Parametric perturbations and suppression of chaos in n-dimensional maps

International Nuclear Information System (INIS)

Loskutov, A.Y.; Rybalko, S.D.

1994-11-01

The problem of a qualitative change in dynamics of n-dimensional chaotic maps under the influence of parametric perturbations is considered. We prove that for certain maps, - the quadratic maps family, a piece wise linear maps family, and a two-dimensional map having a hyberbolic attractor, - there are perturbations which lead to suppression of chaos. Arguments that for such maps the set of parameter values corresponding to the ordered behaviour has the positive Lebesgue measure, are given. (author). 36 refs, 12 figs

Torus Destruction and Chaos-Chaos Intermittency in a Commodity Distribution Chain

DEFF Research Database (Denmark)

Sosnovtseva, O.; Mosekilde, Erik

1997-01-01

The destruction of two-dimensional tori T2 and the transitions to chaos are studied in a high-dimensional model describing the decision-making behavior of human subjects in a simulated managerial environment (the beer production-distribution model). Two different routes from quasiperiodicity...... to chaos can be distinguished. Intermittency transitions between chaotic and hyperchaotic attractors are characterized, and transients in which the system "pursues the ghost" of a vanished hyperchaotic attractor are studied....

Chaos in a complex plasma

International Nuclear Information System (INIS)

Sheridan, T.E.

2005-01-01

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

Devaney chaos, Li-Yorke chaos, and multi-dimensional Li-Yorke chaos for topological dynamics

Science.gov (United States)

Dai, Xiongping; Tang, Xinjia

2017-11-01

Let π : T × X → X, written T↷π X, be a topological semiflow/flow on a uniform space X with T a multiplicative topological semigroup/group not necessarily discrete. We then prove: If T↷π X is non-minimal topologically transitive with dense almost periodic points, then it is sensitive to initial conditions. As a result of this, Devaney chaos ⇒ Sensitivity to initial conditions, for this very general setting. Let R+↷π X be a C0-semiflow on a Polish space; then we show: If R+↷π X is topologically transitive with at least one periodic point p and there is a dense orbit with no nonempty interior, then it is multi-dimensional Li-Yorke chaotic; that is, there is a uncountable set Θ ⊆ X such that for any k ≥ 2 and any distinct points x1 , … ,xk ∈ Θ, one can find two time sequences sn → ∞ ,tn → ∞ with Moreover, let X be a non-singleton Polish space; then we prove: Any weakly-mixing C0-semiflow R+↷π X is densely multi-dimensional Li-Yorke chaotic. Any minimal weakly-mixing topological flow T↷π X with T abelian is densely multi-dimensional Li-Yorke chaotic. Any weakly-mixing topological flow T↷π X is densely Li-Yorke chaotic. We in addition construct a completely Li-Yorke chaotic minimal SL (2 , R)-acting flow on the compact metric space R ∪ { ∞ }. Our various chaotic dynamics are sensitive to the choices of the topology of the phase semigroup/group T.

PHASE CHAOS IN THE DISCRETE KURAMOTO MODEL

DEFF Research Database (Denmark)

Maistrenko, V.; Vasylenko, A.; Maistrenko, Y.

2010-01-01

The paper describes the appearance of a novel, high-dimensional chaotic regime, called phase chaos, in a time-discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It arises from the nonlinear...... interaction among the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional time-discrete Kuramoto model, we outline the region of phase chaos in the parameter plane and determine the regions where phase chaos coexists with different periodic...

Solitons and chaos in plasma

International Nuclear Information System (INIS)

Ichikawa, Y.H.

1990-09-01

Plasma exhibits a full of variety of nonlinear phenomena. Active research in nonlinear plasma physics contributed to explore the concepts of soliton and chaos. Structure of soliton equations and dynamics of low dimensional Hamiltonian systems are discussed to emphasize the universality of these novel concepts in the wide branch of science and engineering. (author) 52 refs

Further discussion on chaos in duopoly games

International Nuclear Information System (INIS)

Lu, Tianxiu; Zhu, Peiyong

2013-01-01

In this paper, we study Li–Yorke chaos, distributional chaos in a sequence, Li–Yorke sensitivity, sensitivity and distributional chaos of two-dimensional dynamical system of the form Φ(x, y) = (f(y), g(x))

Chaos in an imperfectly premixed model combustor.

Science.gov (United States)

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

2015-02-01

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

Phase Chaos and Multistability in the Discrete Kuramoto Model

DEFF Research Database (Denmark)

Maistrenko, V. L.; Vasylenko, A. A.; Maistrenko, Y. L.

2008-01-01

The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear interact......The paper describes the appearance of a novel high-dimensional chaotic regime, called phase chaos, in the discrete Kuramoto model of globally coupled phase oscillators. This type of chaos is observed at small and intermediate values of the coupling strength. It is caused by the nonlinear...... interaction of the oscillators, while the individual oscillators behave periodically when left uncoupled. For the four-dimensional discrete Kuramoto model, we outline the region of phase chaos in the parameter plane, distinguish the region where the phase chaos coexists with other periodic attractors...

Encounters with chaos and fractals

CERN Document Server

Gulick, Denny

2012-01-01

Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.

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

Energy Technology Data Exchange (ETDEWEB)

Hoff, Anderson, E-mail: hoffande@gmail.com; Silva, Denilson T. da; Manchein, Cesar, E-mail: cesar.manchein@udesc.br; Albuquerque, Holokx A., E-mail: holokx.albuquerque@udesc.br

2014-01-10

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

An introduction to chaos theory in CFD

Science.gov (United States)

Pulliam, Thomas H.

1990-01-01

The popular subject 'chaos theory' has captured the imagination of a wide variety of scientists and engineers. CFD has always been faced with nonlinear systems and it is natural to assume that nonlinear dynamics will play a role at sometime in such work. This paper will attempt to introduce some of the concepts and analysis procedures associated with nonlinear dynamics theory. In particular, results from computations of an airfoil at high angle of attack which exhibits a sequence of bifurcations for single frequency unsteady shedding through period doublings cascading into low dimensional chaos are used to present and demonstrate various aspects of nonlinear dynamics in CFD.

Local order and onset of chaos for a family of two-dimensional dissipative mappings

Energy Technology Data Exchange (ETDEWEB)

Brambilla, R [Dipt. di Fisica, Milano Univ. (Italy); Casartelli, M [Dipt. di Fision, Parma Univ. (Italy); Unita Risonanze Magnetiche, G.N.S.M.-C.N.R., Parma (Italy))

1985-08-11

We study the stochastic transition of a family of dissipative mappings of the two-dimensional tours, having a pure rotation and an Anosov hyperbolic automorphism as limit cases. Numerical experiments show that the onset of chaos is characterized by a sudden destruction of basins of previously conserved invariant sets and by the appearance of a strange attractor. The nature of these phenomena is clarified by analytical considerations.

Discrete chaos with applications in science and engineering

CERN Document Server

Elaydi, Saber N

2007-01-01

PREFACE FOREWORD The Stability of One-Dimensional Maps Introduction Maps vs. Difference Equations Maps vs. Differential Equations Linear Maps/Difference Equations Fixed (Equilibrium) Points Graphical Iteration and Stability Criteria for Stability Periodic Points and Their Stability The Period-Doubling Route to Chaos Applications Attraction and Bifurcation Introduction Basin of Attraction of Fixed Points Basin of Attraction of Periodic Orbits Singer's Theorem Bifurcation Sharkovsky's Theorem The Lorenz Map Period-Doubling in the Real World Poincaré Section/Map Appendix Chaos in One Dimension Introduction Density of the Set of Periodic Points Transitivity Sensitive Dependence Definition of Chaos Cantor Sets Symbolic Dynamics Conjugacy Other Notions of Chaos Rössler's Attractor Saturn's Rings Stability of Two-Dimensional Maps Linear Maps vs. Linear Systems Computing An Fundamental Set of Solutions Second-Order Difference Equations Phase Space ...

On the efficiency of chaos optimization algorithms for global optimization

International Nuclear Information System (INIS)

Yang Dixiong; Li Gang; Cheng Gengdong

2007-01-01

Chaos optimization algorithms as a novel method of global optimization have attracted much attention, which were all based on Logistic map. However, we have noticed that the probability density function of the chaotic sequences derived from Logistic map is a Chebyshev-type one, which may affect the global searching capacity and computational efficiency of chaos optimization algorithms considerably. Considering the statistical property of the chaotic sequences of Logistic map and Kent map, the improved hybrid chaos-BFGS optimization algorithm and the Kent map based hybrid chaos-BFGS algorithm are proposed. Five typical nonlinear functions with multimodal characteristic are tested to compare the performance of five hybrid optimization algorithms, which are the conventional Logistic map based chaos-BFGS algorithm, improved Logistic map based chaos-BFGS algorithm, Kent map based chaos-BFGS algorithm, Monte Carlo-BFGS algorithm, mesh-BFGS algorithm. The computational performance of the five algorithms is compared, and the numerical results make us question the high efficiency of the chaos optimization algorithms claimed in some references. It is concluded that the efficiency of the hybrid optimization algorithms is influenced by the statistical property of chaotic/stochastic sequences generated from chaotic/stochastic algorithms, and the location of the global optimum of nonlinear functions. In addition, it is inappropriate to advocate the high efficiency of the global optimization algorithms only depending on several numerical examples of low-dimensional functions

Chaos of discrete dynamical systems in complete metric spaces

International Nuclear Information System (INIS)

Shi Yuming; Chen Guanrong

2004-01-01

This paper is concerned with chaos of discrete dynamical systems in complete metric spaces. Discrete dynamical systems governed by continuous maps in general complete metric spaces are first discussed, and two criteria of chaos are then established. As a special case, two corresponding criteria of chaos for discrete dynamical systems in compact subsets of metric spaces are obtained. These results have extended and improved the existing relevant results of chaos in finite-dimensional Euclidean spaces

Chaos in oil prices? Evidence from futures markets

International Nuclear Information System (INIS)

Adrangi, B.; Chatrath, A.; Dhanda, K.K.; Raffiee, K.

2001-01-01

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 for seasonal variation in prices, generally explain the non-linearities in the data. We also demonstrate that employing seasonally adjusted price series contributes to obtaining robust results via the existing tests for chaotic structure. Maximum likelihood methodologies, that are robust to the non-linear dynamics, lend support for Samuelson's hypothesis on contract-maturity effects in futures price-changes. However, the tests for chaos are not found to be sensitive to the maturity effects in the futures contracts. The results are robust to controls for the oil shocks of 1986 and 1991

Chaos, self-organized criticality, and SETAR nonlinearity: An analysis of purchasing power parity between Canada and the United States

Energy Technology Data Exchange (ETDEWEB)

Serletis, Apostolos [Department of Economics, University of Calgary, Calgary, Alta., T2N 1N4 (Canada)]. E-mail: Serletis@ucalgary.ca; Shahmoradi, Asghar [Faculty of Economics, University of Tehran, Tehran (Iran, Islamic Republic of)

2007-08-15

This paper uses monthly observations for the real exchange rate between Canada and the United States over the recent flexible exchange rate period (from January 1, 1973 to August 1, 2004) to test purchasing power parity between Canada and the United States using unit root and stationarity tests. Moreover, given the apparent random walk behavior in the real exchange rate, various tests from dynamical systems theory, such as for example, the Nychka et al. [Nychka DW, Ellner S, Ronald GA, McCaffrey D. Finding chaos in noisy systems. J Roy Stat Soc B 1992;54:399-426] chaos test, the Li [Li W. Absence of 1/f spectra in Dow Jones average. Int J Bifurcat Chaos 1991;1:583-97] self-organized criticality test, and the Hansen [Hansen, B.E. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 1996;64:413-30] threshold effects test are used to distinguish between stochastic and deterministic origin for the real exchange rate.

Chaos, self-organized criticality, and SETAR nonlinearity: An analysis of purchasing power parity between Canada and the United States

International Nuclear Information System (INIS)

Serletis, Apostolos; Shahmoradi, Asghar

2007-01-01

This paper uses monthly observations for the real exchange rate between Canada and the United States over the recent flexible exchange rate period (from January 1, 1973 to August 1, 2004) to test purchasing power parity between Canada and the United States using unit root and stationarity tests. Moreover, given the apparent random walk behavior in the real exchange rate, various tests from dynamical systems theory, such as for example, the Nychka et al. [Nychka DW, Ellner S, Ronald GA, McCaffrey D. Finding chaos in noisy systems. J Roy Stat Soc B 1992;54:399-426] chaos test, the Li [Li W. Absence of 1/f spectra in Dow Jones average. Int J Bifurcat Chaos 1991;1:583-97] self-organized criticality test, and the Hansen [Hansen, B.E. Inference when a nuisance parameter is not identified under the null hypothesis. Econometrica 1996;64:413-30] threshold effects test are used to distinguish between stochastic and deterministic origin for the real exchange rate

One-dimensional two-fluid model for wavy flow beyond the Kelvin–Helmholtz instability: Limit cycles and chaos

Energy Technology Data Exchange (ETDEWEB)

Lopez de Bertodano, Martín, E-mail: bertodan@purdue.edu [School of Nuclear Engineering, Purdue University, West Lafayette, IN 47907 (United States); Fullmer, William D. [Department of Chemical and Biological Engineering, U. of Colorado, Boulder, CO 80309 (United States); Clausse, Alejandro [CNEA-CONICET and Universidad Nacional del Centro, 7000 Tandil (Argentina)

2016-12-15

A 1D TFM numerical simulation of near horizontal stratified two-phase flow is performed where the TFM, including surface tension and viscous stresses, is simplified to a two-equation model using the fixed-flux approximation. As the angle of inclination of the channel increases so does the driving body force, so the flow becomes KH unstable, and waves grow and develop nonlinearities. It is shown that these waves grow until they reach a limit cycle due to viscous dissipation at wave fronts. Upon further inclination of the channel, chaos is observed. The appearance of chaos in a 1D TFM implies a nonlinear process that transfers energy intermittently from long wavelengths where energy is produced to short wavelengths where energy is dissipated by viscosity, so that an averaged energy equilibrium in frequency space is attained. This is comparable to the well-known turbulent stability mechanism of the multi-dimensional Navier–Stokes equations, i.e., chaos implies Lyapunov stability, but in this case it is strictly a two-phase phenomenon.

Nonlinearly-enhanced energy transport in many dimensional quantum chaos

KAUST Repository

Brambila, D. S.; Fratalocchi, Andrea

2013-01-01

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.

Nonlinearly-enhanced energy transport in many dimensional quantum chaos

KAUST Repository

Brambila, D. S.

2013-08-05

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.

Chaos Control in a New Three-Dimensional Chaotic T System

International Nuclear Information System (INIS)

Chen Yong; Yan Zhenya

2008-01-01

In this paper, we study chaos control of the new 3D chaotic system. We use three feedback methods (the linear, speed, doubly-periodic function controller) to suppress the chaos to unstable equilibrium. As a result, some controllers are obtained. Moreover, numerical simulations are used to verify the effectiveness of the obtained controllers

Origin of chaos near three-dimensional quantum vortices: A general Bohmian theory

Science.gov (United States)

Tzemos, Athanasios C.; Efthymiopoulos, Christos; Contopoulos, George

2018-04-01

We provide a general theory for the structure of the quantum flow near three-dimensional (3D) nodal lines, i.e., one-dimensional loci where the 3D wave function becomes equal to zero. In suitably defined coordinates (comoving with the nodal line) the generic structure of the flow implies the formation of 3D quantum vortices. We show that such vortices are accompanied by nearby invariant lines of the comoving quantum flow, called X lines, which are normally hyperbolic. Furthermore, the stable and unstable manifolds of the X lines produce chaotic scatterings of nearby quantum (Bohmian) trajectories, thus inducing an intricate form of the quantum current in the neighborhood of each 3D quantum vortex. Generic formulas describing the structure around 3D quantum vortices are provided, applicable to an arbitrary choice of 3D wave function. We also give specific numerical examples as well as a discussion of the physical consequences of chaos near 3D quantum vortices.

Generalized Statistical Mechanics at the Onset of Chaos

Directory of Open Access Journals (Sweden)

Alberto Robledo

2013-11-01

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

On the definition of 'chaos'

International Nuclear Information System (INIS)

Kolesov, Andrei Yu; Rozov, Nikolai Kh

2009-01-01

A new definition of a chaotic invariant set is given for a continuous semiflow in a metric space. It generalizes the well-known definition due to Devaney and allows one to take into account a special feature occurring in the non-compact infinite-dimensional case: so-called turbulent chaos. The paper consists of two sections. The first contains several well-known facts from chaotic dynamics, together with new definitions and results. The second presents a concrete example demonstrating that our definition of chaos is meaningful. Namely, an infinite-dimensional system of ordinary differential equations is investigated having an attractor that is chaotic in the sense of the new definition but not in the sense of Devaney or Knudsen. Bibliography: 65 titles.

A Spatiotemporal-Chaos-Based Encryption Having Overall Properties Considerably Better than Advanced Encryption Standard

Science.gov (United States)

Wang, Shi-Hong; Ye, Wei-Ping; Lü, Hua-Ping; Kuang, Jin-Yu; Li, Jing-Hua; Luo, Yun-Lun; Hu, Gang

2003-07-01

Spatiotemporal chaos of a two-dimensional one-way coupled map lattice is used for chaotic cryptography. The chaotic outputs of many space units are used for encryption simultaneously. This system shows satisfactory cryptographic properties of high security, fast encryption (decryption) speed, and robustness against noise disturbances in communication channel. The overall features of this spatiotemporal-chaos-based cryptosystem are better than chaotic cryptosystems known so far, and also than currently used conventional cryptosystems, such as the Advanced Encryption Standard (AES). The project supported by National Natural Science Foundation of China under Grant No. 10175010 and the Special Funds for Major State Basic Research Projects under Grant No. G2000077304

Elimination of spiral chaos by periodic force for the Aliev-Panfilov model

OpenAIRE

Sakaguchi, Hidetsugu; Fujimoto, Takefumi

2003-01-01

Spiral chaos appears in the two dimensional Aliev-Panfilov model. The generation mechanism of the spiral chaos is related to the breathing instability of pulse trains. The spiral chaos can be eliminated by applying periodic force uniformly. The elimination of spiral chaos is most effective, when the frequency of the periodic force is close to that of the breathing motion.

Survival and weak chaos.

Science.gov (United States)

Nee, Sean

2018-05-01

Survival analysis in biology and reliability theory in engineering concern the dynamical functioning of bio/electro/mechanical units. Here we incorporate effects of chaotic dynamics into the classical theory. Dynamical systems theory now distinguishes strong and weak chaos. Strong chaos generates Type II survivorship curves entirely as a result of the internal operation of the system, without any age-independent, external, random forces of mortality. Weak chaos exhibits (a) intermittency and (b) Type III survivorship, defined as a decreasing per capita mortality rate: engineering explicitly defines this pattern of decreasing hazard as 'infant mortality'. Weak chaos generates two phenomena from the normal functioning of the same system. First, infant mortality- sensu engineering-without any external explanatory factors, such as manufacturing defects, which is followed by increased average longevity of survivors. Second, sudden failure of units during their normal period of operation, before the onset of age-dependent mortality arising from senescence. The relevance of these phenomena encompasses, for example: no-fault-found failure of electronic devices; high rates of human early spontaneous miscarriage/abortion; runaway pacemakers; sudden cardiac death in young adults; bipolar disorder; and epilepsy.

