetic algorithms to efficiently extract dynamical rules from the data. The method works very well for confined systems displaying spatiotemporal chaos, as exemplified here by forecasting the evolution of the one-dimensional complex Ginzburg-Landau equation in a finite domain. PMID:10977996

López, C; Alvarez, A; Hernández-García, E

2000-09-11

295

The Lorenz Attractor, Chaos, And Fluid Flow

Abstract This undergraduate-level thesis investigates the Lorenz Attractor and its associated statistical properties. Chaos is discussed in order better to understand the mathematics,and physics behind this attractor, as it displays chaotic statistics. These statistics are analyzed numerically and graphically. The results are compared,with statistics for a couple of other strange attractors. Some statistical and probabilistic formulas are provided. In addition,

Matthew Carriuolo

296

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

297

of current research at the interface of non- linear and stochastic physics with biology. This volume alsoIntroduction to Focus Issue: Nonlinear and Stochastic Physics in Biology Sonya Bahar, Alexander B://chaos.aip.org/about/rights_and_permissions #12;Introduction to Focus Issue: Nonlinear and Stochastic Physics in Biology Sonya Bahar,1 Alexander B

Showalter, Kenneth

298

Nonlinear deterministic modeling of highly varying loads

Typically, the modeling of highly varying, nonlinear loads such as electric arc furnaces has involved stochastic techniques. This paper presents the use of chaotic dynamics to describe the operation of nonlinear loads. Included is a discussion of the Lyapunov exponents, a measure of chaotic behavior. The alternate approach is applied to electric arc furnaces. A tuning mode is described to develop the parameters of a chaotic model. This model is trained to have time and frequency responses that are tuned to match the current from the arc furnace under study. The simulated data are compared to actual arc furnace data to validate the model. This model is used to assess the impact of various highly varying nonlinear loads that exhibit chaos in power systems.

O`Neill-Carrillo, E.; Heydt, G.T.; Kostelich, E.J. [Arizona State Univ., Tempe, AZ (United States)] [Arizona State Univ., Tempe, AZ (United States); Venkate, S.S. [Iowa State Univ., Ames, IA (United States)] [Iowa State Univ., Ames, IA (United States); Sundaram, A. [EPRI, Palo Alto, CA (United States)] [EPRI, Palo Alto, CA (United States)

1999-04-01

299

A Review and Demonstration of The Essence of Chaos by Edward N. Lorenz

A marvelous exposition on chaos is the book The Essence of Chaos by Dr. Edward N. Lorenz. In this book Dr. Lorenz, famous for his butterfly icon of chaos, gives a detailed description of a new and realistic model of chaos; the sliding of a board (a toboggan to those that live in snowy climes) and a sled down a

Robert Lurie

2009-01-01

300

On an example of genuine quantum chaos Department of Physics

]), there still is no model of a purely quantum--mechanical system with genuine quantum chaos. In order to improve understand a classical dynamical system which can be derived from a purely quantum--mechanical system of the semiquantal model reflects ``true'' chaos in the quantum system. The first question we meet concerns

301

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

302

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

303

Quantum Chaos Fundamental Problems an Application to Material Science

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

Katsuhiro Nakamura

1989-01-01

304

Analysis of Discovery of Chaos: Social and Cognitive Aspects.

ERIC Educational Resources Information Center

The purpose of this study was to examine Edward Lorenz's psychological processes and other environmental aspects in the discovery of chaos at that time. The general concept of chaos is discussed based on relations with previous scientific theories such as Newtonian physics and quantum mechanics. The constraints of discovery in terms of available…

Kim, J. B.

305

Analysis of Chaos-Based Coded Modulations under Intersymbol Interference

Analysis of Chaos-Based Coded Modulations under Intersymbol Interference Francisco J. Escribano's) in channels with time-invariant intersymbol interference (ISI). We use the ISI distance spectrum of the CCM are of potential interest in this kind of distorting environment. Index Terms--Chaos, Intersymbol interference

Rey Juan Carlos, Universidad

306

Applications of chaos and fractals in process systems engineering

Applications of chaos and fractals in engineering in general and in chemical processes in particular are presented. Beginning with the historical perspective and a review of the state-of-the-art literature, various developments in the theory of chaos and fractals in a wide area of physical sciences and engineering with particular emphasis on applications in chemical engineering are discussed and presented. The

Joon Suh Lee; Kun Soo Chang

1996-01-01

307

Chaos in Black Holes Surrounded by Electromagnetic Fields

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

308

Determinisme, Chaos en Toeval Instituut voor Wiskunde en Informatica

://www.math.rug.nl/~broer Chaos Â p.2 #12;Newton en Laplace Isaac Newton Pierre-Simon Laplace (1642-1727) (1749-1827) Zonnestelsel Groningen Chaos Â p.1 #12;Helden - Newton en Laplace - Leibniz en Voltaire - PoincarÃ© en Kolmogorov - Lorenz

Broer, H.W.

309

Are three-frequency quasiperiodic orbits to be expected in typical nonlinear dynamical systems

The current state of theoretical understanding related to the question posed in the title is incomplete. This paper presents results of numerical experiments which are consistent with a positive answer. These results also bear on the problem of characterizing possible routes to chaos in nonlinear dynamical systems.

Grebogi, C.; Ott, E.; Yorke, J.A.

1983-08-01

310

Amplitude death in coupled robust-chaos oscillators

NASA Astrophysics Data System (ADS)

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.

Palazzi, M. J.; Cosenza, M. G.

2014-12-01

311

Amplitude death in coupled robust-chaos oscillators

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

M. J. Palazzi; M. G. Cosenza

2014-03-13

312

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

313

Chaotic Dynamics and Synchronization of Delayed-Feedback Nonlinear Oscillators

We describe a flexible and modular delayed-feedback nonlinear oscillator that is capable of generating a wide range of dynamical behaviours, from periodic oscil- lations to high-dimensional chaos. The oscillator uses electrooptic modulation and fibre-optic transmission, with feedback and filtering implemented through real-time digital-signal processing. We consider two such oscillators that are coupled to one another, and we identify the conditions

Thomas E. Murphy; Adam B. Cohen; Bhargava Ravoori; Karl R. B. Schmitt; Anurag V. Setty; Francesco Sorrentino; Caitlin R. S. Williams; Edward Ott; Rajarshi Roy

314

arXiv:chao-dyn/980601716Jun1998 Ray and wave chaos in asymmetric resonant optical cavities

arXiv:chao-dyn/980601716Jun1998 Ray and wave chaos in asymmetric resonant optical cavities Jens U 06520-8284, USA Published in Nature 385, 45 (1997) Optical resonators are essential components of lasers and other wavelength-sensitive optical devices. A resonator is characterized by a set of modes, each

NÃ¶ckelm, Jens

315

NSDL National Science Digital Library

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

316

Studies of Nonlinear and Chaotic Phenomena in Solid State Systems.

NASA Astrophysics Data System (ADS)

This work consists of three parts linked by the common theme of nonlinear phenomena in solid state systems. Part 1. In this part an experimental study is made of the interactions between spin wave modes excited in a YIG sphere. For certain parameter values one can scan through a series of closely spaced spin wave modes. Excitation can be limited to a small number (1,2,3, dots) of these modes. Interactions between excited modes leads to various dynamical phenomena including auto-oscillations, period -doubling cascades, quasiperiodicity, and chaos. Also observed are irregular relaxation oscillations, abrupt transitions to wideband turbulence, and hysteresis at the Suhl threshold. A theoretical model is developed from first principles. The model is studied analytically and numerically explaining a number of the experimental behavior patterns, including relaxation oscillations and quasiperiodicity. A mechanism for generating microwave subharmonics is discussed. Part 2. This is an experimental study of a forced symmetric oscillator containing a saturable inductor with magnetic hysteresis. It displays a Hopf bifurcation to quasiperiodicity, entrainment horns, and chaos. The bifurcations and hysteresis occurring near points of resonance are compared with Arnold's theory. Much of the behavior relating to the entrainment horns and symmetry properties are explored. An initialization technique is used to observe the manifolds of saddle orbits and other hidden structure. An unusual differential equation model is developed which is irreversible and generates a noninvertible Poincare map of the plane. This planar map has important effects on the behavior observed. The Poincare map is also approximated through experimental measurements. Part 3. This part takes a new look at an old problem, namely the observed "noise rise" in superconducting Josephson junction parametric amplifiers. By exploiting recent insights from dynamical systems theory, it is shown how the interplay of random noise and (nonchaotic) deterministic dynamics can result in a noise rise like that observed in experiments. This analysis leads to a universal first order equation which applies to all similar systems. Several predictions are proposed which can be tested experimentally. An analysis is also made of a previously unexplored mode of operation--a "six-photon" mode associated with a symmetry breaking bifurcation.

Bryant, Paul Henry

317

Chaos in nonautonomous discrete dynamical systems

NASA Astrophysics Data System (ADS)

We consider nonautonomous discrete dynamical systems (I,f) given by sequences {fn} of surjective continuous maps fn:I?I converging uniformly to a map f:I?I. Recently it was proved, among others, that generally there is no connection between chaotic behavior of (I,f) and chaotic behavior of the limit function f. We show that even the full Lebesgue measure of a distributionally scrambled set of the nonautonomous system does not guarantee the existence of distributional chaos of the limit map and conversely, that there is a nonautonomous system with arbitrarily small distributionally scrambled set that converges to a map distributionally chaotic a.e.

Dvo?áková, J.

2012-12-01

318

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

319

Delayed Self-Synchronization in Homoclinic Chaos

The chaotic spike train of a homoclinic dynamical system is self-synchronized by re-inserting a small fraction of the delayed output. Due to the sensitive nature of the homoclinic chaos to external perturbations, stabilization of very long periodic orbits is possible. On these orbits, the dynamics appears chaotic over a finite time, but then it repeats with a recurrence time that is slightly longer than the delay time. The effect, called delayed self-synchronization (DSS), displays analogies with neurodynamic events which occur in the build-up of long term memories.

F. T. Arecchi; R. Meucci; E. Allaria; A. Di Garbo; L. S. Tsimring

2001-09-18

320

NASA Astrophysics Data System (ADS)

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

Zavrazhina, T. V.

2007-10-01

321

NASA Astrophysics Data System (ADS)

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.

Petrov, E. Yu.; Kudrin, A. V.

2012-05-01

322

Chaos, Fractal and Quantum Poincare Recurrences in Diamagnetic Kepler Problem

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

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

2006-08-01

323

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

324

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

325

of a message D. Keil Discrete Structures 7. Information theory, chaos 2/14 10 Â· Definition: "the average number7. Information theory, randomness, chaos D. Keil Discrete Structures 2/14 1D. Keil Discrete Structures 7. Information theory, chaos 2/14 David M. Keil, Framingham State University CSCI 317 Discrete

Keil, David M.

326

Chaos suppression in gas-solid fluidization

The present study examines the effect of an opposing oscillatory flow on local, instantaneous heat transfer and pressure in a laboratory scale gas-fluidized bed. The experimental facility models a Pulsed Atmospheric Fluidized Bed Combustor (PAFBC), a hybrid combustor concept that couples a pulsed combustor with an atmospheric bubbling fluidized bed. Time-varying data were acquired at eight angular positions around a horizontal cylinder submerged in a monodisperse distribution of particles having a weight mean diameter of 345 {micro}m. Total flow rates employed in the present study ranged from 10 to 40% greater than the flow required for minimum fluidization. Spectral analyses of local, instantaneous heat flux and pressure clearly indicate that the bed hydrodynamics were significantly altered by the opposing secondary flow. The behavior of time-varying local pressure and heat transfer in fluidized beds in the absence of a secondary flow is consistent with deterministic chaos. Kolmogorov entropy estimates from local, instantaneous pressure suggest that the degree of chaotic behavior was substantially suppressed for operating conditions with low primary and secondary flow rates, and a secondary flow forcing frequency of 15 Hz. In contrast, entropy estimates from measurements of local, instantaneous heat transfer suggest no clear indication of chaos suppression for these operating conditions.

Pence, D.V.; Beasley, D.E.

1997-07-01

327

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

328

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

329

A topological approximation of the nonlinear Anderson model

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

Alexander V. Milovanov; Alexander Iomin

2014-06-05

330

Joint Entropy Coding and Encryption using Robust Chaos

We propose a framework for joint entropy coding and encryption using Chaotic maps. We begin by observing that the message symbols can be treated as the symbolic sequence of a discrete dynamical system. For an appropriate choice of the dynamical system, we could back-iterate and encode the message as the initial condition of the dynamical system. We show that such an encoding achieves Shannon's entropy and hence optimal for compression. It turns out that the appropriate discrete dynamical system to achieve optimality is the piecewise-linear Generalized Luroth Series (GLS) and further that such an entropy coding technique is exactly equivalent to the popular Arithmetic Coding algorithm. GLS is a generalization of Arithmetic Coding with different modes of operation. GLS preserves the Lebesgue measure and is ergodic. We show that these properties of GLS enable a framework for joint compression and encryption and thus give a justification of the recent work of Grangetto et al. and Wen et al. Both these methods have the obvious disadvantage of the key length being equal to the message length for strong security. We derive measure preserving piece-wise non-linear GLS (nGLS) and their skewed cousins, which exhibit Robust Chaos. We propose a joint entropy coding and encryption framework using skewed-nGLS and demonstrate Shannon's desired sensitivity to the key parameter. Potentially, our method could improve the security and key efficiency over Grangetto's method while still maintaining the total compression ratio. This is a new area of research with promising applications in communications.

Nithin Nagaraj; Prabhakar G Vaidya; Kishor G Bhat

2006-08-22

331

NSDL National Science Digital Library

In this unit plan, primary learners explore the five models of subtraction (counting, sets, number line, balanced equations, and inverse of addition) using concrete (links), pictorial, and verbal representations to develop an understanding of symbolic notations. Students also investigate fact families, including those where one addend is 0 and where the addends are alike and also learn that the order (commutative) property) does not hold for subtraction. A brief bibliography of related books for children is provided. Instead of using hands on manipulatives and balances, links to Java applets: Pan Balance-Shapes and Pan Balance-Numbers ( both cataloged separately) are included. Instructional plan, questions for the students, assessment options, extensions,and teacher reflections are given for each lesson as well as links to down load all student resources.

Burton, Grace M.

2011-01-01

332

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

333

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

334

Controlling spatiotemporal chaos in chains of dissipative Kapitza pendula

NASA Astrophysics Data System (ADS)

The control of chaos (suppression and enhancement) of a damped pendulum subjected to two perpendicular periodic excitations of its pivot (one chaos inducing and the other chaos controlling) is investigated. Analytical (Melnikov analysis) and numerical (Lyapunov exponents) results show that the initial phase difference between the two excitations plays a fundamental role in the control scenario. We demonstrate the effectiveness of the method in suppressing spatiotemporal chaos of chains of identical chaotic coupled pendula where homogeneous regularization is obtained under localized control on a minimal number of pendula. Additionally, we demonstrate the robustness of the control scenario against changes in the coupling function. In particular, synchronization-induced homogeneous regularization of chaotic chains can be highly enhanced by considering time-varying couplings instead of stationary couplings.

Chacón, R.; Marcheggiani, L.

2010-07-01

335

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

NASA Astrophysics Data System (ADS)

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

Kuznetsov, Alexey S.; Kuznetsov, Sergey P.

2013-03-01

336

PREFACE: XI Latin American Workshop on Nonlinear Phenomena

NASA Astrophysics Data System (ADS)

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

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

2010-09-01

337

Nonlinear Landau Zener processes in a periodic driving field

NASA Astrophysics Data System (ADS)

Effects of a periodic driving field on Landau Zener (LZ) processes are studied using a nonlinear two-mode model that describes the mean-field dynamics of a many-body system. A variety of different dynamical phenomena in different parameter regimes of the driving field are discussed and analyzed. These include shifted, weakened, or enhanced phase dependence of nonlinear LZ (NLZ) processes, nonlinearity-enhanced population transfer in the adiabatic limit and Hamiltonian chaos on the mean-field level. The emphasis of this work is based on how the impact of a periodic driving field on LZ processes with self-interaction differs from those without self-interaction. Apart from gaining knowledge of driven NLZ processes, our findings can be used to gauge the strength of nonlinearity and for efficient manipulation of the mean-field dynamics of many-body systems.

Zhang, Qi; Hänggi, Peter; Gong, Jiangbin

2008-07-01

338

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

339

High precision framework for chaos many-body engine

NASA Astrophysics Data System (ADS)

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

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

2014-04-01

340

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

341

ERIC Educational Resources Information Center

Three papers are compiled here for research library directors: (1) "Background: Open Systems Interconnection," in which David F. Bishop provides fundamental background information to explain the concept of the emerging technology of linked systems and open systems interconnection--i.e., an agreed upon standard set of conventions or rules that,…

Association of Research Libraries, Washington, DC.

342

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

343

Food chain chaos due to transcritical point

NASA Astrophysics Data System (ADS)

Chaotic dynamics of a classical prey-predator-superpredator ecological model are considered. Although much is known about the behavior of the model numerically, very few results have been proven analytically. A new analytical result is obtained. It is demonstrated that there exists a subset on which a singular Poincaré map generated by the model is conjugate to the shift map on two symbols. The existence of such a Poincaré map is due to two conditions: the assumption that each species has its own time scale ranging from fast for the prey to slow for the superpredator, and the existence of transcritical points, leading to the classical mathematical phenomenon of Pontryagin's delay of loss of stability. This chaos generating mechanism is new, neither suspected in abstract form nor recognized in numerical experiments in the literature.

Deng, Bo; Hines, Gwendolen

2003-06-01

344

A simple guide to chaos and complexity.

The concepts of complexity and chaos are being invoked with increasing frequency in the health sciences literature. However, the concepts underpinning these concepts are foreign to many health scientists and there is some looseness in how they have been translated from their origins in mathematics and physics, which is leading to confusion and error in their application. Nonetheless, used carefully, "complexity science" has the potential to invigorate many areas of health science and may lead to important practical outcomes; but if it is to do so, we need the discipline that comes from a proper and responsible usage of its concepts. Hopefully, this glossary will go some way towards achieving that objective. PMID:17933949

Rickles, Dean; Hawe, Penelope; Shiell, Alan

2007-11-01

345

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

346

Spatial chaos-based image encryption design

NASA Astrophysics Data System (ADS)

In recent years, the chaos based cryptographic algorithms have suggested some new and efficient ways to develop secure image encryption techniques, but the drawbacks of small key space and weak security in one-dimensional chaotic cryptosystems are obvious. In this paper, permutation and substitution methods are incorporated to present a stronger image encryption algorithm. Spatial chaotic maps are used to realize the position permutation, and to confuse the relationship between the cipher-image and the plain-image. The experimental results demonstrate that the suggested encryption scheme of image has the advantages of large key space and high security; moreover, the distribution of grey values of the encrypted image has a random-like behavior.

Liu, Shutang; Sun, Fuyan

2009-02-01

347

NASA Astrophysics Data System (ADS)

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

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

2014-10-01

348

NASA Astrophysics Data System (ADS)

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

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

2007-09-01

349

The Formation of Aromatum Chaos and the Water Discharge Rate at Ravi Vallis

NASA Astrophysics Data System (ADS)

A sill intrusion into the cryosphere formed Aromatum Chaos. The water flux in the associated Ravi Vallis channel implies that cryosphere disruption allowed water released from a deeper aquifer to elutriate crustal material from Aromatum Chaos.

Leask, H. J.; Wilson, L.; Mitchell, K. L.

2004-03-01

350

Quantum chaos algorithms and dissipative decoherence with quantum trajectories Jae Weon Lee of quantum trajectories we investigate the effects of dissipative decoherence in a quan- tum computer algorithm simulating dynamics in various regimes of quantum chaos including dynamical localization

Shepelyansky, Dima

351

NSDL National Science Digital Library

Prion Links, provided by Eiso AB of the Department of Biochemistry at the University of Groningen (Netherlands), contains 39 diverse links related to prion diseases and research. Although prion research has been going on for over 25 years, the scientific and medical communities have only recently acknowledged the existence of prions and there remains serious debate over their role in a variety of neurological diseases. The name "prion" is derived from "proteinaceous infectious particles," and was coined by Dr. Stanley Prusiner, who discovered the agents and who recently received the Nobel Prize for Medicine for his work. Prions are thought to be the first transmissible and heritable disease-causing agents that lack DNA and RNA. They are composed solely of protein and appear to be the cause of such diseases as kuru and Creutzfeldt-Jakob disease in humans, and bovine spongiform encephalopathies, mad cow disease, and scrapie in sheep and goats.

Ab, Eiso.

1996-01-01

352

NSDL National Science Digital Library

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

Illuminations National Council of Teachers of Math

2008-12-18

353

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

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

2011-01-01

354

Towards a computer-assisted proof for chaos in a forced damped pendulum equation

Towards a computer-assisted proof for chaos in a forced damped pendulum equation Tibor Csendes the computational proof of the chaotic behavior of the forced damped pendulum. Although, chaos for this pendulum properties necessary for complicate chaotic behaviour. Key words: Differential equations, Chaos, Pendulum

Csendes, Tibor

355

FOOD CHAIN CHAOS DUE TO SHILNIKOV'S ORBIT BO DENG AND GWENDOLEN HINES

FOOD CHAIN CHAOS DUE TO SHILNIKOV'S ORBIT BO DENG AND GWENDOLEN HINES Abstract. Assume that the reproduction rate ratio # of the predator over the prey is su#ciently small in a basic triÂtrophic food chain understood without understanding the role chaos plays in food chains. Yet chaos generating mechanisms have

Deng, Bo

356

Chaos in a long-term experiment with a plankton community

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

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

2008-01-01

357

Classical and quantum chaos in a circular billiard with a straight cut

We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. This system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos, as we vary the size of the cut. We use a quantum web to show differences in the quantum manifestations of classical chaos for these three different regimes.

Suhan Ree; L. E. Reichl

1998-07-09

358

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

ERIC Educational Resources Information Center

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

Akmansoy, Vesile; Kartal, Sadik

2014-01-01

359

Fault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machine

Fault diagnosis of sensor timely and accurately is very important to improve the reliable operation of systems. In the study, fault diagnosis of sensor by chaos particle swarm optimization algorithm and support vector machine is presented in the paper, where chaos particle swarm optimization is chosen to determine the parameters of SVM. Chaos particle swarm optimization is a kind of

Chenglin Zhao; Xuebin Sun; Songlin Sun; Ting Jiang

2011-01-01

360

The Implications of Chaos Theory for Strategic Planning in Higher Education.

ERIC Educational Resources Information Center

This paper argues that chaos theory may be a an appropriate framework for strategic planing in higher education and presents a brief case study of a strategic planning process underway at Blue Ridge Community College (BRCC) in Virginia where chaos theory is in use. Chaos theory holds that many seemingly random activities and systems evidence…

Cutright, Marc

361

Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long-time

OFFPRINT Peeping at chaos: Nondestructive monitoring of chaotic systems by measuring long) 40001 www.epljournal.org doi: 10.1209/0295-5075/80/40001 Peeping at chaos: Nondestructive monitoring and chaos PACS 05.60.Cd Â Classical transport Abstract Â One or more small holes provide non-destructive

Dettmann, Carl

362

Nonlinear dynamics in flow through unsaturated fractured-porous media: Status and perspectives

The need has long been recognized to improve predictions of flow and transport in partially saturated heterogeneous soils and fractured rock of the vadose zone for many practical applications, such as remediation of contaminated sites, nuclear waste disposal in geological formations, and climate predictions. Until recently, flow and transport processes in heterogeneous subsurface media with oscillating irregularities were assumed to be random and were not analyzed using methods of nonlinear dynamics. The goals of this paper are to review the theoretical concepts, present the results, and provide perspectives on investigations of flow and transport in unsaturated heterogeneous soils and fractured rock, using the methods of nonlinear dynamics and deterministic chaos. The results of laboratory and field investigations indicate that the nonlinear dynamics of flow and transport processes in unsaturated soils and fractured rocks arise from the dynamic feedback and competition between various nonlinear physical processes along with complex geometry of flow paths. Although direct measurements of variables characterizing the individual flow processes are not technically feasible, their cumulative effect can be characterized by analyzing time series data using the models and methods of nonlinear dynamics and chaos. Identifying flow through soil or rock as a nonlinear dynamical system is important for developing appropriate short- and long-time predictive models, evaluating prediction uncertainty, assessing the spatial distribution of flow characteristics from time series data, and improving chemical transport simulations. Inferring the nature of flow processes through the methods of nonlinear dynamics could become widely used in different areas of the earth sciences.

Faybishenko, Boris

2002-11-27

363

Chaos based encryption system for encrypting electroencephalogram signals.

In the paper, we use the Microsoft Visual Studio Development Kit and C# programming language to implement a chaos-based electroencephalogram (EEG) encryption system involving three encryption levels. A chaos logic map, initial value, and bifurcation parameter for the map were used to generate Level I chaos-based EEG encryption bit streams. Two encryption-level parameters were added to these elements to generate Level II chaos-based EEG encryption bit streams. An additional chaotic map and chaotic address index assignment process was used to implement the Level III chaos-based EEG encryption system. Eight 16-channel EEG Vue signals were tested using the encryption system. The encryption was the most rapid and robust in the Level III system. The test yielded superior encryption results, and when the correct deciphering parameter was applied, the EEG signals were completely recovered. However, an input parameter error (e.g., a 0.00001 % initial point error) causes chaotic encryption bit streams, preventing the recovery of 16-channel EEG Vue signals. PMID:24733526

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

2014-05-01

364

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

Ruoxi Xiang; Michael Small

2014-06-18

365

NASA Astrophysics Data System (ADS)

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

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

2012-12-01

366

NSDL National Science Digital Library

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

367

Genotoxicity of drinking water from Chao Lake

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

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

1999-02-01

368

Time-dependent generalized polynomial chaos

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

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

2010-11-01

369

Planck's quantum-driven integer quantum Hall effect in chaos

The integer quantum Hall effect (IQHE) and chaos are commonly conceived as being unrelated. Contrary to common wisdoms, we find in a canonical chaotic system, the kicked spin-$1/2$ rotor, a Planck's quantum($h_e$)-driven phenomenon bearing a firm analogy to IQHE but of chaos origin. Specifically, the rotor's energy growth is unbounded ('metallic' phase) for a discrete set of critical $h_e$-values, but otherwise bounded ('insulating' phase). The latter phase is topological in nature and characterized by a quantum number ('quantized Hall conductance'). The number jumps by unity whenever $h_e$ decreases passing through each critical value. Our findings, within the reach of cold-atom experiments, indicate that rich topological quantum phenomena may emerge from chaos.