Synchronization and suppression of chaos in non-locally coupled ...

Indian Academy of Sciences (India)

Coupled map lattices have been intensively investigated as models to understand many spatiotemporal phenomena observed in extended system, and consequently spatiotemporal chaos. We used the complex order parameter to quantify chaos synchronization for a one-dimensional chain of coupled logistic maps with a ...

Linear Matrix Inequality Based Fuzzy Synchronization for Fractional Order Chaos

Directory of Open Access Journals (Sweden)

Bin Wang

2015-01-01

Full Text Available This paper investigates fuzzy synchronization for fractional order chaos via linear matrix inequality. Based on generalized Takagi-Sugeno fuzzy model, one efficient stability condition for fractional order chaos synchronization or antisynchronization is given. The fractional order stability condition is transformed into a set of linear matrix inequalities and the rigorous proof details are presented. Furthermore, through fractional order linear time-invariant (LTI interval theory, the approach is developed for fractional order chaos synchronization regardless of the system with uncertain parameters. Three typical examples, including synchronization between an integer order three-dimensional (3D chaos and a fractional order 3D chaos, anti-synchronization of two fractional order hyperchaos, and the synchronization between an integer order 3D chaos and a fractional order 4D chaos, are employed to verify the theoretical results.

No evidence of chaos but some evidence of dependence in the US stock market

International Nuclear Information System (INIS)

Serletis, Apostolos; Shintani, Mototsugu

2003-01-01

This paper uses recent advances in the field of applied econometrics and tools from dynamical systems theory to test for random walks and chaos in the US stock market, using daily observations on the Dow Jones Industrial Average (from January 3, 1928 to October 18, 2000 - a total of 18,490 observations). In doing so, we follow the recent contribution by Whang and Linton [J Econometr 91 (1999) 1] and construct the standard error for the Nychka et al. [J Roy Statist Soc B 54 (1992) 399] dominant Lyapunov exponent, thereby providing a statistical test of chaos. We find statistically significant evidence against low-dimensional chaos and point to the use of stochastic models and statistical inference in the modeling of asset markets

No evidence of chaos but some evidence of dependence in the US stock market

Energy Technology Data Exchange (ETDEWEB)

Serletis, Apostolos E-mail: serletis@ucalgary.ca; Shintani, Mototsugu E-mail: mototsugu.shintani@vanderbilt.edu

2003-07-01

This paper uses recent advances in the field of applied econometrics and tools from dynamical systems theory to test for random walks and chaos in the US stock market, using daily observations on the Dow Jones Industrial Average (from January 3, 1928 to October 18, 2000 - a total of 18,490 observations). In doing so, we follow the recent contribution by Whang and Linton [J Econometr 91 (1999) 1] and construct the standard error for the Nychka et al. [J Roy Statist Soc B 54 (1992) 399] dominant Lyapunov exponent, thereby providing a statistical test of chaos. We find statistically significant evidence against low-dimensional chaos and point to the use of stochastic models and statistical inference in the modeling of asset markets.

Generic superweak chaos induced by Hall effect

Science.gov (United States)

Ben-Harush, Moti; Dana, Itzhack

2016-05-01

We introduce and study the "kicked Hall system" (KHS), i.e., charged particles periodically kicked in the presence of uniform magnetic (B ) and electric (E ) fields that are perpendicular to each other and to the kicking direction. We show that for resonant values of B and E and in the weak-chaos regime of sufficiently small nonintegrability parameter κ (the kicking strength), there exists a generic family of periodic kicking potentials for which the Hall effect from B and E significantly suppresses the weak chaos, replacing it by "superweak" chaos (SWC). This means that the system behaves as if the kicking strength were κ2 rather than κ . For E =0 , SWC is known to be a classical fingerprint of quantum antiresonance, but it occurs under much less generic conditions, in particular only for very special kicking potentials. Manifestations of SWC are a decrease in the instability of periodic orbits and a narrowing of the chaotic layers, relative to the ordinary weak-chaos case. Also, for global SWC, taking place on an infinite "stochastic web" in phase space, the chaotic diffusion on the web is much slower than the weak-chaos one. Thus, the Hall effect can be relatively stabilizing for small κ . In some special cases, the effect is shown to cause ballistic motion for almost all parameter values. The generic global SWC on stochastic webs in the KHS appears to be the two-dimensional closest analog to the Arnol'd web in higher dimensional systems.

Chaos on the interval

CERN Document Server

Ruette, Sylvie

2017-01-01

The aim of this book is to survey the relations between the various kinds of chaos and related notions for continuous interval maps from a topological point of view. The papers on this topic are numerous and widely scattered in the literature; some of them are little known, difficult to find, or originally published in Russian, Ukrainian, or Chinese. Dynamical systems given by the iteration of a continuous map on an interval have been broadly studied because they are simple but nevertheless exhibit complex behaviors. They also allow numerical simulations, which enabled the discovery of some chaotic phenomena. Moreover, the "most interesting" part of some higher-dimensional systems can be of lower dimension, which allows, in some cases, boiling it down to systems in dimension one. Some of the more recent developments such as distributional chaos, the relation between entropy and Li-Yorke chaos, sequence entropy, and maps with infinitely many branches are presented in book form for the first time. The author gi...

Quasiperiodic transition to chaos in a plasma

International Nuclear Information System (INIS)

Weixing, D.; Huang Wei; Wang Xiaodong; Yu, C.X.

1993-01-01

The quasiperiodic transition to chaos in an undriven discharge plasma has been investigated. Results from the power spectrum and Lyapunov exponents quantitatively confirm the transition to chaos through quasiperiodicity. A low-dimension strange attractor has been found for this kind of plasma chaos

Bifurcation and chaos in neural excitable system

International Nuclear Information System (INIS)

Jing Zhujun; Yang Jianping; Feng Wei

2006-01-01

In this paper, we investigate the dynamical behaviors of neural excitable system without periodic external current (proposed by Chialvo [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] and with periodic external current as system's parameters vary. The existence and stability of three fixed points, bifurcation of fixed points, the conditions of existences of fold bifurcation, flip bifurcation and Hopf bifurcation are derived by using bifurcation theory and center manifold theorem. The chaotic existence in the sense of Marotto's definition of chaos is proved. We then give the numerical simulated results (using bifurcation diagrams, computations of Maximum Lyapunov exponent and phase portraits), which not only show the consistence with the analytic results but also display new and interesting dynamical behaviors, including the complete period-doubling and inverse period-doubling bifurcation, symmetry period-doubling bifurcations of period-3 orbit, simultaneous occurrence of two different routes (invariant cycle and period-doubling bifurcations) to chaos for a given bifurcation parameter, sudden disappearance of chaos at one critical point, a great abundance of period windows (period 2 to 10, 12, 19, 20 orbits, and so on) in transient chaotic regions with interior crises, strange chaotic attractors and strange non-chaotic attractor. In particular, the parameter k plays a important role in the system, which can leave the chaotic behavior or the quasi-periodic behavior to period-1 orbit as k varies, and it can be considered as an control strategy of chaos by adjusting the parameter k. Combining the existing results in [Generic excitable dynamics on a two-dimensional map. Chaos, Solitons and Fractals 1995;5(3-4):461-79] with the new results reported in this paper, a more complete description of the system is now obtained

Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors

Science.gov (United States)

Schöll, Eckehard

2005-08-01

Nonlinear transport phenomena are an increasingly important aspect of modern semiconductor research. This volume deals with complex nonlinear dynamics, pattern formation, and chaotic behavior in such systems. It bridges the gap between two well-established fields: the theory of dynamic systems and nonlinear charge transport in semiconductors. This unified approach helps reveal important electronic transport instabilities. The initial chapters lay a general framework for the theoretical description of nonlinear self-organized spatio-temporal patterns, such as current filaments, field domains, fronts, and analysis of their stability. Later chapters consider important model systems in detail: impact ionization induced impurity breakdown, Hall instabilities, superlattices, and low-dimensional structures. State-of-the-art results include chaos control, spatio-temporal chaos, multistability, pattern selection, activator-inhibitor kinetics, and global coupling, linking fundamental issues to electronic device applications. This book will be of great value to semiconductor physicists and nonlinear scientists alike.

Shilnikov sense chaos in a simple three-dimensional system

International Nuclear Information System (INIS)

Wei, Wang; Qi-Chang, Zhang; Rui-Lan, Tian

2010-01-01

The Shilnikov sense Smale horseshoe chaos in a simple 3D nonlinear system is studied. The proportional integral derivative (PID) controller is improved by introducing the quadratic and cubic nonlinearities into the governing equations. For the discussion of chaos, the bifurcate parameter value is selected in a reasonable regime at the requirement of the Shilnikov theorem. The analytic expression of the Shilnikov type homoclinic orbit is accomplished. It depends on the series form of the manifolds surrounding the saddle-focus equilibrium. Then the methodology is extended to research the dynamical behaviours of the simplified solar-wind-driven-magnetosphere-ionosphere system. As is illustrated, the Lyapunov characteristic exponent spectra of the two systems indicate the existence of chaotic attractor under some specific parameter conditions

The CHAOS-4 Geomagnetic Field Model

DEFF Research Database (Denmark)

Olsen, Nils; Finlay, Chris; Lühr, H.

We present CHAOS-4, a new version in the CHAOS model series, which aims at describing the Earth's magnetic field with high spatial resolution (terms up to spherical degree n=90 for the crustal field, and up to n=16 for the time-varying core field are robustly determined) and high temporal...... between the coordinate systems of the vector magnetometer and of the star sensor providing attitude information). The final CHAOS-4 model is derived by merging two sub-models: its low-degree part has been obtained using similar model parameterization and data sets as used for previous CHAOS models (but...

Correlations between chaos in a perturbed sine-Gordon equation and a truncated model system

International Nuclear Information System (INIS)

Bishop, A.R.; Flesch, R.; Forests, M.G.; Overman, E.A.

1990-01-01

The purpose of this paper is to present a first step toward providing coordinates and associated dynamics for low-dimensional attractors in nearly integrable partial differential equations (pdes), in particular, where the truncated system reflects salient geometric properties of the pde. This is achieved by correlating: (1) numerical results on the bifurcations to temporal chaos with spatial coherence of the damped, periodically forced sine-Gordon equation with periodic boundary conditions; (2) an interpretation of the spatial and temporal bifurcation structures of this perturbed integrable system with regard to the exact structure of the sine-Gordon phase space; (3) a model dynamical systems problem, which is itself a perturbed integrable Hamiltonian system, derived from the perturbed sine-Gordon equation by a finite mode Fourier truncation in the nonlinear Schroedinger limit; and (4) the bifurcations to chaos in the truncated phase space. In particular, a potential source of chaos in both the pde and the model ordinary differential equation systems is focused on: the existence of homoclinic orbits in the unperturbed integrable phase space and their continuation in the perturbed problem. The evidence presented here supports the thesis that the chaotic attractors of the weakly perturbed periodic sine-Gordon system consists of low-dimensional metastable attacking states together with intermediate states that are O(1) unstable and correspond to homoclinic states in the integrable phase space. It is surmised that the chaotic dynamics on these attractors is due to the perturbation of these homocline integrable configurations

Quantum signatures of chaos or quantum chaos?

International Nuclear Information System (INIS)

Bunakov, V. E.

2016-01-01

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.

Quantum signatures of chaos or quantum chaos?

Energy Technology Data Exchange (ETDEWEB)

Bunakov, V. E., E-mail: bunakov@VB13190.spb.edu [St. Petersburg State University (Russian Federation)

2016-11-15

A critical analysis of the present-day concept of chaos in quantum systems as nothing but a “quantum signature” of chaos in classical mechanics is given. In contrast to the existing semi-intuitive guesses, a definition of classical and quantum chaos is proposed on the basis of the Liouville–Arnold theorem: a quantum chaotic system featuring N degrees of freedom should have M < N independent first integrals of motion (good quantum numbers) specified by the symmetry of the Hamiltonian of the system. Quantitative measures of quantum chaos that, in the classical limit, go over to the Lyapunov exponent and the classical stability parameter are proposed. The proposed criteria of quantum chaos are applied to solving standard problems of modern dynamical chaos theory.

Predictability analysis and validation of a low-dimensional model - an application to the dynamics of cereal crops observed from satellite

Science.gov (United States)

Mangiarotti, Sylvain; Drapeau, Laurent

2013-04-01

The global modeling approach aims to obtain parsimonious models of observed dynamics from few or single time series (Letellier et al. 2009). Specific algorithms were developed and validated for this purpose (Mangiarotti et al. 2012a). This approach was applied to the dynamics of cereal crops in semi-arid region using the vegetation index derived from satellite data as a proxy of the dynamics. A low-dimensional autonomous model could be obtained. The corresponding attractor is characteristic of weakly dissipative chaos and exhibits a toroidal-like structure. At present, only few theoretical cases of such chaos are known, and none was obtained from real world observations. Under smooth conditions, a robust validation of three-dimensional chaotic models can be usually performed based on the topological approach (Gilmore 1998). Such approach becomes more difficult for weakly dissipative systems, and almost impossible under noisy observational conditions. For this reason, another validation approach is developed which consists in comparing the forecasting skill of the model to other forecasts for which no dynamical model is required. A data assimilation process is associated to the model to estimate the model's skill; several schemes are tested (simple re-initialization, Extended and Ensemble Kalman Filters and Back and Forth Nudging). Forecasts without model are performed based on the search of analogous states in the phase space (Mangiarotti et al. 2012b). The comparison reveals the quality of the model's forecasts at short to moderate horizons and contributes to validate the model. These results suggest that the dynamics of cereal crops can be reasonably approximated by low-dimensional chaotic models, and also bring out powerful arguments for chaos. Chaotic models have often been used as benchmark to test data assimilation schemes; the present work shows that such tests may not only have a theoretical interest, but also almost direct applicative potential. Moreover

Digital chaos-masked optical encryption scheme enhanced by two-dimensional key space

Science.gov (United States)

Liu, Ling; Xiao, Shilin; Zhang, Lu; Bi, Meihua; Zhang, Yunhao; Fang, Jiafei; Hu, Weisheng

2017-09-01

A digital chaos-masked optical encryption scheme is proposed and demonstrated. The transmitted signal is completely masked by interference chaotic noise in both bandwidth and amplitude with analog method via dual-drive Mach-Zehnder modulator (DDMZM), making the encrypted signal analog, noise-like and unrecoverable by post-processing techniques. The decryption process requires precise matches of both the amplitude and phase between the cancellation and interference chaotic noises, which provide a large two-dimensional key space with the help of optical interference cancellation technology. For 10-Gb/s 16-quadrature amplitude modulation (QAM) orthogonal frequency division multiplexing (OFDM) signal over the maximum transmission distance of 80 km without dispersion compensation or inline amplifier, the tolerable mismatch ranges of amplitude and phase/delay at the forward error correction (FEC) threshold of 3.8×10-3 are 0.44 dB and 0.08 ns respectively.

An Image Encryption Scheme Based on Hyperchaotic Rabinovich and Exponential Chaos Maps

Directory of Open Access Journals (Sweden)

Xiaojun Tong

2015-01-01

Full Text Available This paper proposes a new four-dimensional hyperchaotic map based on the Rabinovich system to realize chaotic encryption in higher dimension and improve the security. The chaotic sequences generated by Runge-Kutta method are combined with the chaotic sequences generated by an exponential chaos map to generate key sequences. The key sequences are used for image encryption. The security test results indicate that the new hyperchaotic system has high security and complexity. The comparison between the new hyperchaotic system and the several low-dimensional chaotic systems shows that the proposed system performs more efficiently.

Symbolic dynamics of noisy chaos

Energy Technology Data Exchange (ETDEWEB)

Crutchfield, J P; Packard, N H

1983-05-01

One model of randomness observed in physical systems is that low-dimensional deterministic chaotic attractors underly the observations. A phenomenological theory of chaotic dynamics requires an accounting of the information flow fromthe observed system to the observer, the amount of information available in observations, and just how this information affects predictions of the system's future behavior. In an effort to develop such a description, the information theory of highly discretized observations of random behavior is discussed. Metric entropy and topological entropy are well-defined invariant measures of such an attractor's level of chaos, and are computable using symbolic dynamics. Real physical systems that display low dimensional dynamics are, however, inevitably coupled to high-dimensional randomness, e.g. thermal noise. We investigate the effects of such fluctuations coupled to deterministic chaotic systems, in particular, the metric entropy's response to the fluctuations. It is found that the entropy increases with a power law in the noise level, and that the convergence of the entropy and the effect of fluctuations can be cast as a scaling theory. It is also argued that in addition to the metric entropy, there is a second scaling invariant quantity that characterizes a deterministic system with added fluctuations: I/sub 0/, the maximum average information obtainable about the initial condition that produces a particular sequence of measurements (or symbols). 46 references, 14 figures, 1 table.

The CHAOS-4 geomagnetic field model

DEFF Research Database (Denmark)

Olsen, Nils; Lühr, H.; Finlay, Chris

2014-01-01

We present CHAOS-4, a new version in the CHAOS model series, which aims to describe the Earth's magnetic field with high spatial and temporal resolution. Terms up to spherical degree of at least n = 85 for the lithospheric field, and up to n = 16 for the time-varying core field are robustly...... to the core field, but the high-degree lithospheric field is regularized for n > 85. CHAOS-4 model is derived by merging two submodels: its low-degree part has been derived using similar model parametrization and data sets as used for previous CHAOS models (but of course including more recent data), while its...

Bounding the space of holographic CFTs with chaos

Energy Technology Data Exchange (ETDEWEB)

Perlmutter, Eric [Department of Physics, Princeton University,Jadwin Hall, Princeton, NJ 08544 (United States)

2016-10-13

Thermal states of quantum systems with many degrees of freedom are subject to a bound on the rate of onset of chaos, including a bound on the Lyapunov exponent, λ{sub L}≤2π/β. We harness this bound to constrain the space of putative holographic CFTs and their would-be dual theories of AdS gravity. First, by studying out-of-time-order four-point functions, we discuss how λ{sub L}=2π/β in ordinary two-dimensional holographic CFTs is related to properties of the OPE at strong coupling. We then rule out the existence of unitary, sparse two-dimensional CFTs with large central charge and a set of higher spin currents of bounded spin; this implies the inconsistency of weakly coupled AdS{sub 3} higher spin gravities without infinite towers of gauge fields, such as the SL(N) theories. This fits naturally with the structure of higher-dimensional gravity, where finite towers of higher spin fields lead to acausality. On the other hand, unitary CFTs with classical W{sub ∞}[λ] symmetry, dual to 3D Vasiliev or hs[λ] higher spin gravities, do not violate the chaos bound, instead exhibiting no chaos: λ{sub L}=0. Independently, we show that such theories violate unitarity for |λ|>2. These results encourage a tensionless string theory interpretation of the 3D Vasiliev theory.

Shil'nikov chaos control using homoclinic orbits and the Newhouse region

International Nuclear Information System (INIS)

Furui, Sadataka; Niiya, Shohei

2007-01-01

A method of controlling Shil'nikov's type chaos using windows that appear in the 1-dimensional bifurcation diagram when perturbations are applied, and using existence of stable homoclinic orbits near the unstable one is presented and applied to the electronic Chua's circuit. A demonstration of the chaos control in the electronic circuit experiments and their simulations and bifurcation analyses are given

Signatures of chaos in the Brillouin zone.