Yu Chen; Chushun Tian

2014-09-18

370

Evidence of Low Dimensional Chaos in Glow Curves of Thermoluminescence

Electron trapping following exposition to ionising radiations and consequent electron release during variation of temperature in solids represent processes happening at the quantum microphysical level. The interesting feature of the thermally stimulated process, that in fact deserves further investigation, is that the dynamic of electrons release during, variation of the temperature, here examined through the so called thermoluminescent Glow Curve, evidences chaotic and fractal regimes. Phase space reconstruction, Correlation Dimension, largest Lyapunov exponent, Recurrence Quantification Analysis(RQA) and fractal dimension analysis, developed by calculation of Hurst exponent, are performed on three samples. The results unequivocally fix that Glow Curves respond to a chaotic regime. RQA supports such results revealing the inner structure of Glow Curve signals in relation to their properties of recurrence, determinism and intermittency signed from laminarity as well as chaos-chaos and chaos order transitions.

Conte, Elio

2008-01-01

371

Evidence of Low Dimensional Chaos in Glow Curves of Thermoluminescence

Electron trapping following exposition to ionising radiations and consequent electron release during variation of temperature in solids represent processes happening at the quantum microphysical level. The interesting feature of the thermally stimulated process, that in fact deserves further investigation, is that the dynamic of electrons release during, variation of the temperature, here examined through the so called thermoluminescent Glow Curve, evidences chaotic and fractal regimes. Phase space reconstruction, Correlation Dimension, largest Lyapunov exponent, Recurrence Quantification Analysis(RQA) and fractal dimension analysis, developed by calculation of Hurst exponent, are performed on three samples. The results unequivocally fix that Glow Curves respond to a chaotic regime. RQA supports such results revealing the inner structure of Glow Curve signals in relation to their properties of recurrence, determinism and intermittency signed from laminarity as well as chaos-chaos and chaos order transitions.

Elio Conte; Joseph P. Zbilut

2008-12-04

372

Chaos in the mixed even-spin models

We consider a disordered system obtained by coupling two mixed even-spin models together. The chaos problem is concerned with the behavior of the coupled system when the external parameters in the two models, such as, temperature, disorder, or external field, are slightly different. It is conjectured that the overlap between two independently sampled spin configurations from, respectively, the Gibbs measures of the two models is essentially concentrated around a constant under the coupled Gibbs measure. Using the extended Guerra replica symmetry breaking bound together with a recent development of controlling the overlap using the Ghirlanda-Guerra identities as well as a new family of identities, we present rigorous results on chaos in temperature. In addition, chaos in disorder and in external field are addressed.

Wei-Kuo Chen

2012-11-30

373

From Hamiltonian chaos to Maxwell`s Demon

The problem of the existence of Maxwell`s Demon (MD) is formulated for systems with dynamical chaos. Property of stickiness of individual trajectories, anomalous distribution of the Poincare recurrence time, and anomalous (non-Gaussian) transport for a typical system with Hamiltonian chaos results in a possibility to design a situation equivalent to the MD operation. A numerical example demonstrates a possibility to set without expenditure of work a thermodynamically non-equilibrium state between two contacted domains of the phase space lasting for an arbitrarily long time. This result offers a new view of the Hamiltonian chaos and its role in the foundation of statistical mechanics. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.

Zaslavsky, G.M. [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012 (United States)] [Courant Institute of Mathematical Sciences, New York University, 251 Mercer St., New York, New York 10012 (United States); [Department of Physics, 2-4 Washington Pl., New York, New York 10003 (United States)

1995-12-01

374

Wave Chaos and Localization in Closed Billiards and Open Scattering Systems : Microwave Experiments

NASA Astrophysics Data System (ADS)

Microwave experiments are described, which are designed to study the signatures of chaos and localization on the quantum properties of model 2-D closed (billiard) and open scattering geometries. A special advantage of the experiments is the ability to directly measure eigenfunctions. In chaotic billiards, the eigenfunctions display universal density distributions and density autocorrelations, in agreement with expressions derived from random matrix theory and from a 0D nonlinear sigma model of supersymmetry. In contrast, wavefunctions in disordered billiards show deviations from universality due to Anderson localization. The systematics of the distribution functions and inverse participation ratios are studied as a function of frequency and localization length. While results in the regime of incipient localization appear to be successfully described by leading expansions of nonlinear sigma models of supersymmetry, the experiments pose challenges to the theory for the strongly localized regime. Results of experiments on open systems, such as chaotic scattering from n-disks, and observation of proximity resonances, are also discussed. References to recent work available at http://sagar.physics.neu.edu note

Sridhar, S.

1998-03-01

375

Planck's Quantum-Driven Integer Quantum Hall Effect in Chaos

NASA Astrophysics Data System (ADS)

We find in a canonical chaotic system, the kicked spin-1 /2 rotor, a Planck's quantum(he)-driven phenomenon bearing a close analogy to the integer quantum Hall effect but of chaos origin. Specifically, the rotor's energy growth is unbounded ("metallic" phase) for a discrete set of critical values of he, but otherwise bounded ("insulating" phase). The latter phase is topological and characterized by a quantum number ("quantized Hall conductance"). The number jumps by unity whenever he passes through each critical value as it decreases. Our findings indicate that rich topological quantum phenomena can emerge from chaos.

Chen, Yu; Tian, Chushun

2014-11-01

376

An improved key agreement protocol based on chaos

NASA Astrophysics Data System (ADS)

Cryptography based on chaos theory has developed fast in the past few years, but most of the researches focus on secret key cryptography. There are few public key encryption algorithms and cryptographic protocols based on chaos, which are also of great importance for network security. We introduce an enhanced key agreement protocol based on Chebyshev chaotic map. Utilizing the semi-group property of Chebyshev polynomials, the proposed key exchange algorithm works like Diffie-Hellman algorithm. The improved protocol overcomes the drawbacks of several previously proposed chaotic key agreement protocols. Both analytical and experimental results show that it is effective and secure.

Wang, Xingyuan; Zhao, Jianfeng

2010-12-01

377

Bifurcations and Spatial Chaos in an Open Flow Model

It is shown that a coupled map model for open flow may exhibit spatial chaos and spatial quasiperiodicity with temporal periodicity. The locations of these patterns, which cover a substantial part of parameter space, are indicated in a comprehensive phase diagram. In order to analyze the encountered phenomena, a novel class of spatial maps is introduced which is very efficient in accurately reproducing the original spatial patterns. It is found that temporally period one spatial chaos is convectively unstable, and that it is possible to predict an essential aspect of the bifurcation behavior of the coupled system solely by considering its corresponding spatial map.

Frederick H. Willeboordse; Kunihiko Kaneko

1993-12-21

378

Chaos in Static Axisymmetric Spacetimes I : Vacuum Case

We study the motion of test particle in static axisymmetric vacuum spacetimes and discuss two criteria for strong chaos to occur: (1) a local instability measured by the Weyl curvature, and (2) a tangle of a homoclinic orbit, which is closely related to an unstable periodic orbit in general relativity. We analyze several static axisymmetric spacetimes and find that the first criterion is a sufficient condition for chaos, at least qualitatively. Although some test particles which do not satisfy the first criterion show chaotic behavior in some spacetimes, these can be accounted for the second criterion.

Y. Sota; S. Suzuki; K. Maeda

1996-02-27

379

Preface to the Focus Issue: Chaos Detection Methods and Predictability

NASA Astrophysics Data System (ADS)

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

Gottwald, Georg A.; Skokos, Charalampos

2014-06-01

380

Nonlinear Dirac equations and nonlinear gauge transformations

Nonlinear Dirac equations (NLDE) are derived through a group N^2 of nonlinear (gauge) transformation acting in the corresponding state space. The construction generalises a construction for nonlinear Schr\\\\\\

H.-D. Doebner; R. Zhdanov

2003-01-01

381

NSDL National Science Digital Library

Here are some links to Astronomy applets, animations, and movies. Celestial and Terrestrial Motions Sky and telescope Interactive Sky Chart Rotating Sky Explorer Ecliptic (Zodiac) Simulator Seasonal Solar Motions Antarctica Time Lapse: A Year on Ice Aurora Australis: The Southern Lights [Daylight Hours Explorer Season as viewed from Space Animation Sun Position and Season animation Paths of the Sun Seasons and Ecliptic Simulator Sun s Rays Simulator Sun Motions Simulator Time-Lapse Seasons Simulator Kepler's Laws of Planetary Motion Kepler s 1st and 2nd laws Applet Orbit Applet Planetary Orbit Simulator Gravity Simulator Moon Phases and Satellite Motions Lunar and Solar Eclipse Information Moon Phase Animation What Causes Tides Lunar Phase Quizzer Eclipse Shadow Simulator Moon Phases and the Horizon Diagram Synodic Lag The Solar System Solar and Heliospheric Observatory (SOHO) Images Planetary Photo Journal Planetary Configuration Simulator Geocentric Retrograde Motion Animation Epicycle / Orbit Applet Gravity Simulator Ptolemaic Orbit of Mars The Universe Virtual Reality Milky Way Panorama Interactive H-R Diagram Element Absorption and Emision Lines Doppler Shift Demonstrator Lookback Time Simulator Other: SpaceWeather.com ...

Teitelbaum, Mr.

2010-11-18

382

Chaos and stochasticity in space plasmas

This special issue of Geophysical Research Letters presents a collection of papers dealing with stochasticity and nonlinear dynamics in space physics. Its 20 papers represent contributions from a large number of research groups and cover a wide range of topics in space plasma research. Despite this diversity and the use of many different methodologies, the papers have as a common

Maha Ashour-Abdalla; Daniel N. Baker

1991-01-01

383

Nonlinear Dynamics, Magnitude-Period Formula and Forecasts on Earthquake

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

Yi-Fang Chang

2008-02-02

384

Stochastic bifurcation and fractal and chaos control of a giant magnetostrictive film–shape memory alloy (GMF–SMA) composite cantilever plate subjected to in-plane harmonic and stochastic excitation were studied. Van der Pol items were improved to interpret the hysteretic phenomena of both GMF and SMA, and the nonlinear dynamic model of a GMF–SMA composite cantilever plate subjected to in-plane harmonic and stochastic excitation was developed. The probability density function of the dynamic response of the system was obtained, and the conditions of stochastic Hopf bifurcation were analyzed. The conditions of noise-induced chaotic response were obtained in the stochastic Melnikov integral method, and the fractal boundary of the safe basin of the system was provided. Finally, the chaos control strategy was proposed in the stochastic dynamic programming method. Numerical simulation shows that stochastic Hopf bifurcation and chaos appear in the parameter variation process. The boundary of the safe basin of the system has fractal characteristics, and its area decreases when the noise intensifies. The system reliability was improved through stochastic optimal control, and the safe basin area of the system increased.

Zhu, Zhiwen, E-mail: zhuzhiwentju@163.com [Department of Mechanics, Tianjin University, Tianjin 300072 (China); Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control, Tianjin 300072 (China); Zhang, Qingxin, E-mail: zqxfirst@163.com; Xu, Jia, E-mail: xujia-ld@163.com [Department of Mechanics, Tianjin University, Tianjin 300072 (China)

2014-05-07

385

Linear and non-linear dynamic models of a geared rotor-bearing system

NASA Technical Reports Server (NTRS)

A three degree of freedom non-linear model of a geared rotor-bearing system with gear backlash and radial clearances in rolling element bearings is proposed here. This reduced order model can be used to describe the transverse-torsional motion of the system. It is justified by comparing the eigen solutions yielded by corresponding linear model with the finite element method results. Nature of nonlinearities in bearings is examined and two approximate nonlinear stiffness functions are proposed. These approximate bearing models are verified by comparing their frequency responses with the results given by the exact form of nonlinearity. The proposed nonlinear dynamic model of the geared rotor-bearing system can be used to investigate the dynamic behavior and chaos.

Kahraman, Ahmet; Singh, Rajendra

1990-01-01

386

A new method for parameter estimation in nonlinear dynamical equations

NASA Astrophysics Data System (ADS)

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

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

2015-01-01

387

A new method for parameter estimation in nonlinear dynamical equations

NASA Astrophysics Data System (ADS)

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

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

2014-02-01

388

Quantum Chaos in Ultracold Collisions of Erbium

Atomic and molecular samples reduced to temperatures below 1 microkelvin, yet still in the gas phase, afford unprecedented energy resolution in probing and manipulating how their constituent particles interact with one another. For simple atoms, such as alkalis, scattering resonances are extremely well-characterized. However, ultracold physics is now poised to enter a new regime, where far more complex species can be cooled and studied, including magnetic lanthanide atoms and even molecules. For molecules, it has been speculated that a dense forest of resonances in ultracold collision cross sections will likely express essentially random fluctuations, much as the observed energy spectra of nuclear scattering do. According to the Bohigas-Giannoni-Schmit conjecture, these fluctuations would imply chaotic dynamics of the underlying classical motion driving the collision. This would provide a paradigm shift in ultracold atomic and molecular physics, necessitating new ways of looking at the fundamental interactions of atoms in this regime, as well as perhaps new chaos-driven states of ultracold matter. In this report we provide the first experimental demonstration that random spectra are indeed found at ultralow temperatures. In the experiment, an ultracold gas of erbium atoms is shown to exhibit many Fano-Feshbach resonances, for bosons on the order of 3 per gauss. Analysis of their statistics verifies that their distribution of nearest-neighbor spacings is what one would expect from random matrix theory. The density and statistics of these resonances are explained by fully-quantum mechanical scattering calculations that locate their origin in the anisotropy of the atoms' potential energy surface. Our results therefore reveal for the first time chaotic behavior in the native interaction between ultracold atoms.