Science.gov (United States)

Barr, Aaron; Barr, Ariel; Porter, Max D; Reichl, Linda E

2017-10-01

When the classical dynamics of a particle in a finite two-dimensional billiard undergoes a transition to chaos, the quantum dynamics of the particle also shows manifestations of chaos in the form of scarring of wave functions and changes in energy level spacing distributions. If we "tile" an infinite plane with such billiards, we find that the Bloch states on the lattice undergo avoided crossings, energy level spacing statistics change from Poisson-like to Wigner-like, and energy sheets of the Brillouin zone begin to "mix" as the classical dynamics of the billiard changes from regular to chaotic behavior.

Aggregation and sampling in deterministic chaos: implications for chaos identification in hydrological processes

Directory of Open Access Journals (Sweden)

J. D. Salas

2005-01-01

Full Text Available A review of the literature reveals conflicting results regarding the existence and inherent nature of chaos in hydrological processes such as precipitation and streamflow, i.e. whether they are low dimensional chaotic or stochastic. This issue is examined further in this paper, particularly the effect that certain types of transformations, such as aggregation and sampling, may have on the identification of the dynamics of the underlying system. First, we investigate the dynamics of daily streamflows for two rivers in Florida, one with strong surface and groundwater storage contributions and the other with a lesser basin storage contribution. Based on estimates of the delay time, the delay time window, and the correlation integral, our results suggest that the river with the stronger basin storage contribution departs significantly from the behavior of a chaotic system, while the departure is less significant for the river with the smaller basin storage contribution. We pose the hypothesis that the chaotic behavior depicted on continuous precipitation fields or small time-step precipitation series becomes less identifiable as the aggregation (or sampling time step increases. Similarly, because streamflows result from a complex transformation of precipitation that involves accumulating and routing excess rainfall throughout the basin and adding surface and groundwater flows, the end result may be that streamflows at the outlet of the basin depart from low dimensional chaotic behavior. We also investigate the effect of aggregation and sampling using series derived from the Lorenz equations and show that, as the aggregation and sampling scales increase, the chaotic behavior deteriorates and eventually ceases to show evidence of low dimensional determinism.

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

International Nuclear Information System (INIS)

Berman, G.P.; Bulgakov, E.N.; Holm, D.D.

1995-01-01

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, Regular and Stochastic Motion (Springer-Verlag, City, 1983)]. In the general case, the transition to chaos is connected with the overlapping of vibrational-rotational nonlinear resonances and appears even at rather low radiation field intensity, S approx-gt 1 GW/cm 2 . We also discuss the possibility of experimentally observing this transition

Dynamical topology and statistical properties of spatiotemporal chaos.

Science.gov (United States)

Zhuang, Quntao; Gao, Xun; Ouyang, Qi; Wang, Hongli

2012-12-01

For spatiotemporal chaos described by partial differential equations, there are generally locations where the dynamical variable achieves its local extremum or where the time partial derivative of the variable vanishes instantaneously. To a large extent, the location and movement of these topologically special points determine the qualitative structure of the disordered states. We analyze numerically statistical properties of the topologically special points in one-dimensional spatiotemporal chaos. The probability distribution functions for the number of point, the lifespan, and the distance covered during their lifetime are obtained from numerical simulations. Mathematically, we establish a probabilistic model to describe the dynamics of these topologically special points. In spite of the different definitions in different spatiotemporal chaos, the dynamics of these special points can be described in a uniform approach.

Communication with spatial periodic chaos synchronization

International Nuclear Information System (INIS)

Zhou, J.; Huang, H.B.; Qi, G.X.; Yang, P.; Xie, X.

2005-01-01

Based on the spatial periodic chaos synchronization in coupled ring and linear arrays, we proposed a random high-dimensional chaotic encryption scheme. The transmitter can choose hyperchaotic signals randomly from the ring at any different time and simultaneously transmit the information of chaotic oscillators in the ring to receiver through public channel, so that the message can be masked by different hyperchaotic signals in different time intervals during communication, and the receiver can decode the message based on chaos synchronization but the attacker does not know the random hyperchaotic dynamics and cannot decode the message. Furthermore, the high sensitivity to the symmetry of the coupling structure makes the attacker very difficult to obtain any useful message from the channel

Fine Grained Chaos in AdS_{2} Gravity.

Science.gov (United States)

Haehl, Felix M; Rozali, Moshe

2018-03-23

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u[over ^]_{*}. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS_{2}) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2k-point functions, characterized as being both "maximally braided" and "k-out of time order," which exhibit exponential growth until progressively longer time scales u[over ^]_{*}^{(k)}∼(k-1)u[over ^]_{*}. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Fine Grained Chaos in AdS2 Gravity

Science.gov (United States)

Haehl, Felix M.; Rozali, Moshe

2018-03-01

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u^*. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes two-dimensional anti-de Sitter space (AdS2 ) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2 k -point functions, characterized as being both "maximally braided" and "k -out of time order," which exhibit exponential growth until progressively longer time scales u^*(k)˜(k -1 )u^*. We suggest an interpretation as scrambling of increasingly fine grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

Bifurcations and chaos in convection taking non-Fourier heat-flux

Science.gov (United States)

Layek, G. C.; Pati, N. C.

2017-11-01

In this Letter, we report the influences of thermal time-lag on the onset of convection, its bifurcations and chaos of a horizontal layer of Boussinesq fluid heated underneath taking non-Fourier Cattaneo-Christov hyperbolic model for heat propagation. A five-dimensional nonlinear system is obtained for a low-order Galerkin expansion, and it reduces to Lorenz system for Cattaneo number tending to zero. The linear stability agreed with existing results that depend on Cattaneo number C. It also gives a threshold Cattaneo number, CT, above which only oscillatory solutions can persist. The oscillatory solutions branch terminates at the subcritical steady branch with a heteroclinic loop connecting a pair of saddle points for subcritical steady-state solutions. For subcritical onset of convection two stable solutions coexist, that is, hysteresis phenomenon occurs at this stage. The steady solution undergoes a Hopf bifurcation and is of subcritical type for small value of C, while it becomes supercritical for moderate Cattaneo number. The system goes through period-doubling/noisy period-doubling transition to chaos depending on the control parameters. There after the system exhibits Shil'nikov chaos via homoclinic explosion. The complexity of spiral strange attractor is analyzed using fractal dimension and return map.

Onset of dynamical chaos in topologically massive gauge theories

International Nuclear Information System (INIS)

Giansanti, A.; Simic, P.D.

1988-01-01

The onset of dynamical chaos is studied numerically in (2+1)-dimensional non-Abelian field theory with the Chern-Simons topological term. In the limit of strong fields, slowly varying in space (spatially homogeneous fields), this theory is an analog to a system of three charged particles moving in a plane in an orthogonal magnetic field and under the influence of a quartic potential. The ''phase transition'' (order chaos) is observed within a narrow energy range. The threshold of the transition depends on the sign of the angular momentum of the field reflecting parity violation in the underlying field theory. The transition region is investigated in some detail and the hyperfine structure of order-chaos-order-... transitions is observed suggesting the necessity of probabilistic description

Magnetic field induced dynamical chaos.

Science.gov (United States)

Ray, Somrita; Baura, Alendu; Bag, Bidhan Chandra

2013-12-01

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.

Chaos in collective nuclei

International Nuclear Information System (INIS)

Whelan, N.D.

1993-01-01

Random Matrix Theory successfully describes the statistics of the low-lying spectra of some nuclei but not of others. It is currently believed that this theory applies to systems in which the corresponding classical motion is chaotic. This conjecture is tested for collective nuclei by studying the Interacting Boson Model. Quantum and classical measures of chaos are proposed and found to be in agreement throughout the parameter space of the model. For some parameter values the measures indicate the presence of a previously unknown approximate symmetry. A phenomenon called partial dynamical symmetry is explored and shown to lead to a suppression of chaos. A time dependent function calculated from the quantum spectrum is discussed. This function is sensitive to the extent of chaos and provides a robust method of analyzing experimental spectra

Effortful control and school adjustment: The moderating role of classroom chaos.

Science.gov (United States)

Berger, Rebecca H; Valiente, Carlos; Eisenberg, Nancy; Hernandez, Maciel M; Thompson, Marilyn; Spinrad, Tracy; VanSchyndel, Sarah; Silva, Kassondra; Southworth, Jody

2017-11-01

Guided by the person by environment framework, the primary goal of this study was to determine whether classroom chaos moderated the relation between effortful control and kindergarteners' school adjustment. Classroom observers reported on children's ( N = 301) effortful control in the fall. In the spring, teachers reported on classroom chaos and school adjustment outcomes (teacher-student relationship closeness and conflict, and school liking and avoidance). Cross-level interactions between effortful control and classroom chaos predicting school adjustment outcomes were assessed. A consistent pattern of interactions between effortful control and classroom chaos indicated that the relations between effortful control and the school adjustment outcomes were strongest in high chaos classrooms. Post-hoc analyses indicated that classroom chaos was associated with poor school adjustment when effortful control was low, suggesting that the combination of high chaos and low effortful control was associated with the poorest school outcomes.

Chaos for cardiac arrhythmias through a one-dimensional modulation equation for alternans

Science.gov (United States)

Dai, Shu; Schaeffer, David G.

2010-01-01

Instabilities in cardiac dynamics have been widely investigated in recent years. One facet of this work has studied chaotic behavior, especially possible correlations with fatal arrhythmias. Previously chaotic behavior was observed in various models, specifically in the breakup of spiral and scroll waves. In this paper we study cardiac dynamics and find spatiotemporal chaotic behavior through the Echebarria–Karma modulation equation for alternans in one dimension. Although extreme parameter values are required to produce chaos in this model, it seems significant mathematically that chaos may occur by a different mechanism from previous observations. PMID:20590327

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

Energy Technology Data Exchange (ETDEWEB)

Ahlfeld, R., E-mail: r.ahlfeld14@imperial.ac.uk; Belkouchi, B.; Montomoli, F.

2016-09-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5

SAMBA: Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos

International Nuclear Information System (INIS)

Ahlfeld, R.; Belkouchi, B.; Montomoli, F.

2016-01-01

A new arbitrary Polynomial Chaos (aPC) method is presented for moderately high-dimensional problems characterised by limited input data availability. The proposed methodology improves the algorithm of aPC and extends the method, that was previously only introduced as tensor product expansion, to moderately high-dimensional stochastic problems. The fundamental idea of aPC is to use the statistical moments of the input random variables to develop the polynomial chaos expansion. This approach provides the possibility to propagate continuous or discrete probability density functions and also histograms (data sets) as long as their moments exist, are finite and the determinant of the moment matrix is strictly positive. For cases with limited data availability, this approach avoids bias and fitting errors caused by wrong assumptions. In this work, an alternative way to calculate the aPC is suggested, which provides the optimal polynomials, Gaussian quadrature collocation points and weights from the moments using only a handful of matrix operations on the Hankel matrix of moments. It can therefore be implemented without requiring prior knowledge about statistical data analysis or a detailed understanding of the mathematics of polynomial chaos expansions. The extension to more input variables suggested in this work, is an anisotropic and adaptive version of Smolyak's algorithm that is solely based on the moments of the input probability distributions. It is referred to as SAMBA (PC), which is short for Sparse Approximation of Moment-Based Arbitrary Polynomial Chaos. It is illustrated that for moderately high-dimensional problems (up to 20 different input variables or histograms) SAMBA can significantly simplify the calculation of sparse Gaussian quadrature rules. SAMBA's efficiency for multivariate functions with regard to data availability is further demonstrated by analysing higher order convergence and accuracy for a set of nonlinear test functions with 2, 5 and 10

Anticontrol of chaos in continuous-time systems via time-delay feedback.

Science.gov (United States)

Wang, Xiao Fan; Chen, Guanrong; Yu, Xinghuo

2000-12-01

In this paper, a systematic design approach based on time-delay feedback is developed for anticontrol of chaos in a continuous-time system. This anticontrol method can drive a finite-dimensional, continuous-time, autonomous system from nonchaotic to chaotic, and can also enhance the existing chaos of an originally chaotic system. Asymptotic analysis is used to establish an approximate relationship between a time-delay differential equation and a discrete map. Anticontrol of chaos is then accomplished based on this relationship and the differential-geometry control theory. Several examples are given to verify the effectiveness of the methodology and to illustrate the systematic design procedure. (c) 2000 American Institute of Physics.

Complex Nonlinearity Chaos, Phase Transitions, Topology Change and Path Integrals

CERN Document Server

Ivancevic, Vladimir G

2008-01-01

Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to th...

Cracking chaos-based encryption systems ruled by nonlinear time delay differential equations

International Nuclear Information System (INIS)

Udaltsov, Vladimir S.; Goedgebuer, Jean-Pierre; Larger, Laurent; Cuenot, Jean-Baptiste; Levy, Pascal; Rhodes, William T.

2003-01-01

We report that signal encoding with high-dimensional chaos produced by delayed feedback systems with a strong nonlinearity can be broken. We describe the procedure and illustrate the method with chaotic waveforms obtained from a strongly nonlinear optical system that we used previously to demonstrate signal encryption/decryption with chaos in wavelength. The method can be extended to any systems ruled by nonlinear time-delayed differential equations

Detecting chaos, determining the dimensions of tori and predicting slow diffusion in Fermi-Pasta-Ulam lattices by the Generalized Alignment Index method

Science.gov (United States)

Skokos, C.; Bountis, T.; Antonopoulos, C.

2008-12-01

The recently introduced GALI method is used for rapidly detecting chaos, determining the dimensionality of regular motion and predicting slow diffusion in multi-dimensional Hamiltonian systems. We propose an efficient computation of the GALIk indices, which represent volume elements of k randomly chosen deviation vectors from a given orbit, based on the Singular Value Decomposition (SVD) algorithm. We obtain theoretically and verify numerically asymptotic estimates of GALIs long-time behavior in the case of regular orbits lying on low-dimensional tori. The GALIk indices are applied to rapidly detect chaotic oscillations, identify low-dimensional tori of Fermi-Pasta-Ulam (FPU) lattices at low energies and predict weak diffusion away from quasiperiodic motion, long before it is actually observed in the oscillations.

Spatiotemporal chaos and two-dimensional dissipative rogue waves in Lugiato-Lefever model

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Panajotov, Krassimir; Clerc, Marcel G.; Tlidi, Mustapha

2017-06-01

Driven nonlinear optical cavities can exhibit complex spatiotemporal dynamics. We consider the paradigmatic Lugiato-Lefever model describing driven nonlinear optical resonator. This model is one of the most-studied nonlinear equations in optics. It describes a large spectrum of nonlinear phenomena from bistability, to periodic patterns, localized structures, self-pulsating localized structures and to a complex spatiotemporal behavior. The model is considered also as prototype model to describe several optical nonlinear devices such as Kerr media, liquid crystals, left handed materials, nonlinear fiber cavity, and frequency comb generation. We focus our analysis on a spatiotemporal chaotic dynamics in one-dimension. We identify a route to spatiotemporal chaos through an extended quasiperiodicity. We have estimated the Kaplan-Yorke dimension that provides a measure of the strange attractor complexity. Likewise, we show that the Lugiato-Leferver equation supports rogues waves in two-dimensional settings. We characterize rogue-wave formation by computing the probability distribution of the pulse height. Contribution to the Topical Issue "Theory and Applications of the Lugiato-Lefever Equation", edited by Yanne K. Chembo, Damia Gomila, Mustapha Tlidi, Curtis R. Menyuk.

Control of collective network chaos.

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

2014-06-01

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.

Biologically inspired rate control of chaos.

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Olde Scheper, Tjeerd V

2017-10-01

The overall intention of chaotic control is to eliminate chaos and to force the system to become stable in the classical sense. In this paper, I demonstrate a more subtle method that does not eliminate all traces of chaotic behaviour; yet it consistently, and reliably, can provide control as intended. The Rate Control of Chaos (RCC) method is derived from metabolic control processes and has several remarkable properties. RCC can control complex systems continuously, and unsupervised, it can also maintain control across bifurcations, and in the presence of significant systemic noise. Specifically, I show that RCC can control a typical set of chaotic models, including the 3 and 4 dimensional chaotic Lorenz systems, in all modes. Furthermore, it is capable of controlling spatiotemporal chaos without supervision and maintains control of the system across bifurcations. This property of RCC allows a dynamic system to operate in parameter spaces that are difficult to control otherwise. This may be particularly interesting for the control of forced systems or dynamic systems that are chaotically perturbed. These control properties of RCC are applicable to a range of dynamic systems, thereby appearing to have far-reaching effects beyond just controlling chaos. RCC may also point to the existence of a biochemical control function of an enzyme, to stabilise the dynamics of the reaction cascade.

Deterministic chaos at the ocean surface: applications and interpretations

Directory of Open Access Journals (Sweden)

A. J. Palmer

1998-01-01

Full Text Available Ocean surface, grazing-angle radar backscatter data from two separate experiments, one of which provided coincident time series of measured surface winds, were found to exhibit signatures of deterministic chaos. Evidence is presented that the lowest dimensional underlying dynamical system responsible for the radar backscatter chaos is that which governs the surface wind turbulence. Block-averaging time was found to be an important parameter for determining the degree of determinism in the data as measured by the correlation dimension, and by the performance of an artificial neural network in retrieving wind and stress from the radar returns, and in radar detection of an ocean internal wave. The correlation dimensions are lowered and the performance of the deterministic retrieval and detection algorithms are improved by averaging out the higher dimensional surface wave variability in the radar returns.

Chaos in hadrons

International Nuclear Information System (INIS)

Muñoz, L; Fernández-Ramírez, C; Relaño, A; Retamosa, J

2012-01-01

In the last decade quantum chaos has become a well established discipline with outreach to different fields, from condensed-matter to nuclear physics. The most important signature of quantum chaos is the statistical analysis of the energy spectrum, which distinguishes between systems with integrable and chaotic classical analogues. In recent years, spectral statistical techniques inherited from quantum chaos have been applied successfully to the baryon spectrum revealing its likely chaotic behaviour even at the lowest energies. However, the theoretical spectra present a behaviour closer to the statistics of integrable systems which makes theory and experiment statistically incompatible. The usual statement of missing resonances in the experimental spectrum when compared to the theoretical ones cannot account for the discrepancies. In this communication we report an improved analysis of the baryon spectrum, taking into account the low statistics and the error bars associated with each resonance. Our findings give a major support to the previous conclusions. Besides, analogue analyses are performed in the experimental meson spectrum, with comparison to theoretical models.

Quantum chaos in the Heisenberg spin chain: The effect of Dzyaloshinskii-Moriya interaction.

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Vahedi, J; Ashouri, A; Mahdavifar, S

2016-10-01

Using one-dimensional spin-1/2 systems as prototypes of quantum many-body systems, we study the emergence of quantum chaos. The main purpose of this work is to answer the following question: how the spin-orbit interaction, as a pure quantum interaction, may lead to the onset of quantum chaos? We consider the three integrable spin-1/2 systems: the Ising, the XX, and the XXZ limits and analyze whether quantum chaos develops or not after the addition of the Dzyaloshinskii-Moriya interaction. We find that depending on the strength of the anisotropy parameter, the answer is positive for the XXZ and Ising models, whereas no such evidence is observed for the XX model. We also discuss the relationship between quantum chaos and thermalization.

Chaos, patterns, coherent structures, and turbulence: Reflections on nonlinear science.

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Ecke, Robert E

2015-09-01

The paradigms of nonlinear science were succinctly articulated over 25 years ago as deterministic chaos, pattern formation, coherent structures, and adaptation/evolution/learning. For chaos, the main unifying concept was universal routes to chaos in general nonlinear dynamical systems, built upon a framework of bifurcation theory. Pattern formation focused on spatially extended nonlinear systems, taking advantage of symmetry properties to develop highly quantitative amplitude equations of the Ginzburg-Landau type to describe early nonlinear phenomena in the vicinity of critical points. Solitons, mathematically precise localized nonlinear wave states, were generalized to a larger and less precise class of coherent structures such as, for example, concentrated regions of vorticity from laboratory wake flows to the Jovian Great Red Spot. The combination of these three ideas was hoped to provide the tools and concepts for the understanding and characterization of the strongly nonlinear problem of fluid turbulence. Although this early promise has been largely unfulfilled, steady progress has been made using the approaches of nonlinear science. I provide a series of examples of bifurcations and chaos, of one-dimensional and two-dimensional pattern formation, and of turbulence to illustrate both the progress and limitations of the nonlinear science approach. As experimental and computational methods continue to improve, the promise of nonlinear science to elucidate fluid turbulence continues to advance in a steady manner, indicative of the grand challenge nature of strongly nonlinear multi-scale dynamical systems.

Chaos induced by quantum effect due to breakdown of the Born-Oppenheimer adiabaticity

International Nuclear Information System (INIS)

Fujisaki, Hiroshi; Takatsuka, Kazuo

2001-01-01

Chaos in the multimode nonadiabatic system constructed by Heller [J. Chem. Phys. >92, 1718 (1990)], which consists of two diabatic two-dimensional harmonic potentials with the Condon coupling, is studied. A thorough investigation is carried out by scanning the magnitudes of the Condon coupling and the Duschinsky angle. To elucidate mechanisms that can cause chaos in this quantum system, the statistical properties of the energy levels and eigenfunctions of the system are investigated. We find an evidence in terms of the nearest-neighbor spacing distribution of energy levels and other measures that a certain class of chaos is purely induced by the nonadiabatic interaction due to breakdown of the Born-Oppenheimer approximation. Since the nonadiabatic transition can induce repeated bifurcation and merging of a wave packet around the region of quasicrossing between two potential surfaces, and since this interaction does not have a counterpart in the lower adiabatic system, the present chaos deserves being called 'nonadiabatic chaos.' Another type of chaos in a nonadiabatic system was previously identified [D. M. Leitner et al., J. Chem. Phys. >104, 434 (1996)] that reflects the inherent chaos of a corresponding adiabatic potential. We present a comparative study to establish the similarity and difference between these kinds of chaos

Induced fission of nuclei: dynamical chaos and lifetime of compound nucleus

Energy Technology Data Exchange (ETDEWEB)

Krivoshej, I V

1987-01-01

A semi-phenomenological theory is proposed to describe the induced fission of heavy nuclei at low and intermediate excitation energies. The theory is based on the concept of the dynamical chaos, arising because of a negative curvature of the n-dimensional potential energy surface (PES). The nuclear fission is treated as a diffusion of the representing point across a vicinity of the saddle point in PES. The diffusion coefficient is calculated for various metrics in PES as an explicit function of the two-dimensional curvatures at the saddle point of PES. The present theory suggests an estimate for the fission time, tau/sub f/approx.10/sup -14/ s. Coefficients of nuclear friction and viscosity are also calculated in general, and the resulting numerical estimates are in agreement with the experimental data.

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

Science.gov (United States)

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

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 Chaos-like complexity, assessed through the noise limit, increased from pH 7.8 to pH 7.4 (P 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

Early Exposure to Environmental Chaos and Children's Physical and Mental Health.

Science.gov (United States)

Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

Environmental chaos has been proposed as a central influence impeding children's health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children's physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children's functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children's functioning.

Quantum chaos

International Nuclear Information System (INIS)

Steiner, F.

1994-01-01

A short historical overview is given on the development of our knowledge of complex dynamical systems with special emphasis on ergodicity and chaos, and on the semiclassical quantization of integrable and chaotic systems. The general trace formular is discussed as a sound mathematical basis for the semiclassical quantization of chaos. Two conjectures are presented on the basis of which it is argued that there are unique fluctuation properties in quantum mechanics which are universal and, in a well defined sense, maximally random if the corresponding classical system is strongly chaotic. These properties constitute the quantum mechanical analogue of the phenomenon of chaos in classical mechanics. Thus quantum chaos has been found. (orig.)

A novel image encryption algorithm using chaos and reversible cellular automata

Science.gov (United States)

Wang, Xingyuan; Luan, Dapeng

2013-11-01

In this paper, a novel image encryption scheme is proposed based on reversible cellular automata (RCA) combining chaos. In this algorithm, an intertwining logistic map with complex behavior and periodic boundary reversible cellular automata are used. We split each pixel of image into units of 4 bits, then adopt pseudorandom key stream generated by the intertwining logistic map to permute these units in confusion stage. And in diffusion stage, two-dimensional reversible cellular automata which are discrete dynamical systems are applied to iterate many rounds to achieve diffusion on bit-level, in which we only consider the higher 4 bits in a pixel because the higher 4 bits carry almost the information of an image. Theoretical analysis and experimental results demonstrate the proposed algorithm achieves a high security level and processes good performance against common attacks like differential attack and statistical attack. This algorithm belongs to the class of symmetric systems.

Adaptive method for multi-dimensional integration and selection of a base of chaos polynomials

International Nuclear Information System (INIS)

Crestaux, T.

2011-01-01

This research thesis addresses the propagation of uncertainty in numerical simulations and its processing within a probabilistic framework by a functional approach based on random variable functions. The author reports the use of the spectral method to represent random variables by development in polynomial chaos. More precisely, the author uses the method of non-intrusive projection which uses the orthogonality of Chaos Polynomials to compute the development coefficients by approximation of scalar products. The approach is applied to a cavity and to waste storage [fr

A period-doubling cascade precedes chaos for planar maps.

Science.gov (United States)

Sander, Evelyn; Yorke, James A

2013-09-01

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-2π maps for the Duffing equation and the forced damped pendulum equation.

Chaos in high-power high-frequency gyrotrons

International Nuclear Information System (INIS)

Airila, M.

2004-01-01

Gyrotron interaction is a complex nonlinear dynamical process, which may turn chaotic in certain circumstances. The emergence of chaos renders dynamical systems unpredictable and causes bandwidth broadening of signals. Such effects would jeopardize the prospect of advanced gyrotrons in fusion. Therefore, it is important to be aware of the possibility of chaos in gyrotrons. There are three different chaos scenarios closely related to the development of high-power gyrotrons: First, the onset of chaos in electron trajectories would lead to difficulties in the design and efficient operation of depressed potential collectors, which are used for efficiency enhancement. Second, the radio-frequency signal could turn chaotic, decreasing the output power and the spectral purity of the output signal. As a result, mode conversion, transmission, and absorption efficiencies would be reduced. Third, spatio-temporal chaos in the resonator field structure can set a limit for the use of large-diameter interaction cavities and high-order TE modes (large azimuthal index) allowing higher generated power. In this thesis, the issues above are addressed with numerical modeling. It is found that chaos in electron residual energies is practically absent in the parameter region corresponding to high efficiency. Accordingly, depressed collectors are a feasible solution also in advanced high-power gyrotrons. A new method is presented for straightforward numerical solution of the one-dimensional self-consistent time-dependent gyrotron equations, and the method is generalized to two dimensions. In 1D, a chart of gyrotron oscillations is calculated. It is shown that the regions of stationary oscillations, automodulation, and chaos have a complicated topology in the plane of generalized gyrotron variables. The threshold current for chaotic oscillations exceeds typical operating currents by a factor of ten. However, reflection of the output signal may significantly lower the threshold. 2D

A novel image encryption scheme based on spatial chaos map

International Nuclear Information System (INIS)

Sun Fuyan; Liu Shutang; Li Zhongqin; Lue Zongwang

2008-01-01

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, spatial chaos system are used for high degree security image encryption while its speed is acceptable. The proposed algorithm is described in detail. The basic idea is to encrypt the image in space with spatial chaos map pixel by pixel, and then the pixels are confused in multiple directions of space. Using this method one cycle, the image becomes indistinguishable in space due to inherent properties of spatial chaotic systems. Several experimental results, key sensitivity tests, key space analysis, and statistical analysis show that the approach for image cryptosystems provides an efficient and secure way for real time image encryption and transmission from the cryptographic viewpoint

Early Exposure to Environmental Chaos and Children’s Physical and Mental Health

Science.gov (United States)

Coley, Rebekah Levine; Lynch, Alicia Doyle; Kull, Melissa

2015-01-01

Environmental chaos has been proposed as a central influence impeding children’s health and development, with the potential for particularly pernicious effects during the earliest years when children are most susceptible to environmental insults. This study evaluated a high-risk sample, following 495 low-income children living in poor urban neighborhoods from infancy to age 6. Longitudinal multilevel models tested the main tenets of the ecobiodevelopmental theory, finding that: (1) numerous distinct domains of environmental chaos were associated with children’s physical and mental health outcomes, including housing disorder, neighborhood disorder, and relationship instability, with no significant results for residential instability; (2) different patterns emerged in relation to the timing of exposure to chaos, with more proximal exposure most strongly associated with children’s functioning; and (3) the intensity of chaos also was a robust predictor of child functioning. Contrary to expectations, neither biological vulnerability (proxied through low birth weight status), maternal sensitivity, nor maternal distress moderated the role of chaos. Rather, maternal psychological distress functioned as a pathway through which environmental chaos was associated with children’s functioning. PMID:25844016

Generalized Lorenz models and their routes to chaos. II. Energy-conserving horizontal mode truncations

International Nuclear Information System (INIS)

Roy, D.; Musielak, Z.E.

2007-01-01

All attempts to generalize the three-dimensional Lorenz model by selecting higher-order Fourier modes can be divided into three categories, namely: vertical, horizontal and vertical-horizontal mode truncations. The previous study showed that the first method allowed only construction of a nine-dimensional system when the selected modes were energy-conserving. The results presented in this paper demonstrate that a five-dimensional model is the lowest-order generalized Lorenz model that can be constructed by the second method and that its route to chaos is the same as that observed in the original Lorenz model. It is shown that the onset of chaos in both systems is determined by a number of modes that describe the vertical temperature difference in a convection roll. In addition, a simple rule that allows selecting modes that conserve energy for each method is derived

Embrace the Chaos

Science.gov (United States)

Huwe, Terence K.

2009-01-01

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

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Science.gov (United States)

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

2015-12-01

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Onset of chaos in helical vortex breakdown at low Reynolds number

Science.gov (United States)

Pasche, S.; Avellan, F.; Gallaire, F.

2018-06-01

The nonlinear dynamics of a swirling wake flow stemming from a Graboswksi-Berger vortex [Grabowski and Berger, J. Fluid Mech. 75, 525 (1976), 10.1017/S0022112076000360] in a semi-infinite domain is addressed at low Reynolds numbers for a fixed swirl number S =1.095 , defined as the ratio between the characteristic tangential velocity and the centerline axial velocity. In this system, only pure hydrodynamic instabilities develop and interact through the quadratic nonlinearities of the Navier-Stokes equations. Such interactions lead to the onset of chaos at a Reynolds value of Re=220 . This chaotic state is reached by following a Ruelle-Takens-Newhouse scenario, which is initiated by a Hopf bifurcation (the spiral vortex breakdown) as the Reynolds number increases. At larger Reynolds value, a frequency synchronization regime appears followed by a chaotic state again. This scenario is corroborated by nonlinear time series analyses. Stability analysis around the time-average flow and temporal-azimuthal Fourier decomposition of the nonlinear flow distributions both identify successfully the developing vortices and provide deeper insight into the development of the flow patterns leading to this route to chaos. Three single-helical vortices are involved: the primary spiral associated with the spiral vortex breakdown, a downstream spiral, and a near-wake spiral. As the Reynolds number increases, the frequencies of these vortices become closer, increasing their interactions by nonlinearity to eventually generate a strong chaotic axisymmetric oscillation.

The Capabilities of Chaos and Complexity

Directory of Open Access Journals (Sweden)

David L. Abel

2009-01-01

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

Chaos in neurons and its application: perspective of chaos engineering.

Science.gov (United States)

Hirata, Yoshito; Oku, Makito; Aihara, Kazuyuki

2012-12-01

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

Generation of 2N + 1-scroll existence in new three-dimensional chaos systems

Energy Technology Data Exchange (ETDEWEB)

Liu, Yue; Guan, Jian; Ma, Chunyang; Guo, Shuxu, E-mail: guosx@jlu.edu.cn [College of Electronic Science and Engineering, Jilin University, Changchun 130012 (China)

2016-08-15

We propose a systematic methodology for creating 2N + 1-scroll chaotic attractors from a simple three-dimensional system, which is named as the translation chaotic system. It satisfies the condition a{sub 12}a{sub 21} = 0, while the Chua system satisfies a{sub 12}a{sub 21} > 0. In this paper, we also propose a successful (an effective) design and an analytical approach for constructing 2N + 1-scrolls, the translation transformation principle. Also, the dynamics properties of the system are studied in detail. MATLAB simulation results show very sophisticated dynamical behaviors and unique chaotic behaviors of the system. It provides a new approach for 2N + 1-scroll attractors. Finally, to explore the potential use in technological applications, a novel block circuit diagram is also designed for the hardware implementation of 1-, 3-, 5-, and 7-scroll attractors via switching the switches. Translation chaotic system has the merit of convenience and high sensitivity to initial values, emerging potentials in future engineering chaos design.

Generation of flat wideband chaos with suppressed time delay signature by using optical time lens.

Science.gov (United States)

Jiang, Ning; Wang, Chao; Xue, Chenpeng; Li, Guilan; Lin, Shuqing; Qiu, Kun

2017-06-26

We propose a flat wideband chaos generation scheme that shows excellent time delay signature suppression effect, by injecting the chaotic output of general external cavity semiconductor laser into an optical time lens module composed of a phase modulator and two dispersive units. The numerical results demonstrate that by properly setting the parameters of the driving signal of phase modulator and the accumulated dispersion of dispersive units, the relaxation oscillation in chaos can be eliminated, wideband chaos generation with an efficient bandwidth up to several tens of GHz can be achieved, and the RF spectrum of generated chaotic signal is nearly as flat as uniform distribution. Moreover, the periodicity of chaos induced by the external cavity modes can be simultaneously destructed by the optical time lens module, based on this the time delay signature can be completely suppressed.

An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling

Science.gov (United States)

Li, Weixuan; Lin, Guang; Zhang, Dongxiao

2014-02-01

The probabilistic collocation-based Kalman filter (PCKF) is a recently developed approach for solving inverse problems. It resembles the ensemble Kalman filter (EnKF) in every aspect-except that it represents and propagates model uncertainty by polynomial chaos expansion (PCE) instead of an ensemble of model realizations. Previous studies have shown PCKF is a more efficient alternative to EnKF for many data assimilation problems. However, the accuracy and efficiency of PCKF depends on an appropriate truncation of the PCE series. Having more polynomial chaos basis functions in the expansion helps to capture uncertainty more accurately but increases computational cost. Selection of basis functions is particularly important for high-dimensional stochastic problems because the number of polynomial chaos basis functions required to represent model uncertainty grows dramatically as the number of input parameters (random dimensions) increases. In classic PCKF algorithms, the PCE basis functions are pre-set based on users' experience. Also, for sequential data assimilation problems, the basis functions kept in PCE expression remain unchanged in different Kalman filter loops, which could limit the accuracy and computational efficiency of classic PCKF algorithms. To address this issue, we present a new algorithm that adaptively selects PCE basis functions for different problems and automatically adjusts the number of basis functions in different Kalman filter loops. The algorithm is based on adaptive functional ANOVA (analysis of variance) decomposition, which approximates a high-dimensional function with the summation of a set of low-dimensional functions. Thus, instead of expanding the original model into PCE, we implement the PCE expansion on these low-dimensional functions, which is much less costly. We also propose a new adaptive criterion for ANOVA that is more suited for solving inverse problems. The new algorithm was tested with different examples and demonstrated

Order, disorder and chaos in crystal lattice

International Nuclear Information System (INIS)

Oliveira, M.J. de; Salinas, S.R.A.

1985-01-01

The properties of two two-dimensional mappings corresponding to the solutions of spin models on a Cayley tree in infinite coordination limit are analised in detail. The models under consideration are related to some mechanisms which were proposed to explain the occurrence of modulated phases in magnetic crystals. The existence of devil's staircases characterized by fractal dimensionalities which increase with temperature is shown. Numerical evidences to support the existence of a strange attractor, of a fractal character, in the Ising model with competing interactions restricted to the branches of a Cayley tree are presented. The route to chaos agrees with the scenario of Feigenbaum. (Author) [pt

Coupling between temporal and spatial chaos of vortex state in superconductors with periodical pinning arrays

Energy Technology Data Exchange (ETDEWEB)

Lin, H.T. [Department of Information Management, Cheng Shiu University, Kaoshuing, Taiwan (China); Cheng, C.H. [Key Laboratory of Magnetic Levitation and Maglev Trains (Ministry of Education of China), Superconductivity R and D Center (SRDC), Mail Stop 165, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China); Ke, C.; Pan, M. [School of Materials Science and Engineering, University of New South Wale, Sydney, 2052 NSW (Australia); Zhao, Y., E-mail: yzhao@swjtu.edu.cn [Key Laboratory of Magnetic Levitation and Maglev Trains (Ministry of Education of China), Superconductivity R and D Center (SRDC), Mail Stop 165, Southwest Jiaotong University, Chengdu, Sichuan 610031 (China)] [School of Materials Science and Engineering, University of New South Wale, Sydney, 2052 NSW (Australia)

2011-11-15

Mean field approach is a good way of dealing with chaos of vortex motion in a background of many vortices. The vortex motion under the damping mode is a kind of self-organized motion. The spatial chaos can dominate the chaotic behavior of the system. Vortex motion in the background of many vortices is investigated by a mean field approach. Effects of the vortex-vortex coupling, the driving frequency, and the vortex viscosity on the vortex motion have been studied to reveal the interaction between the spatial and temporal chaos. It is found that the mean-field approach is a good approximation to describe the vortex motion in one dimensional vortex system. The vortex motion under the damping mode is a kind of self-organized motion. The spatial chaos can dominate the chaotic behavior of the system.

Controlling chaos in dynamical systems described by maps

International Nuclear Information System (INIS)

Crispin, Y.; Marduel, C.

1994-01-01

The problem of suppressing chaotic behavior in dynamical systems is treated using a feedback control method with limited control effort. The proposed method is validated on archetypal systems described by maps, i.e. discrete-time difference equations. The method is also applicable to dynamical systems described by flows, i.e. by systems of ordinary differential equations. Results are presented for the one-dimensional logistic map and for a two-dimensional Lotka-Volterra map describing predator-prey population dynamics. It is shown that chaos can be suppressed and the system stabilized about a period-1 fixed point of the maps

Low dimensional chaotic models for the plague epidemic in Bombay (1896–1911)

International Nuclear Information System (INIS)

Mangiarotti, Sylvain

2015-01-01

A plague epidemic broke out in Bombay in 1896 and became endemic. From 1905 to 1911, the epidemic was closely monitored by an Advisory Committee appointed to investigate the causes of the disease in any way. An impressive quantity of information was gathered, analyzed and published. Published data include records of the number of people who died from plague, and of the two main populations of rodents which were infected by plague in Bombay city. In the present paper, these data are revisited using a global modeling technique. This technique is applied to both single and multivariate observational time series. Several models are obtained for which a chaotic behavior can be observed. Obtaining such models proves that the dynamics of plague can be approximated by low-dimensional deterministic systems that can produce chaos. The multivariate models give a strong argument for interactive couplings between the epidemic and the epizootics of the two main species of rat. An interpretation of this coupling is given.