Albert Frisch; Michael Mark; Kiyotaka Aikawa; Francesca Ferlaino; John L. Bohn; Constantinos Makrides; Alexander Petrov; Svetlana Kotochigova

2013-12-06

389

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

NASA Astrophysics Data System (ADS)

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

Adams, Helen M.; Russ, John C.

1992-09-01

390

Fallacies of composition in nonlinear marketing models

NASA Astrophysics Data System (ADS)

In this paper we consider some nonlinear discrete-time dynamic models proposed in the literature to represent marketing competition, and we use these models to critically discuss the statement, often made in economic literature, that identical agents behave identically and quasi-identical ones behave in a similar way. We show, through examples and some general mathematical statements, that the one-dimensional model of a representative agent, whose dynamics summarize the common behavior of identical interacting agents, may be misleading. In order to discuss these topics some simple methods for the study of local stability and bifurcations are employed, as well as numerical examples where some results taken from the literature on chaos synchronization are applied to two-dimensional marketing models that exhibit riddling, blowout and other global phenomena related to the existence of measure-theoretic attractors.

Bischi, Gian Italo; Cerboni Baiardi, Lorenzo

2015-01-01

391

Synchrotron light sources: The search for quantum chaos

A storage ring is a specialized synchrotron in which a stored beam of relativistic electrons produces radiation in the vuv and x-ray regions of the spectrum. High-brightness radiation is used at the ALS to study doubly excited autoionizing states of the helium atom in the search for quantum chaos.

Schlachter, Fred

2001-02-01

392

Routes to Chaos in Resonant Extrasolar Planetary Systems

1 Routes to Chaos in Resonant Extrasolar Planetary Systems John D. Hadjidemetriou1 and George the factors that affect the stability and the long term evolu- tion of a resonant planetary system. For the same resonance, the long term evolution of a resonant planetary system depends on the the relative

Hadjidemetriou, John D.

393

Chaos in Electrophysiology Michael R. Guevara, Department of Physiology and

to chaos, extraction of a one-dimensional map from a time series (return map), exami- nation of the power spectrum for a broadband component, reconstitution from the time series of a geometrical portrait or to a modeller carrying out numerical simulations (e.g. defi- nitions involving the existence of an infinite

Guevara, Michael R.

394

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

J. Lages; D. L. Shepelyansky

2006-01-01

395

Chaos in the coherence collapse of semiconductor lasers

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

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

1988-12-01

396

Food chain chaos due to transcritical point and Gwendolen Hinesb)

Food chain chaos due to transcritical point Bo Denga) and Gwendolen Hinesb) Department.1063/1.1576531 Ecological systems consisting of multiple food chains and webs are extremely difficult to analyze. The role is by studying it in mathematical models of basic food chains of length 3. In this paper we investigate a new

Logan, David

397

Chaos in electrovac and non-Abelian plane wave spacetimes

Superposed electrovac pp-waves causes chaos. To show this, we project the particle geodesics onto the (x,y) plane and simulate the phase space's Poincare section numerically. Similar considerations apply, with minor modifications, to the geodesics in a non-Abelian plane wave spacetime.

Sakalli, I.; Halilsoy, M. [Physics Department, Eastern Mediterranean University, G.Magosa, north Cyprus, via Mersin 10 (Turkey)

2006-09-15

398

Works on an information geometrodynamical approach to chaos

In this paper, I propose a theoretical information-geometric framework suitable to characterize chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Specifically, I present an information-geometric analogue of the Zurek-Paz quantum chaos criterion of linear entropy growth and an information-geometric characterization of regular and chaotic quantum energy level statistics.

Carlo Cafaro

2009-05-27

399

High precision module for Chaos Many-Body Engine

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

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

2014-01-01

400

Group Chaos Theory: A Metaphor and Model for Group Work

ERIC Educational Resources Information Center

Group phenomena and interactions are described through the use of the chaos theory constructs and characteristics of sensitive dependence on initial conditions, phase space, turbulence, emergence, self-organization, dissipation, iteration, bifurcation, and attractors and fractals. These constructs and theoretical tenets are presented as applicable…

Rivera, Edil Torres; Wilbur, Michael; Frank-Saraceni, James; Roberts-Wilbur, Janice; Phan, Loan T.; Garrett, Michael T.

2005-01-01

401

SLAC: A Tool for Addressing Chaos in the Ecology Classroom

ERIC Educational Resources Information Center

Until the early 1970s, ecologists generally assumed that erratic fluctuations observed in natural populations were a product of stochastic noise. It is now known that extremely complex dynamics can arise from basic deterministic processes. This field of study is generally called chaos theory. Here, a computer program, SLAC (Stability, Limits, And…

Hamilton, A. J.

2005-01-01

402

AARB at AACRAO From Ad hocery to Organized Chaos

the AARB Â·Community buy-in and shopping the idea Â·Build on existing governance Â·Role of the EnterpriseAARB at AACRAO From Ad hocery to Organized Chaos: Advisors, Enterprise Architects, Registrars, Division of Enrollment Management Jim Phelps Enterprise Architect, Division of Information Technology

Wisconsin at Madison, University of

403

AARB at WACRAO From Ad hocery to Organized Chaos

AARB at WACRAO From Ad hocery to Organized Chaos: Advisors, Enterprise Architects, Registrars* Enterprise Architect, Division of Information Technology Jeffrey Shokler* Assistant Director for Advising of the moment Â·Buy-in and support from leadership Â·Building on a win #12;AARB - Members Â§ Catherine Farry - L

Wisconsin at Madison, University of

404

Chaos expansion of local time of fractional Brownian motions

We find the chaos expansion of local time l(T)((H))(x, (.)) of fractional Brownian motion with Hurst coefficient H is an element of (0, 1) at a point x is an element of R-d. As an application we show that when H(0)d < 1 then l...

Hu, Yaozhong; Oksendal, B.

2002-07-01

405

Group Chaos Theory: A Metaphor and Model for Group Work

Group phenomena and interactions are described through the use of the chaos theory constructs and characteristics of sensitive dependence on initial conditions, phase space, turbulence, emergence, self-organization, dissipation, iteration, bifurcation, and attractors and fractals. These constructs and theoretical tenets are presented as applicable metaphors to benefit, expand, and enhance group work practice and knowledge. Guidelines are suggested for application, as

Edil Torres Rivera; Michael Wilbur; James Frank-Saraceni; Janice Roberts-Wilbur; Loan T. Phan; Michael T. Garrett

2005-01-01

406

Fingerprint Indexing Based on LAS Registration , Chao Zhang1

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

Hao, Pengwei

407

Ocean Acoustics: a novel laboratory for wave chaos Steven Tomsovic

Ocean Acoustics: a novel laboratory for wave chaos Steven Tomsovic Department of Physics of the propagating sound. I. INTRODUCTION Acoustic wave propagation through the ocean became a topic of immense, acoustic waves offer a means with which to probe the ocean itself. It is possible to monitor bulk mean

Tomsovic, Steve

408

Constrained Quantum Mechanics: Chaos in Non-Planar Billiards

ERIC Educational Resources Information Center

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

Salazar, R.; Tellez, G.

2012-01-01

409

The Origin of Chaos in the Outer Solar System

. This disagreement is resolved by a new analytic theory. The theory shows that the chaos among the jovian planets years). The jovian planets must have entered the resonance after all the gas and most are small ( 10Â3 to 10Â9 ), as are the planet's orbital eccentricities e 10Â2 and inclina- tions i 10Â2 (in

Murray, Norman

410

Toward Therapeutic Autopoiesis: Chaos, Complexity, and Narrative Therapy.

ERIC Educational Resources Information Center

The paradigm of modern psychology has been the determinism of Newtonian physics. That model earns psychology status as a science yet tunnels it to a linear way of unraveling human functioning. Responding to demands for a more holistic approach to psychological practice, it is necessary to redefine the "self" and other terms. Chaos, complexity, and…

Chen, Mei-whei

411

Positive Maladjustment as a Transition from Chaos to Order

ERIC Educational Resources Information Center

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

Laycraft, Krystyna

2009-01-01

412

Continuous control of chaos by self-controlling feedback

Two methods of chaos control with a small time continuous perturbation are proposed. The stabilization of unstable periodic orbits of a chaotic system is achieved either by combined feedback with the use of a specially designed external oscillator, or by delayed self-controlling feedback without using of any external force. Both methods do not require an a priori analytical knowledge of

K. Pyragas

1992-01-01

413

Chaos in Robert Hooke's inverted cone BY MEDERIC ARGENTINA

Chaos in Robert Hooke's inverted cone BY MEÂ´DEÂ´RIC ARGENTINA 1,2 , PIERRE COULLET 1,2 , JEAN UniversiteÂ´ de Nice-Sophia Antipolis, Institut Robert Hooke, Parc Valrose, 06108 Nice Cedex 2, France Robert, Robert Hooke was the first to envisage the design of simple experiments with pendula, presented

Argentina, Mederic

414

Impulsive control and synchronization of spatiotemporal chaos q

Impulsive control and synchronization of spatiotemporal chaos q Anmar Khadra a,1 , Xinzhi Liu a Accepted 10 January 2004 Communicated by Prof. Ji-Huaun He Abstract The impulsive control of spatiotemporal is determined and an estimate for the basin of attraction is given in terms of the impulse durations

Shen, Xuemin "Sherman"

415

Fractal Patterns and Chaos Games Robert L. Devaney

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

Devaney, Robert L.

416

Uncertainty and Predictability in Geophysics: Chaos and Multifractal Insights

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

Lovejoy, Shaun

417

Long simulations of the Solar System: Brouwer's Law and Chaos

Long simulations of the Solar System: Brouwer's Law and Chaos K. R. Grazier W. I. Newman James M of motion for self- gravitating systems, particularly in the context of our Solar System's evolution growth can be attained in 3-D Solar System integrations. Our integrations are such that the positions

Sharp, Philip

418

Inheritance - sex-linked recessive; Genetics - sex-linked recessive; X-linked recessive ... X-linked recessive diseases usually occur in males. Males have only one X chromosome. A single recessive ...

419

Non-linear dynamics and energy transfer

NASA Astrophysics Data System (ADS)

Non-linear dynamics is mostly concerned with coupled anharmonic oscillators, a common situation in the classical description of molecule dynamics. Non-linear systems are in general not integrable, but for small enough energy or couplings most trajectories are quasiperiodic (KAM theorem). As energy (or perturbation) of the N-dimensional system increases, and increasing fraction of trajectories becomes chaotic, i.e. the motion is not restricted to an N-dimensional torus, because the number of action variables is less than N. The onset of chaos is produced by the overlap of resonances, and is increasingly widespread when the energy increases, until finally the only constant of motion is energy. Chaos is characterized by a grassy power spectrum of the trajectory frequencies, and by the exponential rate of divergency of nearby trajectories. In the quasiperiodic regime time evolution of the system can be followed by Fourier expansion of the perturbation in terms of the fundamental frequencies, plus overtones and combinations, while this is not possible in the chaotic regime, although allways one can perform numerical integration of trajectories. Energy transfer in the quasiperiodic regime is caused by few low order resonances, and it is reversible process. Irreversible energy transfer (Relaxation) needs not only chaotic behavior, but also ergodic and mixing. From the chemical point of wiew the interest lies in the study of the resonance conditions and the specific nature of the vibration-rotation couplings that produce V-V and V-R energy transfers. Centrifugal interactions play in general a major role than Coriolis force; vibrations promote chaotic motion more effectively than rotation; resonance conditions are present not only between vibrations, but also with the rotational frequency. These studies can be connected with the unimolecular Chemical Kinetics: The rate of trajectory divergency is an upper limit to the microscopic rate constant when RRKM theory can be applied. Specific examples of those effects are presented for illustrative purposes.

Santamaria, J.

1986-03-01

420

SECULAR CHAOS AND THE PRODUCTION OF HOT JUPITERS

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

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

2011-07-10

421

NASA Astrophysics Data System (ADS)

Nonlinear dynamical systems with irrational and fractional nonlinear restoring forces often occur in both science and engineering, and always lead to a barrier for conventional nonlinear techniques. In this paper, we have investigated the global bifurcations and the chaos directly for a nonlinear system with irrational and fractional nonlinear restoring forces avoiding the conventional Taylor's expansion to retain the natural characteristics of the system. By introducing a particular dimensionless representation and a series of transformations, the two-degree-of-freedom system can be transformed into a perturbed Hamiltonian system. The extended Melnikov method is directly used to detect the chaotic threshold of the perturbed system theoretically, which overcomes the barrier caused by solving theoretical solution for the homoclinic orbit of the unperturbed system. The numerical simulations are carried out to demonstrate the complicated dynamics of the nonlinear spring-pendulum system, which show the efficiency of the criteria for chaotic motion in the system.

Tian, Ruilan; Wu, Qiliang; Xiong, Yeping; Yang, Xinwei; Feng, Wenjie

2014-05-01

422

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

Chen, Sheng-Wei

423

ERIC Educational Resources Information Center

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

Pryor, Robert; Bright, Jim

2004-01-01

424

Competing nonlinearities in quadratic nonlinear waveguide arrays

Competing nonlinearities in quadratic nonlinear waveguide arrays Frank Setzpfandt,1, * Dragomir N demonstrate experimentally the existence of competing focusing and defocusing nonlinearities in a double- tively. If an optical system, however, exhibits so- called competing nonlinearities a laser beam can ex

425

Study of the non-linear dynamic response of a rotor system with faults and uncertainties

NASA Astrophysics Data System (ADS)

In this paper, the quantification of uncertainty effects on the variability of the nonlinear response in rotor systems with multi-faults (such as unbalance, asymmetric shaft, bow, parallel and angular misalignments) is investigated. To take account of uncertainties in this kind of nonlinear problem, it is proposed to use the Harmonic Balance Method (HBM) with a polynomial chaos expansion (PCE). The efficiency and robustness of the proposed methodology is demonstrated by comparison with Monte Carlo simulations (MCS) for different kinds and levels of uncertainties.

Didier, Jérôme; Sinou, Jean-Jacques; Faverjon, Béatrice

2012-01-01

426

Order Amidst Chaos of Star's Explosion

NASA Technical Reports Server (NTRS)

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

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

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

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

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

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

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

2006-01-01

427

NASA Astrophysics Data System (ADS)

The proper orthogonal decomposition (POD) method for analysis of nonlinear panel flutter subjected to supersonic flow is presented. Optimal POD modes are extracted from a chaotic Galerkin mode responses. The aeroelastic equations of motion are constructed using von Karman plate theory, first-order piston theory and quasi-steady thermal stress theory. A simply-supported plate with thermal loads from a uniformly distributed temperature is considered. Many types of panel behaviors, including stable flat, dynamically stable buckled, limit cycle oscillation, nonharmonic periodic motion, quasi-periodic motion and chaotic motion are observed. Our primary focus is on chaos and the route to chaos. It is found that a sudden transition from the buckled state to chaos occurs. Time history, phase portrait, Poincaré map, bifurcation diagram and Lyapunov exponent are employed to study chaos. The POD chaotic results obtained are compared with the traditional Galerkin solutions. It is shown that the POD method can obtain accurate chaotic solutions, using fewer modes and less computational effort than the Galerkin mode approach; additionally, the POD method converges faster in the analysis of chaotic transients. Effects of length-to-width ratios and thermal loads are presented. It is found that a smaller width for fixed length will produce more stable flutter response, while the thermal loads degrade the flutter boundary and result in a more complex evolution of dynamic motions. The numerical simulations show that the robustness of the POD modes depends on the dynamic pressure but not on temperature.

Xie, Dan; Xu, Min; Dai, Honghua; Dowell, Earl H.

2015-02-01

428

Gypsum and Associated Sulfates in Iani Chaos, Mars

NASA Astrophysics Data System (ADS)

We have mapped layered deposits in Iani Chaos, part of the Margaritifer - Ares Valles outflow system in the southern hemisphere of Mars. These deposits have high thermal inertia relative to their surroundings and they often appear bright in visible images. Context Camera (CTX) and High Resolution Imaging Science Experiment (HiRise) data show the deposits to typically have a fractured and polygonal texture at the 1 - 10 m scale and preserve few craters. The deposits are commonly layered at the several meter scale and may form cliffs that are actively eroding into blocks and rockfalls. Three primary deposits of these materials are present in Iani covering a total area of ~6000 km2 (approximately the size of Great Salt Lake). The deposits lie in topographic lows within Iani and form mounds of material 100s of meters high (range ~ 0 - 1 km). Bright, layered deposits are recognized within the mounds that comprise the chaos terrain itself. The layered deposits within the mounds are conformable to exposed layered deposits suggesting that the deposits are exposed by differential weathering (likely along fractures) between the chaos mounds. In central Iani, a second generation of layered deposits embay the eroded mounds of the chaos formation. Analysis of Compact Reconnaissance Imaging Spectrometer for Mars (CRISM) data for this site positively identifies gypsum (CaSO4?H2O) in the post-chaos layered deposits. Sulfates also comprise the chaos terrain itself. The spectra of these sulfates are consistent with kieserite (MgSO4?H2O) in a mixture containing additional minerals. The stratigraphy at Iani requires at least two episodes of sulfate formation, separated by an uncomformity. We propose the following geologic sequence for Iani Chaos: 1) Formation of Mg (and possibly other sulfates and evaporite minerals) by evaporation of water. 3) Emplacement of non-evaporite materials in the region. 4) Formation of chaos terrain, presumably due to subsurface failure. 5) Erosion of chaotic mounds. 6) Formation of gypsum deposits due to the influx and evaporation of additional water. 7) Burial. 8) Exhumation and active erosion of layered deposits. This history requires two major episodes of recharge separated by an uncomformity, consistent with previous geophysical and geomorphic constraints. The meter-scale layering is likely due to fluctuations in water depth on a shorter time scale. The positive identification of gypsum at Iani makes it rare among layered deposits of the Valles Marineris system in which Mg, Fe-rich and other polyhydrated sulfates are documented (gypsum has been previously identified in Iani Chaos and subsequently challenged in the literature; each of these analyses utilized OMEGA data, which is at a coarser spatial resolution than CRISM). The presence of gypsum in Iani may reflect more Ca-rich source waters due to differences in source rocks and/or weathering intensity or duration. Alternatively, potential gypsum deposits associated with other sulfates may be rendered undetectable by CRISM and OMEGA due to their conversion to anhydrite which occurs at ~130°C. The presence of both Mg and Ca sulfates within Iani may be a consequence of different source waters through time or due to different exposures of predicted evaporative sequences by erosion.

Gilmore, M. S.; Greenwood, J. P.

2009-12-01

429

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

Rubin, D.M.

1992-01-01

430

Chaos control in DC arc furnaces powered by parallel DC-DC buck converters

We study the effects of chaos based control of the DC arc furnace operation. The chaos models for DC arc furnace have been proposed in several papers(1,2,3), but until now there is no reference to a control strategy concerning chaotic voltage variation in DC arc furnace operation. There is some practical application of chaos suppression for DC-DC converters. However the

Gherman Lucian; Rusu Anghel Stela; Topor Marcel; Sergiu Mezinescu

2011-01-01

431

Nonlinear Dynamics of Wave Packets and Vortices in Bose-Einstein Condensates

NASA Astrophysics Data System (ADS)

We study the dynamics of single and multi-component Bose-Einstein condensates (BECs) in two dimensions with and without a harmonic trap by using various variants of nonlinear Schrödinger (or Gross-Pitaevskii) equation. Firstly, we examine the three-component repulsive BEC with cubic nonlinearity in a harmonic trap, and see the conservative chaos based on a picture of vortex molecules. We obtain an effective nonlinear dynamics for three vortex cores, which are equivalent to three charged particles under the uniform magnetic field with the repulsive inter-particle potential quadratic in the inter-vortex distance r ij on short length scale and logarithmic in r ij on large length scale. The vortices here acquire the inertia in marked contrast to the standard theory of point vortices since Onsager. We then explore chaos in the three-body problem in the context of vortices with inertia. Secondly, by choosing the nonlinear Schrödinger equation with saturable nonlinearity, we investigate the single and multi-component WP dynamics within the hard-walled square and stadium billiards with neither a harmonic trap nor driving field. We analyze the stability of WPs by using the variational (collective-coordinate) method. By emitting the radiation the Gaussian WP becomes deformed to a bell-shaped one and then stabilized. As the velocity increases, WPs tend to be stable against many collisions with billiard walls.

Nakamura, K.

432

Chaos in Simple Rotation-Translation Models

The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting trajectories in the plane are explored and illustrated in the computer experiments done. Characteristic patterns, egg-shaped forms and central chaotic bulges are present when particles are introduced in the rotating system. The resulting forms and chaotic attractors mainly depend on the form of the nonlinear function expressing the rotation angle. Several cases are studied corresponding to a central force rotation system.

Christos H. Skiadas; Charilaos Skiadas

2007-01-05

433

A Review and Demonstration of The Essence of Chaos by Edward N. Lorenz

A marvelous exposition on chaos is the book The Essence of Chaos by Dr. Edward N. Lorenz. In this book Dr. Lorenz, famous for his butterfly icon of chaos, gives a detailed description of a new and realistic model of chaos; the sliding of a board (a toboggan to those that live in snowy climes) and a sled down a "bumpy" hill (moguls to the snow aficionados). His text shows numerous figures which were calculated by him and this reviewer has formulated the model using Mathematica. This report is an update and expansion from previous arXiv publication (0910.2213).

Robert Lurie

2013-06-03

434

Detection of weak chaos in infant respiration.

This paper concerns the application of newly developed methods for decomposition of an infant respiratory signal into locally stable nonsinusoidal periodic components. Each estimated component has dynamical variation in its three periodicity attributes, i.e., periodicity, scaling factors, and the waveform or pattern associated with the successive segments. Earlier, it has been reported with the application of conventional surrogate analysis and with the cylindrical basis function modeling that the underlying system is distinctly different from linearly filtered Gaussian process, and most probably the human respiratory system behaves as a nonlinear periodic oscillator with two or three degrees of freedom being driven by a high-dimensional noise source. Here, the surrogate analysis is extended and four new types of nonlinear surrogates have been proposed, which are produced by randomizing one or multiple periodicity attributes while preserving certain individual relationships. In this way, a new type of dissection of dynamics is possible, which can lead to a proper understanding of couplings between different controlling parameters. PMID:18244827

Bhattacharya, J

2001-01-01

435

Linking Information to Objects: A Hypertext Prototype for Numismatists.

ERIC Educational Resources Information Center

This report focuses on the user of a prototype hypertext application designed to help coin collectors link ancient coins with relevant numismatic information. It is noted that hypertext systems promote the collection of information that may be multimedia in nature and may be linked so that information can be accessed in a non-linear manner. The…

Moline, Judi

1991-01-01

436

High precision framework for Chaos Many-Body Engine

In this paper we present a C# 4.0 high precision framework for simulation of relativistic many-body systems. In order to benefit from, previously developed, chaos analysis instruments, all new modules were designed to be integrated with Chaos Many-Body Engine [1,3]. As a direct application, we used 46 digits precision for analyzing the Butterfly Effect of the gravitational force in a specific relativistic nuclear collision toy-model. Trying to investigate the average Lyapunov Exponent dependency on the incident momentum, an interesting case of intermittency was noticed. Based on the same framework, other high-precision simulations are currently in progress (e.g. study on the possibility of considering, hard to detect, extremely low frequency photons as one of the dark matter components).

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

2013-12-15

437

Quantum biology on the edge of quantum chaos

We give a new explanation for why some biological systems can stay quantum coherent for long times at room temperatures, one of the fundamental puzzles of quantum biology. We show that systems with the right level of complexity between chaos and regularity can increase their coherence time by orders of magnitude. Systems near Critical Quantum Chaos or Metal-Insulator Transition (MIT) can have long coherence times and coherent transport at the same time. The new theory tested in a realistic light harvesting system model can reproduce the scaling of critical fluctuations reported in recent experiments. Scaling of return probability in the FMO light harvesting complex shows the signs of universal return probability decay observed at critical MIT. The results may open up new possibilities to design low loss energy and information transport systems in this Poised Realm hovering reversibly between quantum coherence and classicality.

Gabor Vattay; Stuart Kauffman; Samuli Niiranen

2012-02-29

438

Entropy for A-coupled-expanding Maps and Chaos

The concept of "$A$-coupled-expanding" map for a transition matrix $A$ has been studied as one of the most important criteria of chaos in the past years. In this paper, the lower bound of the topological entropy for strictly $A$-coupled-expanding maps is studied as a criterion for chaos in the sense of Li-Yorke, which is less conservative and more generalized than the latest result is presented. Furthermore, some conditions for $A$-coupled-expanding maps excluding the strictness to be factors of subshifts of finite type are derived. In addition, the topological entropy of partition-$A$-coupled-expanding map, which is put forward in this paper, is further estimated on compact metric spaces. Particularly, the topological entropy for partition-$A$-coupled-expanding circle maps is given, with that for the Kasner map being calculated for illustration and verification.

Chol-Gyun Ri; Hyon-Hui Ju; Xiaoqun Wu

2013-09-26

439

Stimulus-dependent suppression of chaos in recurrent neural networks

Neuronal activity arises from an interaction between ongoing firing generated spontaneously by neural circuits and responses driven by external stimuli. Using mean-field analysis, we ask how a neural network that intrinsically generates chaotic patterns of activity can remain sensitive to extrinsic input. We find that inputs not only drive network responses, but they also actively suppress ongoing activity, ultimately leading to a phase transition in which chaos is completely eliminated. The critical input intensity at the phase transition is a nonmonotonic function of stimulus frequency, revealing a 'resonant' frequency at which the input is most effective at suppressing chaos even though the power spectrum of the spontaneous activity peaks at zero and falls exponentially. A prediction of our analysis is that the variance of neural responses should be most strongly suppressed at frequencies matching the range over which many sensory systems operate.