Defining chaos.

Science.gov (United States)

Hunt, Brian R; Ott, Edward

2015-09-01

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

Prediction of chaos in a Josephson junction by the Melnikov-function technique

DEFF Research Database (Denmark)

Bartuccelli, M.; Christiansen, Peter Leth; Pedersen, Niels Falsig

1986-01-01

The Melnikov function for prediction of Smale horseshoe chaos is applied to the rf-driven Josephson junction. Linear and quadratic damping resistors are considered. In the latter case the analytic solution including damping and dc bias is used to obtain an improved threshold curve for the onset...... of chaos. The prediction is compared to new computational solutions. The Melnikov technique provides a good, but slightly low, estimate of the chaos threshold....

Li-Yorke chaos and synchronous chaos in a globally nonlocal coupled map lattice

International Nuclear Information System (INIS)

Khellat, Farhad; Ghaderi, Akashe; Vasegh, Nastaran

2011-01-01

Highlights: → A globally nonlocal coupled map lattice is introduced. → A sufficient condition for the existence of Li-Yorke chaos is determined. → A sufficient condition for synchronous behaviors is obtained. - Abstract: This paper investigates a globally nonlocal coupled map lattice. A rigorous proof to the existence of chaos in the scene of Li-Yorke in that system is presented in terms of the Marotto theorem. Analytical sufficient conditions under which the system is chaotic, and has synchronous behaviors are determined, respectively. The wider regions associated with chaos and synchronous behaviors are shown by simulations. Spatiotemporal chaos, synchronous chaos and some other synchronous behaviors such as fixed points, 2-cycles and 2 2 -cycles are also shown by simulations for some values of the parameters.

Physics of low-dimensional systems

International Nuclear Information System (INIS)

Anon.

1989-01-01

The physics of low-dimensional systems has developed in a remarkable way over the last decade and has accelerated over the last few years, in particular because of the discovery of the new high temperature superconductors. The new developments started more than fifteen years ago with the discovery of the unexpected quasi-one-dimensional character of the TTF-TCNQ. Since then the field of conducting quasi-one-dimensional organic system have been rapidly growing. Parallel to the experimental work there has been an important theoretical development of great conceptual importance, such as charge density waves, soliton-like excitations, fractional charges, new symmetry properties etc. A new field of fundamental importance was the discovery of the Quantum Hall Effect in 1980. This field is still expanding with new experimental and theoretical discoveries. In 1986, then, came the totally unexpected discovery of high temperature superconductivity which started an explosive development. The three areas just mentioned formed the main themes of the Symposium. They do not in any way exhaust the progress in low-dimensional physics. We should mention the recent important development with both two-dimensional and one-dimensional and even zero-dimensional structures (quantum dots). The physics of mesoscopic systems is another important area where the low dimensionality is a key feature. Because of the small format of this Symposium we could unfortunately not cover these areas

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

Science.gov (United States)

Schmeer, Kammi K.; Taylor, Miles

2013-01-01

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

Quantum chaos

International Nuclear Information System (INIS)

Cejnar, P.

2007-01-01

Chaos is a name given in physics to a branch which, within classical mechanics, studies the consequences of sensitive dependences of the behavior of physical systems on the starting conditions, i.e., the 'butterfly wing effect'. However, how to describe chaotic behavior in the world of quantum particles? It appears that quantum mechanics does not admit the sensitive dependence on the starting conditions, and moreover, predicts a substantial suppression of chaos also at the macroscopic level. Still, the quantum properties of systems that are chaotic in terms of classical mechanics differ basically from the properties of classically arranged systems. This topic is studied by a field of physics referred to as quantum chaos. (author)

Leveraging Chaos in Continuous Thrust Trajectory Design

Data.gov (United States)

National Aeronautics and Space Administration — A trajectory design tool is sought to leverage chaos and nonlinear dynamics present in multi-body gravitational fields to design ultra-low energy transfer...

Low-dimensional molecular metals

CERN Document Server

Toyota, Naoki; Muller, Jens

2007-01-01

Assimilating research in the field of low-dimensional metals, this monograph provides an overview of the status of research on quasi-one- and two-dimensional molecular metals, describing normal-state properties, magnetic field effects, superconductivity, and the phenomena of interacting p and d electrons.

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

Science.gov (United States)

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

2011-05-01

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 acidosis, but in postmetamorphic tadpoles only (P 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.

Autoregressive models as a tool to discriminate chaos from randomness in geoelectrical time series: an application to earthquake prediction

Directory of Open Access Journals (Sweden)

C. Serio

1997-06-01

Full Text Available The time dynamics of geoelectrical precursory time series has been investigated and a method to discriminate chaotic behaviour in geoelectrical precursory time series is proposed. It allows us to detect low-dimensional chaos when the only information about the time series comes from the time series themselves. The short-term predictability of these time series is evaluated using two possible forecasting approaches: global autoregressive approximation and local autoregressive approximation. The first views the data as a realization of a linear stochastic process, whereas the second considers the data points as a realization of a deterministic process, supposedly non-linear. The comparison of the predictive skill of the two techniques is a test to discriminate between low-dimensional chaos and random dynamics. The analyzed time series are geoelectrical measurements recorded by an automatic station located in Tito (Southern Italy in one of the most seismic areas of the Mediterranean region. Our findings are that the global (linear approach is superior to the local one and the physical system governing the phenomena of electrical nature is characterized by a large number of degrees of freedom. Power spectra of the filtered time series follow a P(f = F-a scaling law: they exhibit the typical behaviour of a broad class of fractal stochastic processes and they are a signature of the self-organized systems.

Controlling chaos in low and high dimensional systems with periodic parametric perturbations

International Nuclear Information System (INIS)

Mirus, K.A.; Sprott, J.C.

1998-06-01

The effect of applying a periodic perturbation to an accessible parameter of various chaotic systems is examined. Numerical results indicate that perturbation frequencies near the natural frequencies of the unstable periodic orbits of the chaotic systems can result in limit cycles for relatively small perturbations. Such perturbations can also control or significantly reduce the dimension of high-dimensional systems. Initial application to the control of fluctuations in a prototypical magnetic fusion plasma device will be reviewed

Paths to chaos

International Nuclear Information System (INIS)

Friedrich, H.

1992-01-01

Rapid growth in the study of nonlinear dynamics and chaos in classical mechanics, has led physicists to reappraise their abandonment of this definition of atomic theory in favour of quantum mechanics adopted earlier this century. The concept of chaos in classical mechanics is examined in this paper and manifestations of chaos in quantum mechanics are explored. While quantum mechanics teaches that atomic particles must not be pictured as moving sharply in defined orbits, these precise orbits can be used to describe essential features of the measurable quantum mechanical spectra. (UK)

Hyperchaos and chaotic hierarchy in low-dimensional chemical systems

Science.gov (United States)

Baier, Gerold; Sahle, Sven

1994-06-01

Chemical reaction chains with feedback of one of the products on the source of the chain are considered. A strategy is presented in terms of ordinary differential equations which creates one, two, and three positive Lyapunov exponents as the finite dimension of the system is increased. In particular, a nonlinear inhibition loop in a chemical reaction sequence controls the type of chaos. The bifurcation scenarios are studied and chaos and hyperchaos are found for broad regions of bifurcation parameter. Some implications for the occurrence of higher chaos in real systems are discussed.

Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits

Directory of Open Access Journals (Sweden)

Arun Kaintura

2018-02-01

Full Text Available Advances in manufacturing process technology are key ensembles for the production of integrated circuits in the sub-micrometer region. It is of paramount importance to assess the effects of tolerances in the manufacturing process on the performance of modern integrated circuits. The polynomial chaos expansion has emerged as a suitable alternative to standard Monte Carlo-based methods that are accurate, but computationally cumbersome. This paper provides an overview of the most recent developments and challenges in the application of polynomial chaos-based techniques for uncertainty quantification in integrated circuits, with particular focus on high-dimensional problems.

Optical properties of low-dimensional materials

CERN Document Server

Ogawa, T

1998-01-01

This book surveys recent theoretical and experimental studies of optical properties of low-dimensional materials. As an extended version of Optical Properties of Low-Dimensional Materials (Volume 1, published in 1995 by World Scientific), Volume 2 covers a wide range of interesting low-dimensional materials including both inorganic and organic systems, such as disordered polymers, deformable molecular crystals, dilute magnetic semiconductors, SiGe/Si short-period superlattices, GaAs quantum wires, semiconductor microcavities, and photonic crystals. There are excellent review articles by promis

Model for Shock Wave Chaos

KAUST Repository

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

2013-01-01

: 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

Western Eos Chaos on Mars: A Potential Site for Future Landing and Returning Samples

Science.gov (United States)

Asif Iqbal Kakkassery; Rajesh, V. J.

2018-04-01

Introducing Eos Chaos as a potential area for collecting samples. Eos Chaos contains a number of aqueous minerals. We have detected zoisite — a least reported low-grade metamorphic mineral from this area.

Does chaos assist localization or delocalization?

Science.gov (United States)

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

2014-12-01

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.

Study of chaos in chaotic satellite systems

Science.gov (United States)

Khan, Ayub; Kumar, Sanjay

2018-01-01

In this paper, we study the qualitative behaviour of satellite systems using bifurcation diagrams, Poincaré section, Lyapunov exponents, dissipation, equilibrium points, Kaplan-Yorke dimension etc. Bifurcation diagrams with respect to the known parameters of satellite systems are analysed. Poincaré sections with different sowing axes of the satellite are drawn. Eigenvalues of Jacobian matrices for the satellite system at different equilibrium points are calculated to justify the unstable regions. Lyapunov exponents are estimated. From these studies, chaos in satellite system has been established. Solution of equations of motion of the satellite system are drawn in the form of three-dimensional, two-dimensional and time series phase portraits. Phase portraits and time series display the chaotic nature of the considered system.

Theory and Applications of Discontinuous State Feedback Generating Chaos for Linear Systems

International Nuclear Information System (INIS)

Xiao-Dan, Zhang; Zhen, Wang; Pin-Dong, Zhao

2008-01-01

We investigate a kind of chaos generating technique on a type of n-dimensional linear differential systems by adding feedback control items under a discontinuous state. This method is checked with some examples of numeric simulation. A constructive theorem is proposed for generalized synchronization related to the above chaotic system

[Shedding light on chaos theory].

Science.gov (United States)

Chou, Shieu-Ming

2004-06-01

Gleick (1987) said that only three twentieth century scientific theories would be important enough to continue be of use in the twenty-first century: The Theory of Relativity, Quantum Theory, and Chaos Theory. Chaos Theory has become a craze which is being used to forge a new scientific system. It has also been extensively applied in a variety of professions. The purpose of this article is to introduce chaos theory and its nursing applications. Chaos is a sign of regular order. This is to say that chaos theory emphasizes the intrinsic potential for regular order within disordered phenomena. It is to be hoped that this article will inspire more nursing scientists to apply this concept to clinical, research, or administrative fields in our profession.

Some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers of finite extent

Energy Technology Data Exchange (ETDEWEB)

Li, K., E-mail: likai@imech.ac.cn [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China); University of Chinese Academy of Sciences, Beijing 100190 (China); Xun, B.; Hu, W. R. [Key Laboratory of Microgravity, Chinese Academy of Sciences, Beijing 100190, China and National Microgravity Laboratory, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190 (China)

2016-05-15

As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.

Some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers of finite extent

International Nuclear Information System (INIS)

Li, K.; Xun, B.; Hu, W. R.

2016-01-01

As a part of the preliminary studies for the future space experiment (Zona-K) in the Russian module of the International Space Station, some bifurcation routes to chaos of thermocapillary convection in two-dimensional liquid layers filled with 10 cSt silicone oil have been numerically studied in this paper. As the laterally applied temperature difference is raised, variations in the spatial structure and temporal evolution of the thermocapillary convection and a complex sequence of transitions are observed. The results show that the finite extent of the liquid layer significantly influences the tempo-spatial evolution of the thermocapillary convection. Moreover, the bifurcation route of the thermocapillary convection changes very sensitively by the aspect ratio of the liquid layer. With the increasing Reynolds number (applied temperature difference), the steady thermocapillary convection experiences two consecutive transitions from periodic oscillatory state to quasi-periodic oscillatory state with frequency-locking before emergence of chaotic convection in a liquid layer of aspect ratio 14.25, and the thermocapillary convection undergoes period-doubling cascades leading to chaotic convection in a liquid layer of aspect ratio 13.0.

A low dimensional dynamical system for the wall layer

Science.gov (United States)

Aubry, N.; Keefe, L. R.

1987-01-01

Low dimensional dynamical systems which model a fully developed turbulent wall layer were derived.The model is based on the optimally fast convergent proper orthogonal decomposition, or Karhunen-Loeve expansion. This decomposition provides a set of eigenfunctions which are derived from the autocorrelation tensor at zero time lag. Via Galerkin projection, low dimensional sets of ordinary differential equations in time, for the coefficients of the expansion, were derived from the Navier-Stokes equations. The energy loss to the unresolved modes was modeled by an eddy viscosity representation, analogous to Heisenberg's spectral model. A set of eigenfunctions and eigenvalues were obtained from direct numerical simulation of a plane channel at a Reynolds number of 6600, based on the mean centerline velocity and the channel width flow and compared with previous work done by Herzog. Using the new eigenvalues and eigenfunctions, a new ten dimensional set of ordinary differential equations were derived using five non-zero cross-stream Fourier modes with a periodic length of 377 wall units. The dynamical system was integrated for a range of the eddy viscosity prameter alpha. This work is encouraging.

Research on the relation of EEG signal chaos characteristics with high-level intelligence activity of human brain.

Science.gov (United States)

Wang, Xingyuan; Meng, Juan; Tan, Guilin; Zou, Lixian

2010-04-27

Using phase space reconstruct technique from one-dimensional and multi-dimensional time series and the quantitative criterion rule of system chaos, and combining the neural network; analyses, computations and sort are conducted on electroencephalogram (EEG) signals of five kinds of human consciousness activities (relaxation, mental arithmetic of multiplication, mental composition of a letter, visualizing a 3-dimensional object being revolved about an axis, and visualizing numbers being written or erased on a blackboard). Through comparative studies on the determinacy, the phase graph, the power spectra, the approximate entropy, the correlation dimension and the Lyapunov exponent of EEG signals of 5 kinds of consciousness activities, the following conclusions are shown: (1) The statistic results of the deterministic computation indicate that chaos characteristic may lie in human consciousness activities, and central tendency measure (CTM) is consistent with phase graph, so it can be used as a division way of EEG attractor. (2) The analyses of power spectra show that ideology of single subject is almost identical but the frequency channels of different consciousness activities have slight difference. (3) The approximate entropy between different subjects exist discrepancy. Under the same conditions, the larger the approximate entropy of subject is, the better the subject's innovation is. (4) The results of the correlation dimension and the Lyapunov exponent indicate that activities of human brain exist in attractors with fractional dimensions. (5) Nonlinear quantitative criterion rule, which unites the neural network, can classify different kinds of consciousness activities well. In this paper, the results of classification indicate that the consciousness activity of arithmetic has better differentiation degree than that of abstract.

Death and revival of chaos.

Science.gov (United States)

Kaszás, Bálint; Feudel, Ulrike; Tél, Tamás

2016-12-01

We investigate the death and revival of chaos under the impact of a monotonous time-dependent forcing that changes its strength with a non-negligible rate. Starting on a chaotic attractor it is found that the complexity of the dynamics remains very pronounced even when the driving amplitude has decayed to rather small values. When after the death of chaos the strength of the forcing is increased again with the same rate of change, chaos is found to revive but with a different history. This leads to the appearance of a hysteresis in the complexity of the dynamics. To characterize these dynamics, the concept of snapshot attractors is used, and the corresponding ensemble approach proves to be superior to a single trajectory description, that turns out to be nonrepresentative. The death (revival) of chaos is manifested in a drop (jump) of the standard deviation of one of the phase-space coordinates of the ensemble; the details of this chaos-nonchaos transition depend on the ratio of the characteristic times of the amplitude change and of the internal dynamics. It is demonstrated that chaos cannot die out as long as underlying transient chaos is present in the parameter space. As a condition for a "quasistatically slow" switch-off, we derive an inequality which cannot be fulfilled in practice over extended parameter ranges where transient chaos is present. These observations need to be taken into account when discussing the implications of "climate change scenarios" in any nonlinear dynamical system.

Colpitts and Chaos

DEFF Research Database (Denmark)

Lindberg, Erik

1996-01-01

The chaotic behaviour of the Colpitts oscillator reported by M.P. Kennedy is further investigated by means of PSpice simulations. Chaos is also observed with the default Ebers-Moll BJT transistor model with no memory. When the model is extended with memory and losses chaos do not occur and a 3'rd...... order limit cycle is found. If the the forward Early voltage parameter is added chaos is observed again. An examination of the eigenvalues of the oscillator with the simple memoryless Ebers-Moll BJT injection model is presented. By adding bulk resistors to the model stable limit cycles of orders 1, 2, 3...

Noise tolerant spatiotemporal chaos computing.

Science.gov (United States)

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

2014-12-01

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

Dynamic colloidal assembly pathways via low dimensional models

Energy Technology Data Exchange (ETDEWEB)

Yang, Yuguang; Bevan, Michael A., E-mail: mabevan@jhu.edu [Chemical and Biomolecular Engineering, Johns Hopkins University, Baltimore, Maryland 21218 (United States); Thyagarajan, Raghuram; Ford, David M. [Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003 (United States)

2016-05-28

Here we construct a low-dimensional Smoluchowski model for electric field mediated colloidal crystallization using Brownian dynamic simulations, which were previously matched to experiments. Diffusion mapping is used to infer dimensionality and confirm the use of two order parameters, one for degree of condensation and one for global crystallinity. Free energy and diffusivity landscapes are obtained as the coefficients of a low-dimensional Smoluchowski equation to capture the thermodynamics and kinetics of microstructure evolution. The resulting low-dimensional model quantitatively captures the dynamics of different assembly pathways between fluid, polycrystal, and single crystals states, in agreement with the full N-dimensional data as characterized by first passage time distributions. Numerical solution of the low-dimensional Smoluchowski equation reveals statistical properties of the dynamic evolution of states vs. applied field amplitude and system size. The low-dimensional Smoluchowski equation and associated landscapes calculated here can serve as models for predictive control of electric field mediated assembly of colloidal ensembles into two-dimensional crystalline objects.

Enlightenment philosophers’ ideas about chaos

Directory of Open Access Journals (Sweden)

A. V. Kulik

2014-07-01

 It is grounded that the philosopher and enlightener Johann Gottfried von Herder advanced an idea of objectivity of process of transformation chaos into order. It is shown that idea of «The law of nature» existing as for ordering chaos opened far­reaching prospects for researches of interaction with chaos.

Evidence of low dimensional chaos in renal blood flow control in genetic and experimental hypertension

Science.gov (United States)

Yip, K.-P.; Marsh, D. J.; Holstein-Rathlou, N.-H.