Rajan, Kanaka; Abbott, L. F.; Sompolinsky, Haim [Lewis-Sigler Institute for Integrative Genomics, Icahn 262, Princeton University, Princeton, New Jersey 08544 (United States); Department of Neuroscience and Department of Physiology and Cellular Biophysics, College of Physicians and Surgeons, Columbia University, New York, New York 10032-2695 (United States); Racah Institute of Physics, Interdisciplinary Center for Neural Computation, Hebrew University, Jerusalem (Israel)

2010-07-15

440

Quantum Biology on the Edge of Quantum Chaos

We give a new explanation for why some biological systems can stay quantum coherent for a long time at room temperature, one of the fundamental puzzles of quantum biology. We show that systems with the right level of complexity between chaos and regularity can increase their coherence time by orders of magnitude. Systems near Critical Quantum Chaos or Metal-Insulator Transition (MIT) can have long coherence times and coherent transport at the same time. The new theory tested in a realistic light harvesting system model can reproduce the scaling of critical fluctuations reported in recent experiments. Scaling of return probability in the FMO light harvesting complex shows the signs of universal return probability decay observed at critical MIT. The results may open up new possibilities to design low loss energy and information transport systems in this Poised Realm hovering reversibly between quantum coherence and classicality. PMID:24603620

Vattay, Gabor; Kauffman, Stuart; Niiranen, Samuli

2014-01-01

441

Chaos in the courtroom reconsidered: emotional bias and juror nullification.

A widespread presumption in the law is that giving jurors nullification instructions would result in "chaos"-jurors guided not by law but by their emotions and personal biases. We propose a model of juror nullification that posits an interaction between the nature of the trial (viz. whether the fairness of the law is at issue), nullification instructions, and emotional biases on juror decision-making. Mock jurors considered a trial online which varied the presence a nullification instructions, whether the trial raised issues of the law's fairness (murder for profit vs. euthanasia), and emotionally biasing information (that affected jurors' liking for the victim). Only when jurors were in receipt of nullification instructions in a nullification-relevant trial were they sensitive to emotionally biasing information. Emotional biases did not affect evidence processing but did affect emotional reactions and verdicts, providing the strongest support to date for the chaos theory. PMID:16786405

Horowitz, Irwin A; Kerr, Norbert L; Park, Ernest S; Gockel, Christine

2006-04-01

442

Large-Scale Chaos and Fluctuations in Active Nematics

NASA Astrophysics Data System (ADS)

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations describing these systems and of the self-propelled particle model they were derived from. We prove, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations. Revisiting the status of the strong fluctuations and long-range correlations in the particle model, we show that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation. However anomalous, curvature-driven number fluctuations are present in the homogeneous quasiordered nematic phase and characterized by a nontrivial scaling exponent.

Ngo, Sandrine; Peshkov, Anton; Aranson, Igor S.; Bertin, Eric; Ginelli, Francesco; Chaté, Hugues

2014-07-01

443

Transition to chaos in an open unforced 2D flow

NASA Technical Reports Server (NTRS)

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

Pulliam, Thomas H.; Vastano, John A.

1993-01-01

444

Catastrophic ice lake collapse in Aram Chaos, Mars

Hesperian chaotic terrains have been recognized as the source of outflow channels formed by catastrophic outflows. Four main scenarios have been proposed for the formation of chaotic terrains that involve different amounts of water and single or multiple outflow events. Here, we test these scenarios with morphological and structural analyses of imagery and elevation data for Aram Chaos in conjunction with numerical modeling of the morphological evolution of the catastrophic carving of the outflow valley. The morphological and geological analyses of Aram Chaos suggest large-scale collapse and subsidence (1500 m) of the entire area, which is consistent with a massive expulsion of liquid water from the subsurface in one single event. The combined observations suggest a complex process starting with the outflow of water from two small channels, followed by continuous groundwater sapping and headward erosion and ending with a catastrophic lake rim collapse and carving of the Aram Valley, which is synchronous with ...

Roda, Manuel; Zegers, Tanja E; Oosthoek, Jelmer H P

2014-01-01

445

Computational complexity of symbolic dynamics at the onset of chaos

NASA Astrophysics Data System (ADS)

In a variety of studies of dynamical systems, the edge of order and chaos has been singled out as a region of complexity. It was suggested by Wolfram, on the basis of qualitative behavior of cellular automata, that the computational basis for modeling this region is the universal Turing machine. In this paper, following a suggestion of Crutchfield, we try to show that the Turing machine model may often be too powerful as a computational model to describe the boundary of order and chaos. In particular we study the region of the first accumulation of period doubling in unimodal and bimodal maps of the interval, from the point of view of language theory. We show that in relation to the ``extended'' Chomsky hierarchy, the relevant computational model in the unimodal case is the nested stack automaton or the related indexed languages, while the bimodal case is modeled by the linear bounded automaton or the related context-sensitive languages.

Lakdawala, Porus

1996-05-01

446

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

We aim at assessing the validity limits of some simplifying hypotheses that, within a Riemmannian geometric framework, have provided an explanation of the origin of Hamiltonian chaos and have made it possible to develop a method of analytically computing the largest Lyapunov exponent of Hamiltonian systems with many degrees of freedom. Therefore, a numerical hypotheses testing has been performed for the Fermi-Pasta-Ulam beta model and for a chain of coupled rotators. These models, for which analytic computations of the largest Lyapunov exponents have been carried out in the mentioned Riemannian geometric framework, appear as paradigmatic examples to unveil the reason why the main hypothesis of quasi-isotropy of the mechanical manifolds sometimes breaks down. The breakdown is expected whenever the topology of the mechanical manifolds is nontrivial. This is an important step forward in view of developing a geometric theory of Hamiltonian chaos of general validity. PMID:18999506

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

2008-10-01

447

A simple method to improve a torsion pendulum for studying chaos

NASA Astrophysics Data System (ADS)

In this paper, the dynamic process from period-doubling bifurcations to chaos is observed by changing the driving period of a modified Pohl’s torsion pendulum that formally exhibits periodical dynamics. A data acquisition system with a CCD camera connected to a computer and corresponding image processing software is designed to exhibit the dynamics of the modified pendulum automatically by recording the oscillating angle of the copper rotating wheel. As a result, abundant chaotic sequence diagrams and phase diagrams can be clearly seen in real time. In our experiment, we come up with a simple method simply by adding a fine iron bar with a matching nut on a Pohl’s torsion pendulum to improve the existing apparatus. As a result, the experiment itself is feasible—it is easy, cheap, and convenient to carry out—which allows undergraduate students to observe and to understand the unpredictability of deterministic mechanical systems and at the same time stimulates their interest in nonlinear dynamics and related experiments.

Miao, Congcong; Luo, Wu; Ma, Yaqi; Liu, Weiqing; Xiao, Jinghua

2014-09-01

448

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

Edward H. Hellen; J. Keith Thomas

2010-01-14

449

NASA Astrophysics Data System (ADS)

Randomly connected networks of neurons exhibit a transition from fixed-point to chaotic activity as the variance of their synaptic connection strengths is increased. In this study, we analytically evaluate how well a small external input can be reconstructed from a sparse linear readout of network activity. At the transition point, known as the edge of chaos, networks display a number of desirable features, including large gains and integration times. Away from this edge, in the nonchaotic regime that has been the focus of most models and studies, gains and integration times fall off dramatically, which implies that parameters must be fine tuned with considerable precision if high performance is required. Here we show that, near the edge, decoding performance is characterized by a critical exponent that takes a different value on the two sides. As a result, when the network units have an odd saturating nonlinear response function, the falloff in gains and integration times is much slower on the chaotic side of the transition. This means that, under appropriate conditions, good performance can be achieved with less fine tuning beyond the edge, within the chaotic regime.

Toyoizumi, T.; Abbott, L. F.

2011-11-01

450

Chaos in electronic circuits and studies of bifurcation mechanisms

NASA Astrophysics Data System (ADS)

We study the chaotic memristic circuit proposed by Chua and Muthuswamy and analyze the behavior of the voltage of the memristor, capacitor and that of electric currents. We add harmonic voltage to the memristor, and study nature of Strange Nonchaotic Attractor (SNA) and soft chaos. We compare the chaotic circuit proposed by Chua, Komuro and Matsumoto in 1986, and that we analyzed in 2008, and whose SNA was observed by Zhu and Liu in 1997.

Furui, Sadataka

2013-10-01

451

Chaos in the North Caucasus and Russia's future

Chechen-style turmoil is spreading across the rest of the North Caucasus, and the Kremlin seems incapable of coping with the mounting chaos, or even understanding its causes - among them poverty, unemployment, ethnic tensions, corrupt pro-Moscow elites and high-handed policies by local authorities. Islam has become an increasingly powerful political force, and some Islamist groups are unquestionably radical and violent,

John B. Dunlop; Rajan Menon

2006-01-01

452

Chaos synchronization of the Chua system with a fractional order

Chaos synchronization of two identical Chua systems with the same fractional order is studied by utilizing the Pecora–Carroll (PC) method, the active–passive decomposition (PAD) method, the one-way coupling method and the bidirectional coupling one. The sufficient conditions for achieving synchronization between these two systems are derived via the Laplace transformation theory. Numerical simulations show the effectiveness of the theoretical analyses.

C. P. Li; W. H. Deng; D. Xu

2006-01-01

453

Optimizing Hydropower Reservoir Operation Using Hybrid Genetic Algorithm and Chaos

Genetic algorithms (GA) have been widely applied to solve water resources system optimization. With the increase of the complexity\\u000a and the larger problem scale of water resources system, GAs are most frequently faced with the problems of premature convergence,\\u000a slow iterations to reach the global optimal solution and getting stuck at a local optimum. A novel chaos genetic algorithm\\u000a (CGA)

Chun-Tian Cheng; Wen-Chuan Wang; Dong-Mei Xu; K. W. Chau

2008-01-01

454

Ionization waves: from stability to chaos and turbulence

NASA Astrophysics Data System (ADS)

The spatio-temporal dynamics of self-excited ionization waves in a neon glow discharge is experimentally investigated. Various mechanisms leading to ionization waves chaos and turbulence are identified: subharmonics cascade, Ruelle-Takens-Newhouse scenario, and spatio-temporal intermittency. The dynamical states involved in the transition scenarios from stability to chaotic regimes are characterized through both temporal and spatio-temporal analysis by means of the Biorthogonal Decomposition (BD).

Atipo, A.; Bonhomme, G.; Pierre, T.

2002-04-01

455

On non-extensive statistics, chaos and fractal strings

Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics (with a non-additive q-entropy) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics

C. Castro

2005-01-01

456

Chaos in East European black market exchange rates

In this paper we test for deterministic chaos in seven East European black market exchange rates, using Koedijk and Kool's (1992, Journal of Business and Economic Statistics, 10, 83-96) monthly data from January 1955 through May 1990. In doing so we use three (non-parametric) inference methods, the BDS (Brocket al., 1996, Econometric Reviews, 15, 197-235) test for whiteness, the Lyapunov

APOSTOLOS SERLETIS; PERIKLIS GOGAS

1997-01-01

457

Bifurcation and Chaos in a Model of Cardiac Early Afterdepolarizations

NASA Astrophysics Data System (ADS)

Excitable cells can exhibit complex patterns of oscillations, such as spiking and bursting. In cardiac cells, pathological voltage oscillations, called early afterdepolarizations (EADs), have been widely observed under disease conditions, yet their dynamical mechanisms remain unknown. Here, we show that EADs are caused by Hopf and homoclinic bifurcations. During period pacing, chaos always occurs at the transition from no EAD to EADs as the stimulation frequency decreases, providing a distinct explanation for the irregular EAD behavior frequently observed in experiments.