1995-01-01

We applied a surrogate data technique to test for nonlinear structure in spontaneous fluctuations of hydrostatic pressure in renal tubules of hypertensive rats. Tubular pressure oscillates at 0.03-0.05 Hz in animals with normal blood pressure, but the fluctuations become irregular with chronic hypertension. Using time series from rats with hypertension we produced surrogate data sets to test whether they represent linearly correlated noise or ‘static’ nonlinear transforms of a linear stochastic process. The correlation dimension and the forecasting error were used as discriminating statistics to compare surrogate with experimental data. The results show that the original experimental time series can be distinguished from both linearly and static nonlinearly correlated noise, indicating that the nonlinear behavior is due to the intrinsic dynamics of the system. Together with other evidence this strongly suggests that a low dimensional chaotic attractor governs renal hemodynamics in hypertension. This appears to be the first demonstration of a transition to chaotic dynamics in an integrated physiological control system occurring in association with a pathological condition.

Chaos Criminology: A critical analysis

Science.gov (United States)

McCarthy, Adrienne L.

There has been a push since the early 1980's for a paradigm shift in criminology from a Newtonian-based ontology to one of quantum physics. Primarily this effort has taken the form of integrating Chaos Theory into Criminology into what this thesis calls 'Chaos Criminology'. However, with the melding of any two fields, terms and concepts need to be translated properly, which has yet to be done. In addition to proving a translation between fields, this thesis also uses a set of criteria to evaluate the effectiveness of the current use of Chaos Theory in Criminology. While the results of the theory evaluation reveal that the current Chaos Criminology work is severely lacking and in need of development, there is some promise in the development of Marx's dialectical materialism with Chaos Theory.

Chaos excited chaos synchronizations of integral and fractional order generalized van der Pol systems

International Nuclear Information System (INIS)

Ge Zhengming; Hsu Maoyuan

2008-01-01

In this paper, chaos excited chaos synchronizations of generalized van der Pol systems with integral and fractional order are studied. Synchronizations of two identified autonomous generalized van der Pol chaotic systems are obtained by replacing their corresponding exciting terms by the same function of chaotic states of a third nonautonomous or autonomous generalized van der Pol system. Numerical simulations, such as phase portraits, Poincare maps and state error plots are given. It is found that chaos excited chaos synchronizations exist for the fractional order systems with the total fractional order both less than and more than the number of the states of the integer order generalized van der Pol system

A digital bandlimited chaos-based communication system

Science.gov (United States)

Fontes, Rodrigo T.; Eisencraft, Marcio

2016-08-01

In recent years, many communication systems that use a function to encode an information in a chaotic signal were proposed. Since every transmission channel is bandlimited in nature, it is required to determine and to control the chaotic signal spectrum. This way, a bandlimited chaos-based communication system (CBCS) was proposed using digital filters and chaotic synchronization. As the filters modify the original chaotic system, it is necessary to study how their insertion affects chaotic synchronization. In this work, we present a digital discrete-time bandlimited CBCS system analysis, considering practical settings encountered in conventional communication systems. The proposed system is based on master-slave chaotic synchronization and the required conditions for its synchronization is obtained analytically for a general K-dimensional chaos generator map. The performance of this system is evaluated in terms of bit error rate. As a way to improve the signal to noise ratio, we also propose to filter the out-of-band noise in the receiver. Numerical simulations show the advantages of using such a scheme.

Chaos theory in politics

CERN Document Server

Erçetin, Şefika; Tekin, Ali

2014-01-01

The present work investigates global politics and political implications of social science and management with the aid of the latest complexity and chaos theories. Until now, deterministic chaos and nonlinear analysis have not been a focal point in this area of research. This book remedies this deficiency by utilizing these methods in the analysis of the subject matter. The authors provide the reader a detailed analysis on politics and its associated applications with the help of chaos theory, in a single edited volume.

Stochastic Estimation via Polynomial Chaos

Science.gov (United States)

2015-10-01

AFRL-RW-EG-TR-2015-108 Stochastic Estimation via Polynomial Chaos Douglas V. Nance Air Force Research...COVERED (From - To) 20-04-2015 – 07-08-2015 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Stochastic Estimation via Polynomial Chaos ...This expository report discusses fundamental aspects of the polynomial chaos method for representing the properties of second order stochastic

Chaos and noise.

Science.gov (United States)

He, Temple; Habib, Salman

2013-09-01

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

Life Chaos and Perceived Social Support Among Methamphetamine-Using Men Who Have Sex With Men Engaging in Transactional Sexual Encounters.

Science.gov (United States)

Viswanath, Humsini; Wilkerson, J Michael; Breckenridge, Ellen; Selwyn, Beatrice J

2017-01-02

Social support and life chaos have been inversely associated with increased risk of HIV infection. The purpose of this study was to explore among a sample of HIV-negative methamphetamine-using men who have sex with men (MSM) the association between engaging in transactional sex, life chaos, and low social support. HIV-negative methamphetamine-using MSM completed an online questionnaire between July and October 2012 about recent substance use and sexual behavior. Bivariate and multivariate tests were used to obtain statistically significant associations between demographic characteristics, engaging in transactional sex, life chaos, and the participants' perception of their social support. Of the 325 participants, 23.7% reported engaging in transactional sex, 45.2% reported high life chaos, and 53.5% reported low perceived social support. Participants who engaged in transactional sex were more likely to have high life chaos than participants who did not (aOR = 1.70, 95% CI = [1.01, 2.84]); transactional sex was not associated with social support. Participants with high life chaos were more out about their sexual orientation (aOR = 2.29, 95% CI = [1.18, 4.42]) and more likely to perceive they had low social support (aOR = 3.78, 95% CI = [2.31, 6.22]) than participants with low life chaos. Non-Latinos perceived they had less social support than Latinos (aOR = 0.48, 95% CI = [0.25, 0.92]). Methamphetamine-using MSM engaging in transactional sex experience more life chaos than those who do not engage in transactional sex. Outness, perceived social support, and ethnicity are associated with life chaos.

"Chaos Rules" Revisited

Science.gov (United States)

Murphy, David

2011-01-01

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

Improved PSO algorithm based on chaos theory and its application to design flood hydrograph

Directory of Open Access Journals (Sweden)

Si-Fang Dong

2010-06-01

Full Text Available The deficiencies of basic particle swarm optimization (bPSO are its ubiquitous prematurity and its inability to seek the global optimal solution when optimizing complex high-dimensional functions. To overcome such deficiencies, the chaos-PSO (COSPSO algorithm was established by introducing the chaos optimization mechanism and a global particle stagnation-disturbance strategy into bPSO. In the improved algorithm, chaotic movement was adopted for the particles' initial movement trajectories to replace the former stochastic movement, and the chaos factor was used to guide the particles' path. When the global particles were stagnant, the disturbance strategy was used to keep the particles in motion. Five benchmark optimizations were introduced to test COSPSO, and they proved that COSPSO can remarkably improve efficiency in optimizing complex functions. Finally, a case study of COSPSO in calculating design flood hydrographs demonstrated the applicability of the improved algorithm.

Gullies of Gorgonus Chaos

Science.gov (United States)

2002-01-01

above image to get a high-resolution view, and then focus on the trenches at the bottom. Running down the walls of the trough are the thin, dark lines of the gullies. Beneath the grooved, gully channels are faint, softer-looking fans of material. These are called alluvial deposits. Alluvial simply means all of the sand, gravel, and dirt that is carried and deposited by a liquid. On Earth, that liquid is typically water. As the liquid carves the gully, the eroded material from the channels get carried along and deposited below in fan-like shapes. These gully features were initially discovered by Odyssey's sister orbiter, Mars Global Surveyor, and caused quite a bit of emotional chaos in the scientific community when they were announced. Why? If you look closely, you can see that the gullies seem to form from a specific layer in the wall. That is, they all seem to begin at roughly the same point on the wall. That suggests that maybe, just maybe, there's a subsurface source of water at that layer that sometimes leaks out and runs down the walls to form both the gullies and the skirt-like fans of deposits beneath them. Other scientists, however, loudly assert that another liquid besides water could have carved the gullies. The debate sometimes gets so intense, you'd think that the opposing sides would want to turn each other's ideas to stone! But not for long. While the debate rages on, the neat thing is that everyone's really united. The goal is to find out, and the way to find out is to keep proposing different hypotheses and testing them out. That's the excitement of science, where everyone's solid research counts, and divergent views are appreciated for keeping science sound.

Chaos, dynamical structure and climate variability

Energy Technology Data Exchange (ETDEWEB)

Stewart, H.B. [Brookhaven National Lab., Upton, NY (United States). Dept. of Applied Science

1995-09-01

Deterministic chaos in dynamical systems offers a new paradigm for understanding irregular fluctuations. Techniques for identifying deterministic chaos from observed data, without recourse to mathematical models, are being developed. Powerful methods exist for reconstructing multidimensional phase space from an observed time series of a single scalar variable; these methods are invaluable when only a single scalar record of the dynamics is available. However, in some applications multiple concurrent time series may be available for consideration as phase space coordinates. Here the authors propose some basic analytical tools for such multichannel time series data, and illustrate them by applications to a simple synthetic model of chaos, to a low-order model of atmospheric circulation, and to two high-resolution paleoclimate proxy data series. The atmospheric circulation model, originally proposed by Lorenz, has 27 principal unknowns; they establish that the chaotic attractor can be embedded in a subspace of eight dimensions by exhibiting a specific subset of eight unknowns which pass multichannel tests for false nearest neighbors. They also show that one of the principal unknowns in the 27-variable model--the global mean sea surface temperature--is of no discernible usefulness in making short-term forecasts.

Chaos applications in telecommunications

CERN Document Server

Stavroulakis, Peter

2005-01-01

IntroductionPeter StavroulakisChaotic Signal Generation and Transmission Antonio Cândido Faleiros,Waldecir João Perrella,TâniaNunes Rabello,Adalberto Sampaio Santos, andNeiYoshihiro SomaChaotic Transceiver Design Arthur Fleming-DahlChaos-Based Modulation and DemodulationTechniques Francis C.M. Lau and Chi K. TseA Chaos Approach to Asynchronous DS-CDMASystems S. Callegari, G. Mazzini, R. Rovatti, and G. SettiChannel Equalization in Chaotic CommunicationSystems Mahmut CiftciOptical Communications using ChaoticTechniques Gregory D. VanWiggerenAPPENDIX AFundamental Concepts of the Theory ofChaos a

A bound on chaos

Energy Technology Data Exchange (ETDEWEB)

Maldacena, Juan [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States); Shenker, Stephen H. [Stanford Institute for Theoretical Physics and Department of Physics, Stanford University,382 Via Pueblo Mall, Stanford, CA (United States); Stanford, Douglas [School of Natural Sciences, Institute for Advanced Study,1 Einstein Drive, Princeton, NJ (United States)

2016-08-17

We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λ{sub L}≤2πk{sub B}T/ℏ. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture.

Hastily Formed Networks-Chaos to Recovery

Science.gov (United States)

2015-09-01

NETWORKS— CHAOS TO RECOVERY by Mark Arezzi September 2015 Thesis Co-Advisors: Douglas J. MacKinnon Brian Steckler THIS PAGE......systems to self-organize, adapt, and exert control over the chaos . Defining the role of communications requires an understanding of complexity, chaos

A New 3-D Piecewise-Linear System for Chaos Generation

Directory of Open Access Journals (Sweden)

Z. Elhadj

2007-06-01

Full Text Available We propose in this paper a new simple continuous-time piecewise-linear three dimensional system for chaos generation. Nonlinearity in this model is introduced by the characteristic function of the Chua's circuit given in [1]. Simulated results of some chaotic attractors are shown and justified numerically via computing the largest Lyapunov exponent. The possibility and the robustness of the circuitry realization is also given and discussed.

Puzzles in studies of quantum chaos

International Nuclear Information System (INIS)

Xu Gongou

1994-01-01

Puzzles in studies of quantum chaos are discussed. From the view of global properties of quantum states, it is clarified that quantum chaos originates from the break-down of invariant properties of quantum canonical transformations. There exist precise correspondences between quantum and classical chaos

3D pulsed chaos lidar system.

Science.gov (United States)

Cheng, Chih-Hao; Chen, Chih-Ying; Chen, Jun-Da; Pan, Da-Kung; Ting, Kai-Ting; Lin, Fan-Yi

2018-04-30

We develop an unprecedented 3D pulsed chaos lidar system for potential intelligent machinery applications. Benefited from the random nature of the chaos, conventional CW chaos lidars already possess excellent anti-jamming and anti-interference capabilities and have no range ambiguity. In our system, we further employ self-homodyning and time gating to generate a pulsed homodyned chaos to boost the energy-utilization efficiency. Compared to the original chaos, we show that the pulsed homodyned chaos improves the detection SNR by more than 20 dB. With a sampling rate of just 1.25 GS/s that has a native sampling spacing of 12 cm, we successfully achieve millimeter-level accuracy and precision in ranging. Compared with two commercial lidars tested side-by-side, namely the pulsed Spectroscan and the random-modulation continuous-wave Lidar-lite, the pulsed chaos lidar that is in compliance with the class-1 eye-safe regulation shows significantly better precision and a much longer detection range up to 100 m. Moreover, by employing a 2-axis MEMS mirror for active laser scanning, we also demonstrate real-time 3D imaging with errors of less than 4 mm in depth.

Controlling chaos through compactification in cosmological models with a collapsing phase

International Nuclear Information System (INIS)

Wesley, Daniel H.; Steinhardt, Paul J.; Turok, Neil

2005-01-01

We consider the effect of compactification of extra dimensions on the onset of classical chaotic mixmaster behavior during cosmic contraction. Assuming a universe that is well-approximated as a four-dimensional Friedmann-Robertson-Walker model (with negligible Kaluza-Klein excitations) when the contraction phase begins, we identify compactifications that allow a smooth contraction and delay the onset of chaos until arbitrarily close to the big crunch. These compactifications are defined by the de Rham cohomology (Betti numbers) and Killing vectors of the compactification manifold. We find compactifications that control chaos in vacuum Einstein gravity, as well as in string theories with N=1 supersymmetry and M-theory. In models where chaos is controlled in this way, the universe can remain homogeneous and flat until it enters the quantum gravity regime. At this point, the classical equations leading to chaotic behavior can no longer be trusted, and quantum effects may allow a smooth approach to the big crunch and transition into a subsequent expanding phase. Our results may be useful for constructing cosmological models with contracting phases, such as the ekpyrotic/cyclic and pre-big bang models

Recent development of chaos theory in topological dynamics

OpenAIRE

Li, Jian; Ye, Xiangdong

2015-01-01

We give a summary on the recent development of chaos theory in topological dynamics, focusing on Li-Yorke chaos, Devaney chaos, distributional chaos, positive topological entropy, weakly mixing sets and so on, and their relationships.

Compressive Sensing with Cross-Validation and Stop-Sampling for Sparse Polynomial Chaos Expansions

Energy Technology Data Exchange (ETDEWEB)

Huan, Xun; Safta, Cosmin; Sargsyan, Khachik; Vane, Zachary Phillips; Lacaze, Guilhem; Oefelein, Joseph C.; Najm, Habib N.

2017-07-01

Compressive sensing is a powerful technique for recovering sparse solutions of underdetermined linear systems, which is often encountered in uncertainty quanti cation analysis of expensive and high-dimensional physical models. We perform numerical investigations employing several com- pressive sensing solvers that target the unconstrained LASSO formulation, with a focus on linear systems that arise in the construction of polynomial chaos expansions. With core solvers of l1 ls, SpaRSA, CGIST, FPC AS, and ADMM, we develop techniques to mitigate over tting through an automated selection of regularization constant based on cross-validation, and a heuristic strategy to guide the stop-sampling decision. Practical recommendations on parameter settings for these tech- niques are provided and discussed. The overall method is applied to a series of numerical examples of increasing complexity, including large eddy simulations of supersonic turbulent jet-in-cross flow involving a 24-dimensional input. Through empirical phase-transition diagrams and convergence plots, we illustrate sparse recovery performance under structures induced by polynomial chaos, accuracy and computational tradeoffs between polynomial bases of different degrees, and practi- cability of conducting compressive sensing for a realistic, high-dimensional physical application. Across test cases studied in this paper, we find ADMM to have demonstrated empirical advantages through consistent lower errors and faster computational times.

Li and Yorke chaos with respect to the cardinality of the scrambled sets

Energy Technology Data Exchange (ETDEWEB)

Garcia Guirao, Juan Luis [Department of Mathematics, University of Castilla-La Mancha, 16071-Cuenca (Castilla-La Mancha) (Spain)]. E-mail: jlguirao@tel-cu.uclm.es; Lampart, Marek [Mathematical Institute, Silesian University at Opava, Na Rybnicku 1, 746 01 Opava (Czech Republic)]. E-mail: marek.lampart@math.slu.cz

2005-06-01

In the present paper we study Li and Yorke chaos on several spaces in connection with the cardinality of its scrambled sets. We prove that there is a map on a Cantor set and a map on a two-dimensional arcwise connected continuum (with empty interior) such that each scrambled set contains exactly two points.

Nuclear structure and order-to-chaos transition

International Nuclear Information System (INIS)

Solov'ev, V.G.

1995-01-01

A general scheme of the nuclear many-body problem is presented. Different models for description of low-lying states and giant resonances are discussed. The wave functions of the low-lying states have a single dominating one-quasiparticle or quasiparticle O+ phonon or one-phonon component. They demonstrate the regularity in nuclei. Giant resonances are determined by strongly fragmented one-phonon components of the wave functions. The wave functions at higher excitation energies have two-, three-and many-phonon components. Based on the statement that there is order in the large and chaos in the small components of the nuclear wave functions, the order-to-chaos transition is treated as a transition from the large to the small components of the wave functions. A quasiparticle-phonon interaction is responsible for the fragmentation of one- and many-quasiparticle and phonon states and for the mixing of closely spaced states. Therefore, experimental investigation of the fragmentation of many-quasiparticle and phonon states plays a decisive role. 30 refs

Chaos at High School

Directory of Open Access Journals (Sweden)

Tamás Meszéna

2017-04-01

Full Text Available We are faced with chaotic processes in many segments of our life: meteorology, environmental pollution, financial and economic processes, sociology, mechanics, electronics, biology, chemistry. The spreading of high-performance computers and the development of simulation methods made the examination of these processes easily available. Regular, periodic motions (pendulum, harmonic oscillatory motion, bouncing ball, as taught at secondary level, become chaotic even due minor changes. If it is true that the most considerable achievements of twentieth century physics were the theory of relativity, quantum mechanics and chaos theory, then it is presumably time to think about, examine and test how and to what extent chaos can be presented to the students. Here I would like to introduce a 12 lesson long facultative curriculum framework on chaos designed for students aged seventeen. The investigation of chaos phenomenon in this work is based on a freeware, “Dynamics Solver”. This software, with some assistance from the teacher, is suitable for classroom use at secondary level.

Topological chaos, braiding and bifurcation of almost-cyclic sets.