Tran, Diana X.; Sato, Daisuke; Yochelis, Arik; Weiss, James N.; Garfinkel, Alan; Qu, Zhilin

2009-06-01

458

Ionization waves: from stability to chaos and turbulence

The spatio-temporal dynamics of self-excited ionization waves in a neon glow discharge is experimentally investigated. Various\\u000a mechanisms leading to ionization waves chaos and turbulence are identified: subharmonics cascade, Ruelle-Takens-Newhouse scenario,\\u000a and spatio-temporal intermittency. The dynamical states involved in the transition scenarios from stability to chaotic regimes\\u000a are characterized through both temporal and spatio-temporal analysis by means of the Biorthogonal Decomposition

A. Atipo; G. Bonhomme; T. Pierre

2002-01-01

459

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

NASA Astrophysics Data System (ADS)

The physics of non-linear phenomena has developed in a remarkable way over the last couple of decades and has accelerated over the last few years, in particular because of the recent progress in the study of chaotic behaviour. In particular the discovery of the universal properties of the transition into chaos for certain classes of systems has stimulated much recent work in different directions both theoretically and experimentally. Chaos theory has become a real challenge to physicists in many different fields and also in many other disciplines such as astronomy, chemistry, medicine, meteorology and economics and social theory. The study of chaos-related phenomena has a truly interdisciplinary character and makes use of important concepts and methods from other disciplines. For the description of chaotic structures one needs a new, recently developed geometry called fractal geometry. For the discussion of the enormous richness of ordered structures which appear, one uses the theory of pattern recognition. In order to study even the simplest theoretical models describing chaos, a computer is essential. It should finally be mentioned that important aspects of computer science are related to the theory of order and chaos. A Nobel Symposium provides an excellent opportunity to bring together a group of prominent scientists for a stimulating exchange of new ideas and results. The Nobel Symposia are very small meetings by invitation only and the number of key participants is typically in the range 20-40. These symposia are organized through a special Nobel Symposium Committee after proposals from individuals. This symposium was sponsored by the Nobel Foundation through its Nobel Symposium Fund with grants from The Tercentenary Fund of the Bank of Sweden and The Knut Alice Wallenberg Foundation. Additional support was obtained from the Royal Academy of Sciences, The Nordic Institute for Theoretical Atomic Physics (NORDITA), Chalmers University of Technology and Gothenburg University. The idea to arrange a Nobel symposium on the physics of chaos and related problems came up more than three years ago. The rapid progress in the field since then seemed a bit frightening, to say the least, in view of the small format of the meeting. Nevertheless, we found the idea attractive - provided that we could restrict the programme to a few selected topics of current interest in order to generate a strong interaction between the participants and produce an intensive discussion. I feel that I need to express my apologies to all prominent scientists who could not be invited as a result of our planning. In the first place we did not attempt to review areas which seemed to be well established and have reached a certain level of maturity or saturation, irrespective of how great the individual contributions might have been. We decided firmly to concentrate on just a few of the recent developments which seemed to be in the focus of interest, deliberately leaving out important areas equally exciting. These proceedings contain practically all the material presented in the papers given at the Symposium. We felt that some participants might have found it inconvenient to prepare a full-length paper, which in some cases would have been merely modified versions of material due to appear in regular journals. We therefore took a liberal attitude and accepted everything from a brief abstract with some key references, up to a full-length paper. We would like to place on record our sincere thanks to all the participants who have contributed substantially in the planning of the Symposium by making valuable comments and suggestions about participants and topics. In particular, Jerry Gollub and Pierre Hohenberg helped me in organizing the programme and they also did a beautiful job with the concluding session and the conference summary. My co-organizers played a crucial role in the planning and during the Symposium week and always seemed to show an outstanding patience with my often rather chaotic actions. Our secretary, Yvonne Steen, deserves very special thank

Lundqvist, Stig

1985-01-01

460

New Nonlinear Multigrid Analysis

NASA Technical Reports Server (NTRS)

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

Xie, Dexuan

1996-01-01

461

Tutorials in Contemporary Nonlinear Methods for the Behavioral Sciences

... these PDF files and is available from the NSF Help Center. Tutorials in Contemporary Nonlinear ... Policies and Important Links | Privacy | FOIA | Help | Contact NSF | Contact Web Master | SiteMap ...

462

Bifurcation and control of chaos in Induction motor drives

The induction motor controlled by Indirect Field Oriented Control (IFOC) is known to have high performance and better stability. This paper reports the dynamical behavior of an indirect field oriented control (IFOC) induction motor drive in the light of bifurcation theory. The speed of high performance induction motor drive is controlled by IFOC method. The knowledge of qualitative change of the behavior of the motor such as equilibrium points, limit cycles and chaos with the change of motor parameters and load torque are essential for proper control of the motor. This paper provides a numerical approach to understand better the dynamical behavior of an indirect field oriented control of a current-fed induction motor. The focus is on bifurcation analysis of the IFOC motor, with a particular emphasis on the change that affects the dynamics and stability under small variations of Proportional Integral controller (PI) parameters, load torque and k, the ratio of the rotor time constant and its estimate etc. Bifurcation diagrams are computed. This paper also attempts to discuss various types of the transition to chaos in the induction motor. The results of the obtained bifurcation simulations give useful guidelines for adjusting both motor model and PI controller parameters. It is also important to ensure desired operation of the motor when the motor shows chaotic behavior. Infinite numbers of unstable periodic orbits are embedded in a chaotic attractor. Any unstable periodic orbit can be stabilized by proper control algorithm. The delayed feedback control method to control chaos has been implemented in this system.

Krishnendu Chakrabarty; Urmila Kar

2014-10-24

463

A period-doubling cascade precedes chaos for planar maps

NASA Astrophysics Data System (ADS)

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

Sander, Evelyn; Yorke, James A.

2013-09-01

464

Bursting, beating, and chaos in an excitable membrane model.

We have studied periodic as well as aperiodic behavior in the self-sustained oscillations exhibited by the Hodgkin-Huxley type model of Chay, T. R., and J. Keizer (Biophys. J., 1983, 42:181-190) for the pancreatic beta-cell. Numerical solutions reveal a variety of patterns as the glucose-dependent parameter kCa is varied. These include regimes of periodic beating (continuous spiking) and bursting modes and, in the transition between these modes, aperiodic responses. Such aperiodic behavior for a nonrandom system has been called deterministic chaos and is characterized by distinguishing features found in previous studies of chaos in nonbiophysical systems and here identified for an (endogenously active) excitable membrane model. To parallel the successful analysis of chaos in other physical/chemical contexts we introduce a simplified, but quantitative, one-variable, discrete-time representation of the dynamics. It describes the evolution of intracellular calcium (which activates a potassium conductance) from one spike upstroke to the next and exhibits the various modes of behavior. PMID:3884058

Chay, T R; Rinzel, J

1985-01-01

465

We have developed the {\\it general method} for the description of {\\it separatrix chaos}, basing on the analysis of the separatrix map dynamics. Matching it with the resonant Hamiltonian analysis, we show that, for a given amplitude of perturbation, the maximum width of the chaotic layer in energy may be much larger than it was assumed before. We apply the above theory to explain the drastic facilitation of global chaos onset in time-periodically perturbed Hamiltonian systems possessing two or more separatrices, previously discovered (PRL 90, 174101 (2003)). The theory well agrees with simulations. We also discuss generalizations and applications. Examples of applications of the facilitation include: the increase of the DC conductivity in spatially periodic structures, the reduction of activation barriers for noise-induced transitions and the related acceleration of spatial diffusion, the facilitation of the stochastic web formation in a wave-driven or kicked oscillator.

S. M. Soskin; R. Mannella; O. M. Yevtushenko

2007-10-31

466

The aim of this paper is to review the classical limit of Quantum Mechanics and to precise the well known threat of chaos (and fundamental graininess)to the correspondence principle. We will introduce a formalism for this classical limit that allows us to find the surfaces defined by the constants of the motion in phase space. Then in the integrable case we will find the classical trajectories, and in the non-integrable one the fact that regular initial cells become "amoeboid-like". This deformations and their consequences can be considered as a threat to the correspondence principle unless we take into account the characteristic timescales of quantum chaos. Essentially we present an analysis of the problem similar to the one of Omn\\`{e}s [10,11], but with a simpler mathematical structure.

Ignacio Gomez; Mario Castagnino

2014-11-12

467

Break of reciprocity principle due to localized nonlinearities in concrete.

The effects of localized nonlinearities on the reciprocity principle in the context of ultrasounds and nonlinear elasticity are discussed in this paper. Experiments will be presented to prove that a localized crack in a concrete beam causes a break of reciprocity in the ultrasonic response to a mechanical excitation. The link between non-reciprocity and asymmetry in the nonlinear response will be demonstrated and discussed as a tool for NonDestructive Evaluation. PMID:22386302

Scalerandi, M; Bruno, C L E; Gliozzi, A S; Bocca, P G

2012-08-01

468

Analysis of ECG records using ECG Chaos Extractor platform and Weka system

Clustering and classification of ECG records for four patient classes from the Internet databases by using the Weka system. Patient classes include normal, atrial arrhythmia, supraventricular arrhythmia and CHF. Chaos features are extracted automatically by using the ECG Chaos Extractor platform and recorded in Arff files. The list of features includes: correlation dimension, central tendency measure, spatial filling index and

Alan Jovic; Nikola Bogunovic

2008-01-01

469

Suppression of quantum chaos in a quantum computer hardware J. Lages* and D. L. Shepelyansky

Suppression of quantum chaos in a quantum computer hardware J. Lages* and D. L. Shepelyansky regimes in the quantum computer hardware are identified as a function of magnetic field gradient chaos and melting of quantum computer hardware 15Â17 . It has been also shown 18,19 that these static

Shepelyansky, Dima

470

Chaos in a Three-Species Food Chain Author(s): Alan Hastings and Thomas Powell

Chaos in a Three-Species Food Chain Author(s): Alan Hastings and Thomas Powell Source: Ecology, Vol(3), 1991, pp. 896-903 ?3 1991 bytheEcological SocietyofAmerica CHAOS IN A THREE-SPECIES FOOD CHAIN' ALAN chain;food web,functionalresponse;predation. INTRODUCTION The classical ecological models

de Aguiar, Marcus A. M.

471

Chaos suppression in the SU(2) Yang-Mills-Higgs system

We study the classical chaos-order transition in the spatially homogeneous SU(2) Yang-Mills-Higgs system by using a quantal analogue of Chirikov's resonance overlap criterion. We obtain an analytical estimation of the range of parameters for which there is chaos suppression.

Luca Salasnich; G. Galilei

1995-01-01

472

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

to determine if chaos existed in a real-life rotor system supported by ball bearings. This research will later be used to continue the original objective, control and elimination of chaos in the system. A Bently Nevada rotor system was assembled and connected...

Ortiz, Steven Rey

2013-02-22

473

Probing chaos and biodiversity in a simple competition model Lionel Roques a,

Probing chaos and biodiversity in a simple competition model Lionel Roques a, and MickaÂ¨el D. Abstract Recent theoretical work has reported that chaos facilitates biodiversity. In this paper, we study of biodiversity with respect to parameter variations in the chaotic regions. Additionally, in regions where

Boyer, Edmond

474

Audrey Terras 10/17/2008 Ihara zeta functions and quantum chaos

Audrey Terras 10/17/2008 1 Ihara zeta functions and quantum chaos Audrey Terrasy Vancouver AMS Chaos 3. Ihara zeta 4. Picture Gallery from Experiments #12;Audrey Terras 10/17/2008 2 Riemann s Happening in the Mathematical Sciences, 1998-1999, A.M.S., 1999. #12;Audrey Terras 10/17/2008 3 From O

Terras, Audrey

475

Test identification to fault-chaos relation of two-support rotator

NASA Astrophysics Data System (ADS)

The relation between fault and chaos is studied by tests for a two-support rotator. Some kinds of figures of the rotator vibration are observed in the fault situation such as oil- film eddy and loose bearing. The measures, which are the power spectra distribution and Poincare images, are used to identify the chaos characteristics in the signal data got from the rotator.

Xu, Xiaolin; Zhang, Yu

2000-05-01

476

This paper presents the chaotic analysis of the single-walled carbon nanotubes on elastic medium. Due to small scales of the nanotubes, the nonlocal elastic theory is applied. Besides, due to large-amplitude vibrations of the nanotubes, the geometrical nonlinearity is taken into account, so the von Kármán strain is incorporated. The results show that the period-three oscillation, the chaos and the period-one oscillation are excited by the different excitation amplitudes. In addition, the excitation amplitude of the chaos increases as the nonlocal parameter increases. These results are also validated by the steady-state time responses, the FFT spectrums, the phase portraits, and the Poincaré sections. PMID:24745231

Kuo, Yong-Lin

2014-03-01

477

Nonlinear Dynamics of Biofilm Growth on Sediment Surfaces

NASA Astrophysics Data System (ADS)

Bioclogging often begins with the establishment of small colonies (microcolonies), which then form biofilms on the surfaces of a porous medium. These biofilm-porous media surfaces are not simple coatings of single microbes, but complex assemblages of cooperative and competing microbes, interacting with their chemical environment. This leads one to ask: what are the underlying dynamics involved with biofilm growth? To begin answering this question, we have extended the work of Kot et al. (1992, Bull. Mathematical Bio.) from a fully mixed chemostat to an idealized, one-dimensional, biofilm environment, taking into account a simple predator-prey microbial competition, with the prey feeding on a specified food source. With a variable (periodic) food source, Kot et al. (1992) were able to demonstrate chaotic dynamics in the coupled substrate-prey-predator system. Initially, deterministic chaos was thought by many to be mainly a mathematical phenomenon. However, several recent publications (e.g., Becks et al, 2005, Nature Letters; Graham et al. 2007, Int. Soc Microb. Eco. J.; Beninca et al., 2008, Nature Letters; Saleh, 2011, IJBAS) have brought together, using experimental studies and relevant mathematics, a breakthrough discovery that deterministic chaos is present in relatively simple biochemical systems. Two of us (Faybishenko and Molz, 2013, Procedia Environ. Sci)) have numerically analyzed a mathematical model of rhizosphere dynamics (Kravchenko et al., 2004, Microbiology) and detected patterns of nonlinear dynamical interactions supporting evidence of synchronized synergetic oscillations of microbial populations, carbon and oxygen concentrations driven by root exudation into a fully mixed system. In this study, we have extended the application of the Kot et al. model to investigate a spatially-dependent biofilm system. We will present the results of numerical simulations obtained using COMSOL Multi-Physics software, which we used to determine the nature of the complex dynamics. We found that complex dynamics occur even with a constant food supply maintained at the upstream boundary of the biofilm. Results will be presented along with a description of the model, including 3 coupled partial differential equations and examples of the localized and propagating nonlinear dynamics inherent in the system. Contrary to a common opinion that chaos in many mechanical systems is a type of instability, appearing when energy is added, we hypothesize, based on the results of our modeling, that chaos in biofilm dynamics and other microbial ecosystems is driven by a competitive decrease in the food supply (i.e., chemical energy). We also hypothesize that, somewhat paradoxically, this, in turn, may support a long-term system stability that could cause bioclogging in porous media.