Science.gov (United States)

Grover, Piyush; Ross, Shane D; Stremler, Mark A; Kumar, Pankaj

2012-12-01

In certain two-dimensional time-dependent flows, the braiding of periodic orbits provides a way to analyze chaos in the system through application of the Thurston-Nielsen classification theorem (TNCT). We expand upon earlier work that introduced the application of the TNCT to braiding of almost-cyclic sets, which are individual components of almost-invariant sets [Stremler et al., "Topological chaos and periodic braiding of almost-cyclic sets," Phys. Rev. Lett. 106, 114101 (2011)]. In this context, almost-cyclic sets are periodic regions in the flow with high local residence time that act as stirrers or "ghost rods" around which the surrounding fluid appears to be stretched and folded. In the present work, we discuss the bifurcation of the almost-cyclic sets as a system parameter is varied, which results in a sequence of topologically distinct braids. We show that, for Stokes' flow in a lid-driven cavity, these various braids give good lower bounds on the topological entropy over the respective parameter regimes in which they exist. We make the case that a topological analysis based on spatiotemporal braiding of almost-cyclic sets can be used for analyzing chaos in fluid flows. Hence, we further develop a connection between set-oriented statistical methods and topological methods, which promises to be an important analysis tool in the study of complex systems.

Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems

International Nuclear Information System (INIS)

Ge Zhengming; Chang Chingming; Chen Yensheng

2006-01-01

Anti-control of chaos of single time scale brushless dc motors (BLDCM) and chaos synchronization of different order systems are studied in this paper. By addition of an external nonlinear term, we can obtain anti-control of chaos. Then, by addition of the coupling terms, by the use of Lyapunov stability theorem and by the linearization of the error dynamics, chaos synchronization between a third-order BLDCM and a second-order Duffing system are presented

Careers Education: Evolving, Adapting and Building Resilience through Chaos

Science.gov (United States)

Loader, Trent

2011-01-01

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

The joy of transient chaos

Energy Technology Data Exchange (ETDEWEB)

Tél, Tamás [Institute for Theoretical Physics, Eötvös University, and MTA-ELTE Theoretical Physics Research Group, Pázmány P. s. 1/A, Budapest H-1117 (Hungary)

2015-09-15

We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.

The joy of transient chaos.

Science.gov (United States)

Tél, Tamás

2015-09-01

We intend to show that transient chaos is a very appealing, but still not widely appreciated, subfield of nonlinear dynamics. Besides flashing its basic properties and giving a brief overview of the many applications, a few recent transient-chaos-related subjects are introduced in some detail. These include the dynamics of decision making, dispersion, and sedimentation of volcanic ash, doubly transient chaos of undriven autonomous mechanical systems, and a dynamical systems approach to energy absorption or explosion.

Chaos and its synchronization in two-neuron systems with discrete delays

International Nuclear Information System (INIS)

Zhou Shangbo; Liao Xiaofeng; Yu Juebang; Wong Kwokwo

2004-01-01

It is well known that complex dynamic behaviors exist in time-delayed neural systems. Infinite positive Lyapunov exponents can be found in time-delayed chaotic systems since the dimension of such systems is infinite. However, theoretical and experimental models studied thus far are low dimensional systems with only one positive Lyapunov exponent. Consequently, messages masked by such chaotic systems are shown to be easily extracted in some cases. Therefore, communication system with a higher security level can be design by means of the time-delayed neuron systems. In this paper, we firstly investigate the dynamical behaviors of two-neuron systems with discrete delays. Then, the chaos synchronization in time-delayed neuron system is studied based on the method of designing the coupled system and employing Krasovskii-Lyapunov theory to search the synchronization conditions. Numerical results illustrate the correctness of our theoretical analyses

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

International Nuclear Information System (INIS)

Basko, D.M.

2011-01-01

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.

2012 Symposium on Chaos, Complexity and Leadership

CERN Document Server

Erçetin, Şefika

2014-01-01

These proceedings from the 2012 symposium on "Chaos, complexity and leadership"  reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are  Leadership and Management applications of Chaos and Complexity Theory.

Relationships of family conflict, cohesion, and chaos in the home environment on maternal and child food-related behaviours.

Science.gov (United States)

Martin-Biggers, Jennifer; Quick, Virginia; Zhang, Man; Jin, Yanhong; Byrd-Bredbenner, Carol

2018-04-01

This study examined how food-related behaviours differed in mothers and their preschool children by levels of family functioning (cohesion and conflict) and household disorganization (chaos). A nationally representative sample of mothers of preschoolers completed an online survey assessing food-related behaviours of themselves and their children. Maternal and child diet, eating behaviours, and health status; household availability of fruits/vegetables, salty/fatty snacks, and sugar-sweetened beverages; family mealtime atmosphere; and family conflict, cohesion, and household chaos were assessed with valid, reliable scales. Cluster analyses assigned families into low, middle, and high conflict, cohesion, and chaos groups. Participants (n = 550) were 72% White, and 82% had some post-secondary education. Regression analysis examining the association of cluster grouping levels on diet-related behaviour measures revealed that positive home environments (i.e., low family conflict, high family cohesion, and low household chaos) were associated with healthier food-related behaviours (e.g., increased fruits/vegetables intake), whereas negative home environments (i.e., high family conflict, low family cohesion, and high household chaos) were associated with unhealthy food-related behaviours (e.g., greater % total calories from fat) even after controlling for sociodemographic and related behavioural factors. Findings suggest family functioning and household chaos are associated with food-related behaviours. This frequently overlooked component of family interaction may affect intervention outcomes and objectives of educational and interventional initiatives. © 2017 John Wiley & Sons Ltd.

Low-Dimensional Models of "Neuro-Glio-Vascular Unit" for Describing Neural Dynamics under Normal and Energy-Starved Conditions.

Science.gov (United States)

Chhabria, Karishma; Chakravarthy, V Srinivasa

2016-01-01

The motivation of developing simple minimal models for neuro-glio-vascular (NGV) system arises from a recent modeling study elucidating the bidirectional information flow within the NGV system having 89 dynamic equations (1). While this was one of the first attempts at formulating a comprehensive model for neuro-glio-vascular system, it poses severe restrictions in scaling up to network levels. On the contrary, low--dimensional models are convenient devices in simulating large networks that also provide an intuitive understanding of the complex interactions occurring within the NGV system. The key idea underlying the proposed models is to describe the glio-vascular system as a lumped system, which takes neural firing rate as input and returns an "energy" variable (analogous to ATP) as output. To this end, we present two models: biophysical neuro-energy (Model 1 with five variables), comprising KATP channel activity governed by neuronal ATP dynamics, and the dynamic threshold (Model 2 with three variables), depicting the dependence of neural firing threshold on the ATP dynamics. Both the models show different firing regimes, such as continuous spiking, phasic, and tonic bursting depending on the ATP production coefficient, ɛp, and external current. We then demonstrate that in a network comprising such energy-dependent neuron units, ɛp could modulate the local field potential (LFP) frequency and amplitude. Interestingly, low-frequency LFP dominates under low ɛp conditions, which is thought to be reminiscent of seizure-like activity observed in epilepsy. The proposed "neuron-energy" unit may be implemented in building models of NGV networks to simulate data obtained from multimodal neuroimaging systems, such as functional near infrared spectroscopy coupled to electroencephalogram and functional magnetic resonance imaging coupled to electroencephalogram. Such models could also provide a theoretical basis for devising optimal neurorehabilitation strategies, such as

Chaos synchronization in autonomous chaotic system via hybrid feedback control

International Nuclear Information System (INIS)

Yang Lixin; Chu Yandong; Zhang Jiangang; Li Xianfeng; Chang Yingxiang

2009-01-01

This paper presents the synchronization of chaos by designing united controller. First, this method is implemented in synchronization of a simple system, then we realize the synchronization of Lue hyperchaotic system, we also take tracking control to realize the synchronization of Lue hyperchaotic system. Comparing with results, we can find that hybrid feedback control approach is more effective than tracking control for hyperchaotic system. Numerical simulations show the united synchronization method works well.

Nonlinear chaos control and synchronization

NARCIS (Netherlands)

Huijberts, H.J.C.; Nijmeijer, H.; Schöll, E.; Schuster, H.G.

2007-01-01

This chapter contains sections titled: Introduction Nonlinear Geometric Control Some Differential Geometric Concepts Nonlinear Controllability Chaos Control Through Feedback Linearization Chaos Control Through Input-Output Linearization Lyapunov Design Lyapunov Stability and Lyapunov's First Method

Cryptography with chaos and shadowing

International Nuclear Information System (INIS)

Smaoui, Nejib; Kanso, Ali

2009-01-01

In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.

Experimental Induction of Genome Chaos.

Science.gov (United States)

Ye, Christine J; Liu, Guo; Heng, Henry H

2018-01-01

Genome chaos, or karyotype chaos, represents a powerful survival strategy for somatic cells under high levels of stress/selection. Since the genome context, not the gene content, encodes the genomic blueprint of the cell, stress-induced rapid and massive reorganization of genome topology functions as a very important mechanism for genome (karyotype) evolution. In recent years, the phenomenon of genome chaos has been confirmed by various sequencing efforts, and many different terms have been coined to describe different subtypes of the chaotic genome including "chromothripsis," "chromoplexy," and "structural mutations." To advance this exciting field, we need an effective experimental system to induce and characterize the karyotype reorganization process. In this chapter, an experimental protocol to induce chaotic genomes is described, following a brief discussion of the mechanism and implication of genome chaos in cancer evolution.

Cryptography with chaos and shadowing

Energy Technology Data Exchange (ETDEWEB)

Smaoui, Nejib [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: nsmaoui64@yahoo.com; Kanso, Ali [Department of Mathematics and Computer Science, Kuwait University, P.O. Box 5969, Safat 13060 (Kuwait)], E-mail: akanso@hotmail.com

2009-11-30

In this paper, we present a novel approach to encrypt a message (a text composed by some alphabets) using chaos and shadowing. First, we generate a numerical chaotic orbit based on the logistic map, and use the shadowing algorithm of Smaoui and Kostelich [Smaoui N, Kostelich E. Using chaos to shadow the quadratic map for all time. Int J Comput Math 1998;70:117-29] to show that there exists a finite number of true orbits that shadow the numerical orbit. Then, the finite number of maps generated is used in Baptista's algorithm [Baptista MS. Cryptography with chaos. Phys Lett A 1998;240:50-4] to encrypt each character of the message. It is shown that the use of chaos and shadowing in the encryption process enhances the security level.

Using chaos theory: the implications for nursing.

Science.gov (United States)

Haigh, Carol

2002-03-01

The purpose of this paper is to review chaos theory and to examine the role that it may have in the discipline of nursing. In this paper, the fundamental ingredients of chaotic thinking are outlined. The earlier days of chaos thinking were characterized by an almost exclusively physiological focus. By the 21st century, nurse theorists were applying its principles to the organization and evaluation of care delivery with varying levels of success. Whilst the biological use of chaos has focused on pragmatic approaches to knowledge enhancement, nursing has often focused on the mystical aspects of chaos as a concept. The contention that chaos theory has yet to find a niche within nursing theory and practice is examined. The application of chaotic thinking across nursing practice, nursing research and statistical modelling is reviewed. The use of chaos theory as a way of identifying the attractor state of specific systems is considered and the suggestion is made that it is within statistical modelling of services that chaos theory is most effective.

A Generalized Stability Theorem for Discrete-Time Nonautonomous Chaos System with Applications

Directory of Open Access Journals (Sweden)

Mei Zhang

2015-01-01

Full Text Available Firstly, this study introduces a definition of generalized stability (GST in discrete-time nonautonomous chaos system (DNCS, which is an extension for chaos generalized synchronization. Secondly, a constructive theorem of DNCS has been proposed. As an example, a GST DNCS is constructed based on a novel 4-dimensional discrete chaotic map. Numerical simulations show that the dynamic behaviors of this map have chaotic attractor characteristics. As one application, we design a chaotic pseudorandom number generator (CPRNG based on the GST DNCS. We use the SP800-22 test suite to test the randomness of four 100-key streams consisting of 1,000,000 bits generated by the CPRNG, the RC4 algorithm, the ZUC algorithm, and a 6-dimensional CGS-based CPRNG, respectively. The numerical results show that the randomness performances of the two CPRNGs are promising. In addition, theoretically the key space of the CPRNG is larger than 21116. As another application, this study designs a stream avalanche encryption scheme (SAES in RGB image encryption. The results show that the GST DNCS is able to generate the avalanche effects which are similar to those generated via ideal CPRNGs.

Quantum chaos: Statistical relaxation in discrete spectrum

International Nuclear Information System (INIS)

Chirikov, B.V.

1991-01-01

The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Various mechanisms of the quantum suppression of classical chaos are considered with an application to the excitation and ionization of Rydberg atoms in a microwave field. Several definitions of the quantum chaos are discussed. (author). 27 refs

Quantum Fluctuations of Low Dimensional Bose-Einstein ...

African Journals Online (AJOL)

A system of low dimensional condensed ultracold atomic gases inside a field of a laser-driven optical cavity exhibits dispersive optical bistability. During such a process the system also shows quantum fluctuations. Condensate fluctuations are highly manifested particularly in low dimensional systems. In this paper we have ...

Chaos Modelling with Computers

Indian Academy of Sciences (India)

Chaos is one of the major scientific discoveries of our times. In fact many scientists ... But there are other natural phenomena that are not predictable though ... characteristics of chaos. ... The position and velocity are all that are needed to determine the motion of a .... a system of equations that modelled the earth's weather ...

Counterintuitive Constraints on Chaos Formation Set by Heat Flux through Europa's Ocean

Science.gov (United States)

Goodman, J. C.

2013-12-01

heat transport is governed by geostrophic quasi-two-dimensional convection, which delivers less heat to the tropics and more to the poles. By the argument above, this implies that the ice layer should be thicker in the tropics, and thus more prone to diapiric convection: thus, chaos should be more common there. Recent mapping efforts by other investigators have shown that this does appear to be the case.

On Nonextensive Statistics, Chaos and Fractal Strings

CERN Document Server

Castro, C

2004-01-01

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 is a particular representative of such class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature ( Kelvin ) corresponds to zero dimensions (energy ) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum...

Metal-insulator transition in one-dimensional lattices with chaotic energy sequences

International Nuclear Information System (INIS)

Pinto, R.A.; Rodriguez, M.; Gonzalez, J.A.; Medina, E.

2005-01-01

We study electronic transport through a one-dimensional array of sites by using a tight binding Hamiltonian, whose site-energies are drawn from a chaotic sequence. The correlation degree between these energies is controlled by a parameter regulating the dynamic Lyapunov exponent measuring the degree of chaos. We observe the effect of chaotic sequences on the localization length, conductance, conductance distribution and wave function, finding evidence of a metal-insulator transition (MIT) at a critical degree of chaos. The one-dimensional metallic phase is characterized by a Gaussian conductance distribution and exhibits a peculiar non-selfaveraging

Metal-insulator transition in one-dimensional lattices with chaotic energy sequences

Energy Technology Data Exchange (ETDEWEB)

Pinto, R.A. [Laboratorio de Fisica Estadistica, Centro de Fisica, Instituto Venezolano de Investigaciones Cientificas, Apartado 21827, Caracas 1020-A (Venezuela)]. E-mail: ripinto@ivic.ve; Rodriguez, M. [Laboratorio de Fisica Estadistica, Centro de Fisica, Instituto Venezolano de Investigaciones Cientificas, Apartado 21827, Caracas 1020-A (Venezuela); Gonzalez, J.A. [Laboratorio de Fisica Computacional, Centro de Fisica, Instituto Venezolano de Investigaciones Cientificas, Apartado 21827, Caracas 1020-A (Venezuela); Medina, E. [Laboratorio de Fisica Estadistica, Centro de Fisica, Instituto Venezolano de Investigaciones Cientificas, Apartado 21827, Caracas 1020-A (Venezuela)

2005-06-20

We study electronic transport through a one-dimensional array of sites by using a tight binding Hamiltonian, whose site-energies are drawn from a chaotic sequence. The correlation degree between these energies is controlled by a parameter regulating the dynamic Lyapunov exponent measuring the degree of chaos. We observe the effect of chaotic sequences on the localization length, conductance, conductance distribution and wave function, finding evidence of a metal-insulator transition (MIT) at a critical degree of chaos. The one-dimensional metallic phase is characterized by a Gaussian conductance distribution and exhibits a peculiar non-selfaveraging.

Towards chaos criterion in quantum field theory

OpenAIRE

Kuvshinov, V. I.; Kuzmin, A. V.

2002-01-01

Chaos criterion for quantum field theory is proposed. Its correspondence with classical chaos criterion in semi-classical regime is shown. It is demonstrated for real scalar field that proposed chaos criterion can be used to investigate stability of classical solutions of field equations.

Semiconductor Lasers Stability, Instability and Chaos

CERN Document Server

Ohtsubo, Junji

2013-01-01

This third edition of “Semiconductor Lasers, Stability, Instability and Chaos” was significantly extended.  In the previous edition, the dynamics and characteristics of chaos in semiconductor lasers after the introduction of the fundamental theory of laser chaos and chaotic dynamics induced by self-optical feedback and optical injection was discussed. Semiconductor lasers with new device structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are interesting devices from the viewpoint of chaotic dynamics since they essentially involve chaotic dynamics even in their free-running oscillations. These topics are also treated with respect to the new developments in the current edition. Also the control of such instabilities and chaos control are critical issues for applications. Another interesting and important issue of semiconductor laser chaos in this third edition is chaos synchronization between two lasers and the application to optical secure communication. One o...

Advances in chaos theory and intelligent control

CERN Document Server

Vaidyanathan, Sundarapandian

2016-01-01

The book reports on the latest advances in and applications of chaos theory and intelligent control. Written by eminent scientists and active researchers and using a clear, matter-of-fact style, it covers advanced theories, methods, and applications in a variety of research areas, and explains key concepts in modeling, analysis, and control of chaotic and hyperchaotic systems. Topics include fractional chaotic systems, chaos control, chaos synchronization, memristors, jerk circuits, chaotic systems with hidden attractors, mechanical and biological chaos, and circuit realization of chaotic systems. The book further covers fuzzy logic controllers, evolutionary algorithms, swarm intelligence, and petri nets among other topics. Not only does it provide the readers with chaos fundamentals and intelligent control-based algorithms; it also discusses key applications of chaos as well as multidisciplinary solutions developed via intelligent control. The book is a timely and comprehensive reference guide for graduate s...

Ocean-driven heating of Europa's icy shell at low latitudes

Science.gov (United States)

Soderlund, K. M.; Schmidt, B. E.; Wicht, J.; Blankenship, D. D.

2014-01-01

The ice shell of Jupiter's moon Europa is marked by regions of disrupted ice known as chaos terrains that cover up to 40% of the satellite's surface, most commonly occurring within 40° of the equator. Concurrence with salt deposits implies a coupling between the geologically active ice shell and the underlying liquid water ocean at lower latitudes. Europa's ocean dynamics have been assumed to adopt a two-dimensional pattern, which channels the moon's internal heat to higher latitudes. Here we present a numerical model of thermal convection in a thin, rotating spherical shell where small-scale convection instead adopts a three-dimensional structure and is more vigorous at lower latitudes. Global-scale currents are organized into three zonal jets and two equatorial Hadley-like circulation cells. We find that these convective motions transmit Europa's internal heat towards the surface most effectively in equatorial regions, where they can directly influence the thermo-compositional state and structure of the ice shell. We suggest that such heterogeneous heating promotes the formation of chaos features through increased melting of the ice shell and subsequent deposition of marine ice at low latitudes. We conclude that Europa's ocean dynamics can modulate the exchange of heat and materials between the surface and interior and explain the observed distribution of chaos terrains.