Molz, F. J.; Murdoch, L. C.; Faybishenko, B.

2013-12-01

478

On chaos in the pulsations of stars

NASA Astrophysics Data System (ADS)

In an earlier paper, we have described an investigation of a resonance in a quasi-homologous model of certain non-linear pulsations of a star, which is composed of a perfect gas with a constant ratio of specific heats. The governing equations of the model are the tensor virial equations of the second order and the first law of thermodynamics in the form of an equation governing the evolution of the internal energy of the star. We close that system of equations by letting the model be a heterogeneous ellipsoid with a density distribution stratified on similar and similarly situated ellipsoidal surfaces and requiring that the internal fluid motion sustain the adopted density distribution consistently with the equation of continuity. In this paper, we describe an application of the model to an investigation of chaotic behaviour in axisymmetric pulsations of non-rotating, spherically symmetric configurations and of rotating, axisymmetric configurations. The model represents the dynamics of such pulsations in terms of the dynamics of an oscillator with two degrees of freedom. The pulsations are generally periodic, quasi-periodic, or chaotic, and the quasi-periodic pulsations are arranged in families associated with the stable, periodic pulsations. Pulsations of sufficiently small excitation energies in a given equilibrium configuration are all periodic or quasi-periodic. The onset of chaotic behaviour as the excitation energy increases is explored in a survey of pulsations with the aid of Poincaré return maps.

Vandervoort, Peter O.

2014-09-01

479

then travel along the flame, distorting its surface and causing flame area fluctuations that result in unsteady heat release rate oscillations. For this reason the perturbation velocity is modelled as a travelling wave that originates at the burner lip... affects the heat release rate, which in turn depends very sensitively on the velocity perturbation at the inlet plane. The formation of cusps, their advection along the flame surface, their destruction by flame propagation normal to itself, pinch...

Kashinath, Karthik; Waugh, Iain C.; Juniper, Matthew P.

2014-01-01

480

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

, United States of America, 3 Affymetrix, Inc., Santa Clara, California, United States of America, 4 Jianbo Gao1,2 *, Jing Hu3 , Wen-wen Tung4 1 PMB Intelligence LLC, West Lafayette, Indiana, United States of America, 2 Department of Mechanical and Materials Engineering, Wright State University, Dayton, Ohio

Gao, Jianbo

481

Published in Nonlinear Structures in Physical Systems--Pattern Formation, Chaos and Waves,

theory of observing chaotic behavior is necessitated by (i) a chaotic process's extreme (exponential. The proper framework for the description of such behavior is information theory.[2] As Renyi has noted,[3 produced by a source is defined as the class of sources that are recoding- equivalent. Shannon entropy

California at Davis, University of

482

Nonlinear airship aeroelasticity

The aeroelastic derivatives for today's aircraft are calculated in the concept phase using a standard procedure. This scheme has to be extended for large airships, due to various nonlinearities in structural and aerodynamic behaviour. In general, the structural model of an airship is physically as well as geometrically nonlinear. The main sources of nonlinearity are large deformations and the nonlinear

N. Bessert; O. Frederich

2005-01-01

483

Analyzing Optical Communications Links

NASA Technical Reports Server (NTRS)

Optical Communication Link Analysis Program, OPTI, analyzes optical and near-infrared communication links using pulse-position modulation (PPM) and direct detention. Link margins and design-control tables generated from input parameters supplied by user. Enables user to save sets of input parameters that define given link and read them back into program later. Alters automatically any of input parameters to achieve desired link margin. Written in FORTRAN 77.

Marshall, William K.; Burk, Brian D.

1990-01-01

484

Linking numbers, spin, and statistics of solitons

NASA Technical Reports Server (NTRS)

The spin and statistics of solitons in the (2 + 1)- and (3 + 1)-dimensional nonlinear sigma models is considered. For the (2 + 1)-dimensional case, there is the possibility of fractional spin and exotic statistics; for 3 + 1 dimensions, the usual spin-statistics relation is demonstrated. The linking-number interpretation of the Hopf invariant and the use of suspension considerably simplify the analysis.

Wilczek, F.; Zee, A.

1983-01-01

485

A nonlinear generalization of spectral Granger causality.

Spectral measures of linear Granger causality have been widely applied to study the causal connectivity between time series data in neuroscience, biology, and economics. Traditional Granger causality measures are based on linear autoregressive with exogenous (ARX) inputs models of time series data, which cannot truly reveal nonlinear effects in the data especially in the frequency domain. In this study, it is shown that the classical Geweke's spectral causality measure can be explicitly linked with the output spectra of corresponding restricted and unrestricted time-domain models. The latter representation is then generalized to nonlinear bivariate signals and for the first time nonlinear causality analysis in the frequency domain. This is achieved by using the nonlinear ARX (NARX) modeling of signals, and decomposition of the recently defined output frequency response function which is related to the NARX model. PMID:24845279

He, Fei; Wei, Hua-Liang; Billings, Stephen A; Sarrigiannis, Ptolemaios G

2014-06-01

486

NASA Astrophysics Data System (ADS)

Unlike books that focus on the devices used in links, such as lasers and photodiodes, among others, this text focuses on the next level. It covers the collection of devices that form a link, how the individual device performance affects the link performance, or the reverse. Analog links are used for the distribution of cable TV signals, and in conveying the signals to and from antennas (so called antenna remoting). The design of analog links differs significantly from digital links which are primarily used in telecommunications.

Cox, Charles H., III

2004-05-01

487

Chaos, storms and climate on Mars

Channel networks on the plateau adjacent to Juventae Chasma have the highest drainage densities reported on Mars.We model frozen precipitation on the Juventae plateau,finding that the trigger for forming these channel networks could have been ephemeral lakeshore precipitation,and that they do not require past temperatures higher than today.If short-lived and localized events explain some dendritic channel networks on Mars, this would weaken the link between dendritic valley networks and surface climate conditions that could sustain life. Our analysis uses MRAMS simulations and HiRISE DTMs.We model localized weather systems driven by water vapor release from ephemeral lakes during outflow channel formation.At Juventae Chasma,mean snowfall reaches a maximum of 0.9mm/hr water equivalent on the SW rim of the chasm.Radiative effects of the thick cloud cover raise maximum (minimum, mean) plateau surface temperatures by up to 24K(9K, 17K)locally.The key result is that the area of maximum modeled precipitation shows ...

Kite, Edwin S; Michaels, Timothy; Dietrich, William E; Manga, Michael

2011-01-01

488

A Case for Hydrothermal Gray Hematite in Aram Chaos

NASA Technical Reports Server (NTRS)

The Thermal Emission Spectrometer (TES) on Mars Global Surveyor has detected deposits of coarsegrained, gray crystalline hematite in Sinus Meridiani, Aram Chaos, and Vallis Marineris [1]. Detailed features in the hematite spectral signature of the Sinus Meridiani region show that the spectrum is consistent with emission dominated by crystal c-faces of hematite, implying that the hematite is specular [2]. Gray specular hematite (also known as specularite ) is a particular gray crystalline form that has intergrown, hexagonal plates with a silvery metallic luster. We believe that the key to the origin of specularite is that it requires crystallization at temperatures in excess of about 100 C. In reviewing the occurrence of gray hematite on Earth, we find no exceptions to this warm temperature requirement [3]. Thermal crystallization on Mars could occur (1) as diagenesis at a depth of a few kilometers of sediments originally formed in lowtemperature waters, or (2) as direct precipitation from hydrothermal solution. Aram Chaos has unique chaotic terrain that offers more clues to the formation of the hematite than the relatively featureless flat terrain (as seen from orbit) of Sinus Meridiani. Aram Chaos provides the opportunity to look at a combination of TES data, Mars Orbiter Camera images, and Mars Orbiter Laser Altimeter (MOLA) topography. This combination of data suggests that high concentrations of hematite were formed in planar strata and have since been exposed by erosion of an overlying light-toned, caprock. Lesser concentrations of hematite are found adjacent to these strata at lower elevations, which we interpret as perhaps a lag deposit. The topography and the collapsed nature of the chaotic terrain favor a hydrothermally charged aquifer as the original setting where the hematite formed. An alternative sedimentary origin requires post-depositional burial to a depth of 3-5 km to induce thermally driven recrystallization of fine-grained iron oxides to coarse-grained hematite.

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

2003-01-01

489

Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology

We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynamical systems, and in particular, on the theory of chaos. On one hand, there is the direct classic relation: the application of mathematics to psychology. On the other hand, we propose the converse relation which consists in the formulation of new abstract mathematical problems appearing from processes and structures under research of psychology. The bidirectional multidisciplinary relation from-to pure mathematics, largely holds with the "hard" sciences, typically physics and astronomy. But it is rather new, from the social and human sciences, towards pure mathematics.

Catsigeras, Eleonora

2011-01-01

490

Deterministic Dynamics and Chaos: Epistemology and Interdisciplinary Methodology

We analyze, from a theoretical viewpoint, the bidirectional interdisciplinary relation between mathematics and psychology, focused on the mathematical theory of deterministic dynamical systems, and in particular, on the theory of chaos. On one hand, there is the direct classic relation: the application of mathematics to psychology. On the other hand, we propose the converse relation which consists in the formulation of new abstract mathematical problems appearing from processes and structures under research of psychology. The bidirectional multidisciplinary relation from-to pure mathematics, largely holds with the "hard" sciences, typically physics and astronomy. But it is rather new, from the social and human sciences, towards pure mathematics.

Eleonora Catsigeras

2011-06-21

491

Light-toned Rock Outcrop in Aureum Chaos

NASA Technical Reports Server (NTRS)

30 October 2006 This Mars Global Surveyor (MGS) Mars Orbiter Camera (MOC) image shows an outcrop of light-toned, layered, sedimentary rock in Aureum Chaos. The darker material, which includes ripples, is composed of windblown sand and granules. This scene is located near 3.8oS, 26.2oW, and covers an area roughly 7.7 km by 3 km (4.8 by 1.9 mi) wide. Sunlight illuminates the terrain from the top/upper right. This southern autumn image was acquired on 14 July 2006.

2006-01-01

492

Notions of Chaotic Cryptography: Sketch of a Chaos based Cryptosystem

Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a cryptographic system. In the end, the question is, can chaotic systems provide alternative techniques able to enhance cryptographic algorithms?. This chapter can be a worthy material to guide the reader in order to answer himself this question. Thus, the objective of this chapter is to give a general vision of what chaotic cryptography is and a comprehensive example that illustrates the main techniques used in this field.

Carmen Pellicer-Lostao; Ricardo Lopez-Ruiz

2012-03-19

493

Notions of Chaotic Cryptography: Sketch of a Chaos based Cryptosystem

Chaotic cryptography describes the use of chaos theory (in particular physical dynamical systems working in chaotic regime as part of communication techniques and computation algorithms) to perform different cryptographic tasks in a cryptographic system. In the end, the question is, can chaotic systems provide alternative techniques able to enhance cryptographic algorithms?. This chapter can be a worthy material to guide the reader in order to answer himself this question. Thus, the objective of this chapter is to give a general vision of what chaotic cryptography is and a comprehensive example that illustrates the main techniques used in this field.

Pellicer-Lostao, Carmen

2012-01-01

494

Bistability and chaos in the Taylor-Green dynamo.

Using direct numerical simulations, we study dynamo action under Taylor-Green forcing for a magnetic Prandtl number of 0.5. We observe bistability with weak- and strong-magnetic-field branches. Both the dynamo branches undergo subcritical dynamo transition. We also observe a host of dynamo states including constant, periodic, quasiperiodic, and chaotic magnetic fields. One of the chaotic states originates through a quasiperiodic route with phase locking, while the other chaotic attractor appears to follow the Newhouse-Ruelle-Takens route to chaos. We also observe intermittent transitions between quasiperiodic and chaotic states for a given Taylor-Green forcing. PMID:22587174

Yadav, Rakesh K; Verma, Mahendra K; Wahi, Pankaj

2012-03-01

495

Semiclassical Study on Tunneling Processes via Complex-Domain Chaos

We investigate the semiclassical mechanism of tunneling process in non-integrable systems. The significant role of complex-phase-space chaos in the description of the tunneling process is elucidated by studying a simple scattering map model. Behaviors of tunneling orbits are encoded into symbolic sequences based on the structure of complex homoclinic tanglement. By means of the symbolic coding, the phase space itineraries of tunneling orbits are related with the amounts of imaginary