Analysing spatially extended high-dimensional dynamics by recurrence plots

Energy Technology Data Exchange (ETDEWEB)

Marwan, Norbert, E-mail: marwan@pik-potsdam.de [Potsdam Institute for Climate Impact Research, 14412 Potsdam (Germany); Kurths, Jürgen [Potsdam Institute for Climate Impact Research, 14412 Potsdam (Germany); Humboldt Universität zu Berlin, Institut für Physik (Germany); Nizhny Novgorod State University, Department of Control Theory, Nizhny Novgorod (Russian Federation); Foerster, Saskia [GFZ German Research Centre for Geosciences, Section 1.4 Remote Sensing, Telegrafenberg, 14473 Potsdam (Germany)

2015-05-08

Recurrence plot based measures of complexity are capable tools for characterizing complex dynamics. In this letter we show the potential of selected recurrence plot measures for the investigation of even high-dimensional dynamics. We apply this method on spatially extended chaos, such as derived from the Lorenz96 model and show that the recurrence plot based measures can qualitatively characterize typical dynamical properties such as chaotic or periodic dynamics. Moreover, we demonstrate its power by analysing satellite image time series of vegetation cover with contrasting dynamics as a spatially extended and potentially high-dimensional example from the real world. - Highlights: • We use recurrence plots for analysing partially extended dynamics. • We investigate the high-dimensional chaos of the Lorenz96 model. • The approach distinguishes different spatio-temporal dynamics. • We use the method for studying vegetation cover time series.

Chaos theory for clinical manifestations in multiple sclerosis.

Science.gov (United States)

Akaishi, Tetsuya; Takahashi, Toshiyuki; Nakashima, Ichiro

2018-06-01

Multiple sclerosis (MS) is a demyelinating disease which characteristically shows repeated relapses and remissions irregularly in the central nervous system. At present, the pathological mechanism of MS is unknown and we do not have any theories or mathematical models to explain its disseminated patterns in time and space. In this paper, we present a new theoretical model from a viewpoint of complex system with chaos model to reproduce and explain the non-linear clinical and pathological manifestations in MS. First, we adopted a discrete logistic equation with non-linear dynamics to prepare a scalar quantity for the strength of pathogenic factor at a specific location of the central nervous system at a specific time to reflect the negative feedback in immunity. Then, we set distinct minimum thresholds in the above-mentioned scalar quantity for demyelination possibly causing clinical relapses and for cerebral atrophy. With this simple model, we could theoretically reproduce all the subtypes of relapsing-remitting MS, primary progressive MS, and secondary progressive MS. With the sensitivity to initial conditions and sensitivity to minute change in parameters of the chaos theory, we could also reproduce the spatial dissemination. Such chaotic behavior could be reproduced with other similar upward-convex functions with appropriate set of initial conditions and parameters. In conclusion, by applying chaos theory to the three-dimensional scalar field of the central nervous system, we can reproduce the non-linear outcome of the clinical course and explain the unsolved disseminations in time and space of the MS patients. Copyright © 2018 Elsevier Ltd. All rights reserved.

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

International Nuclear Information System (INIS)

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

2005-01-01

New results are reported on the routes to chaos in increasingly complex Duffing oscillator systems, which are formed by coupling several oscillators, thereby increasing the number of degrees of freedom. Other forms of increasing system complexity through distributed excitation, different forcing function phasing, different excitation frequency ratios, and higher order coupling are also studied. Changes in the quantitative aspects of the chaotic regions and in the routes to chaos of complex Duffing systems are investigated by performing numerical simulations. It is shown that the number of chaotic regions in these systems is significantly reduced when compared to the original Duffing system, and that crisis replaces period doubling as the dominant route to chaos when the number of degrees of freedom is increased. A new discovered phenomenon is that chaos emerges in the symmetrically and asymmetrically coupled Duffing oscillators only after the quasi-periodic torus breaks down through a 3-periodic and 2-periodic window, respectively

Chaos based video encryption using maps and Ikeda time delay system

Science.gov (United States)

Valli, D.; Ganesan, K.

2017-12-01

Chaos based cryptosystems are an efficient method to deal with improved speed and highly secured multimedia encryption because of its elegant features, such as randomness, mixing, ergodicity, sensitivity to initial conditions and control parameters. In this paper, two chaos based cryptosystems are proposed: one is the higher-dimensional 12D chaotic map and the other is based on the Ikeda delay differential equation (DDE) suitable for designing a real-time secure symmetric video encryption scheme. These encryption schemes employ a substitution box (S-box) to diffuse the relationship between pixels of plain video and cipher video along with the diffusion of current input pixel with the previous cipher pixel, called cipher block chaining (CBC). The proposed method enhances the robustness against statistical, differential and chosen/known plain text attacks. Detailed analysis is carried out in this paper to demonstrate the security and uniqueness of the proposed scheme.

4th international interdisciplinary chaos symposium

CERN Document Server

Banerjee, Santo; Caglar, Suleyman; Ozer, Mehmet; Chaos and complex systems

2013-01-01

Complexity Science and Chaos Theory are fascinating areas of scientific research with wide-ranging applications.  The interdisciplinary nature and ubiquity of complexity and chaos are features that provides scientists with a motivation to pursue general theoretical tools and frameworks. Complex systems give rise to emergent behaviors, which in turn produce novel and interesting phenomena in science, engineering, as well as in the socio-economic sciences. The aim of all Symposia on Chaos and Complex Systems (CCS) is to bring together scientists, engineers, economists and social scientists, and to discuss the latest insights and results obtained in the area of corresponding nonlinear-system complex (chaotic) behavior. Especially for the “4th International Interdisciplinary Chaos Symposium on Chaos and Complex Systems,” which took place April 29th to May 2nd, 2012 in Antalya, Turkey, the scope of the symposium had been further enlarged so as to encompass the presentation of work from circuits to econophysic...

Chaos to periodicity and periodicity to chaos by periodic perturbations in the Belousov-Zhabotinsky reaction

International Nuclear Information System (INIS)

Li Qianshu; Zhu Rui

2004-01-01

A three-variable model of the Belousov-Zhabotinsky reaction system subject to external sinusoidal perturbations is investigated by means of frequency spectrum analysis. In the period-1 window of the model, the transitions from periodicity to chaos are observed; in the chaotic window, the transitions from chaos to periodicity are found. The former might be understood by the circle map of two coupled oscillators, and the latter is partly explained by the resonance between the main frequency of the chaos and the frequency of the external periodic perturbations

Chaos and periodicity in Vallis model for El Niño

International Nuclear Information System (INIS)

Borghezan, Monik; Rech, Paulo C.

2017-01-01

We investigate a two-dimensional parameter-space of a three-parameter, three-variable, continuous-time dynamical system, namely the Vallis model for El Niño phenomenon. We report on modifications in this parameter-space, as a function of the third parameter which is varied. More specifically we report on organization of chaos and periodicity, showing the existence of periodic structures embedded in a chaotic region, which are organized in period-adding sequences.

Secure DS-CDMA spreading codes using fully digital multidimensional multiscroll chaos

KAUST Repository

Mansingka, Abhinav S.

2014-06-18

This paper introduces a generalized fully digital hardware implementation of 1-D, 2-D and 3-D multiscroll chaos through sawtooth nonlinearities in a 3rd order ODE with the Euler approximation, wherein low-significance bits pass all NIST SP. 800-22 tests. The low-significance bits show good performance as spreading code for multiple-access DS-CDMA in AWGN and multipath environments, equivalent to Gold codes. This system capitalizes on complex nonlinear dynamics afforded by multiscroll chaos to provide higher security than conventional codes with the same BER performance demonstrated experimentally on a Xilinx Virtex 4 FPGA with logic utilization less than 1.25% and throughput up to 10.92 Gbits/s.

Cryptography with chaos at the physical level

International Nuclear Information System (INIS)

Machado, Romuel F.; Baptista, Murilo S.; Grebogi, C.

2004-01-01

In this work, we devise a chaos-based secret key cryptography scheme for digital communication where the encryption is realized at the physical level, that is, the encrypting transformations are applied to the wave signal instead to the symbolic sequence. The encryption process consists of transformations applied to a two-dimensional signal composed of the message carrying signal and an encrypting signal that has to be a chaotic one. The secret key, in this case, is related to the number of times the transformations are applied. Furthermore, we show that due to its chaotic nature, the encrypting signal is able to hide the statistics of the original signal

Pattern formation and chaos in synergetic systems

Energy Technology Data Exchange (ETDEWEB)

Haken, H

1985-01-01

A general approach to the reduction of the equations of systems composed of many subsystems of equations for, in general, few order parameters at instability points is sketched. As special case generalized Ginzburg-Landau equations are obtained. Recent results based on these equations, showing pattern formation in the convection instability and flames, are presented. Bifurcations from tori to other tori are treated, and some general conclusions are drawn. Analogies between fluid dynamics and lasers which led to the prediction of laser light chaos by Haken (1975) are pointed out. Finally the suspension of a class of discrete one-dimensional maps is discussed and explicitly presented for a typical case. 21 references.

Fractals and chaos

CERN Document Server

Earnshow, R; Jones, H

1991-01-01

This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...

Quantum chaos: statistical relaxation in discrete spectrum

International Nuclear Information System (INIS)

Chirikov, B.V.

1990-01-01

The controversial phenomenon of quantum chaos is discussed using the quantized standard map, or the kicked rotator, as a simple model. The relation to the classical dynamical chaos is tracked down on the basis of the correspondence principle. Several definitions of the quantum chaos are discussed. 27 refs

Scaling of chaos in strongly nonlinear lattices.

Science.gov (United States)

Mulansky, Mario

2014-06-01

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

Ancient and Current Chaos Theories

Directory of Open Access Journals (Sweden)

Güngör Gündüz

2006-07-01

Full Text Available Chaos theories developed in the last three decades have made very important contributions to our understanding of dynamical systems and natural phenomena. The meaning of chaos in the current theories and in the past is somewhat different from each other. In this work, the properties of dynamical systems and the evolution of chaotic systems were discussed in terms of the views of ancient philosophers. The meaning of chaos in Anaximenes’ philosophy and its role in the Ancient natural philosophy has been discussed in relation to other natural philosophers such as of Anaximander, Parmenides, Heraclitus, Empedocles, Leucippus (i.e. atomists and Aristotle. In addition, the fundamental concepts of statistical mechanics and the current chaos theories were discussed in relation to the views in Ancient natural philosophy. The roots of the scientific concepts such as randomness, autocatalysis, nonlinear growth, information, pattern, etc. in the Ancient natural philosophy were investigated.

Colored chaos

International Nuclear Information System (INIS)

Mueller, B.

1997-01-01

The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results

Colored chaos

Energy Technology Data Exchange (ETDEWEB)

Mueller, B.

1997-09-22

The report contains viewgraphs on the following: ergodicity and chaos; Hamiltonian dynamics; metric properties; Lyapunov exponents; KS entropy; dynamical realization; lattice formulation; and numerical results.

Si'lnikov chaos and Hopf bifurcation analysis of Rucklidge system

International Nuclear Information System (INIS)

Wang Xia

2009-01-01

A three-dimensional autonomous system - the Rucklidge system is considered. By the analytical method, Hopf bifurcation of Rucklidge system may occur when choosing an appropriate bifurcation parameter. Using the undetermined coefficient method, the existence of heteroclinic and homoclinic orbits in the Rucklidge system is proved, and the explicit and uniformly convergent algebraic expressions of Si'lnikov type orbits are given. As a result, the Si'lnikov criterion guarantees that there exists the Smale horseshoe chaos motion for the Rucklidge system.

SECULAR CHAOS AND THE PRODUCTION OF HOT JUPITERS

International Nuclear Information System (INIS)

Wu Yanqin; Lithwick, Yoram

2011-01-01

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.

Chaos in body-vortex interactions

DEFF Research Database (Denmark)

Pedersen, Johan Rønby; Aref, Hassan

2010-01-01

of a circle is integrable. As the body is made slightly elliptic, a chaotic region grows from an unstable relative equilibrium of the circle-vortex case. The case of a cylindrical body of any shape moving in fluid otherwise at rest is also integrable. A second transition to chaos arises from the limit between...... rocking and tumbling motion of the body known in this case. In both instances, the chaos may be detected both in the body motion and in the vortex motion. The effect of increasing body mass at a fixed body shape is to damp the chaos....

Electromagnetic Wave Chaos in Gradient Refractive Index Optical Cavities

International Nuclear Information System (INIS)

Wilkinson, P. B.; Fromhold, T. M.; Taylor, R. P.; Micolich, A. P.

2001-01-01

Electromagnetic wave chaos is investigated using two-dimensional optical cavities formed in a cylindrical gradient refractive index lens with reflective surfaces. When the planar ends of the lens are cut at an angle to its axis, the geometrical ray paths are chaotic. In this regime, the electromagnetic mode spectrum of the cavity is modulated by both real and ghost periodic ray paths, which also 'scar' the electric field intensity distributions of many modes. When the cavity is coupled to waveguides, the eigenmodes generate complex series of resonant peaks in the electromagnetic transmission spectrum

Robinson's chaos in set-valued discrete systems

International Nuclear Information System (INIS)

Roman-Flores, Heriberto; Chalco-Cano, Y.

2005-01-01

Let (X,d) be a compact metric space and f:X->X a continuous function. If we consider the space (K(X),H) of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and f-bar :K(X)->K(X), f-bar (A)={f(a)/a-bar A}, then the aim of this work is to show that Robinson's chaos in f-bar implies Robinson's chaos in f. Also, we give an example showing that R-chaos in f does not implies R-chaos in f-bar

A quantum harmonic oscillator and strong chaos

International Nuclear Information System (INIS)

Oprocha, Piotr

2006-01-01

It is known that many physical systems which do not exhibit deterministic chaos when treated classically may exhibit such behaviour if treated from the quantum mechanics point of view. In this paper, we will show that an annihilation operator of the unforced quantum harmonic oscillator exhibits distributional chaos as introduced in B Schweizer and J SmItal (1994 Trans. Am. Math. Soc. 344 737-54). Our approach strengthens previous results on chaos in this model and provides a very powerful tool to measure chaos in other (quantum or classical) models

The chaos cookbook a practical programming guide

CERN Document Server

Pritchard, Joe

2014-01-01

The Chaos Cookbook: A Practical Programming Guide discusses the use of chaos in computer programming. The book is comprised of 11 chapters that tackle various topics relevant to chaos and programming. Chapter 1 reviews the concept of chaos, and Chapter 2 discusses the iterative functions. Chapters 3 and 4 cover differential and Lorenz equations. Chapter 5 talks about strange attractors, while Chapter 6 deals with the fractal link. The book also discusses the Mandelbrot set, and then covers the Julia sets. The other fractal systems and the cellular automata are also explained. The last chapter

Genome chaos: survival strategy during crisis.

Science.gov (United States)

Liu, Guo; Stevens, Joshua B; Horne, Steven D; Abdallah, Batoul Y; Ye, Karen J; Bremer, Steven W; Ye, Christine J; Chen, David J; Heng, Henry H

2014-01-01

Genome chaos, a process of complex, rapid genome re-organization, results in the formation of chaotic genomes, which is followed by the potential to establish stable genomes. It was initially detected through cytogenetic analyses, and recently confirmed by whole-genome sequencing efforts which identified multiple subtypes including "chromothripsis", "chromoplexy", "chromoanasynthesis", and "chromoanagenesis". Although genome chaos occurs commonly in tumors, both the mechanism and detailed aspects of the process are unknown due to the inability of observing its evolution over time in clinical samples. Here, an experimental system to monitor the evolutionary process of genome chaos was developed to elucidate its mechanisms. Genome chaos occurs following exposure to chemotherapeutics with different mechanisms, which act collectively as stressors. Characterization of the karyotype and its dynamic changes prior to, during, and after induction of genome chaos demonstrates that chromosome fragmentation (C-Frag) occurs just prior to chaotic genome formation. Chaotic genomes seem to form by random rejoining of chromosomal fragments, in part through non-homologous end joining (NHEJ). Stress induced genome chaos results in increased karyotypic heterogeneity. Such increased evolutionary potential is demonstrated by the identification of increased transcriptome dynamics associated with high levels of karyotypic variance. In contrast to impacting on a limited number of cancer genes, re-organized genomes lead to new system dynamics essential for cancer evolution. Genome chaos acts as a mechanism of rapid, adaptive, genome-based evolution that plays an essential role in promoting rapid macroevolution of new genome-defined systems during crisis, which may explain some unwanted consequences of cancer treatment.

Markov transitions and the propagation of chaos

International Nuclear Information System (INIS)

Gottlieb, A.

1998-01-01

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 show 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

How to test for partially predictable chaos.

Science.gov (United States)

Wernecke, Hendrik; Sándor, Bulcsú; Gros, Claudius

2017-04-24

For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0-1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0-1 manner solely from the properties of pairs of trajectories.

Channeling and dynamic chaos

Energy Technology Data Exchange (ETDEWEB)

Bolotin, IU L; Gonchar, V IU; Truten, V I; Shulga, N F

1986-01-01

It is shown that axial channeling of relativistic electrons can give rise to the effect of dynamic chaos which involves essentially chaotic motion of a particle in the channel. The conditions leading to the effect of dynamic chaos and the manifestations of this effect in physical processes associated with the passage of particles through a crystal are examined using a silicon crystal as an example. 7 references.

The bane of low-dimensionality clustering

DEFF Research Database (Denmark)

Cohen-Addad, Vincent; de Mesmay, Arnaud; Rotenberg, Eva

2018-01-01

geometric problems such as the traveling salesman problem, or computing an independent set of unit spheres. While these problems benefit from the so-called (limited) blessing of dimensionality, as they can be solved in time nO(k1--1/d) or 2

Homoclinic tubes and chaos in perturbed sine-Gordon equation

International Nuclear Information System (INIS)

Li, Y. Charles

2004-01-01

Sine-Gordon equation under a quasi-periodic perturbation or a chaotic perturbation is studied. Existence of a homoclinic tube is proved. Established are chaos associated with the homoclinic tube, and 'chaos cascade' referring to the embeddings of smaller scale chaos in larger scale chaos

Common phase diagram for low-dimensional superconductors

International Nuclear Information System (INIS)

Michalak, Rudi

2003-01-01

A phenomenological phase diagram which has been derived for high-temperature superconductors from NMR Knight-shift measurements of the pseudogap is compared to the phase diagram that is obtained for organic superconductors and spin-ladder superconductors, both low-dimensional systems. This is contrasted to the phase diagram of some Heavy Fermion superconductors, i.e. superconductors not constrained to a low dimensionality

Chaos and complexity by design

Energy Technology Data Exchange (ETDEWEB)

Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics,Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 (United States); School of Natural Sciences, Institute for Advanced Study,Princeton, NJ 08540 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,Waterloo, Ontario N2L 2Y5 (Canada)

2017-04-20

We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame potential,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.

Chaos and complexity by design

International Nuclear Information System (INIS)

Roberts, Daniel A.; Yoshida, Beni

2017-01-01

We study the relationship between quantum chaos and pseudorandomness by developing probes of unitary design. A natural probe of randomness is the “frame potential,” which is minimized by unitary k-designs and measures the 2-norm distance between the Haar random unitary ensemble and another ensemble. A natural probe of quantum chaos is out-of-time-order (OTO) four-point correlation functions. We show that the norm squared of a generalization of out-of-time-order 2k-point correlators is proportional to the kth frame potential, providing a quantitative connection between chaos and pseudorandomness. Additionally, we prove that these 2k-point correlators for Pauli operators completely determine the k-fold channel of an ensemble of unitary operators. Finally, we use a counting argument to obtain a lower bound on the quantum circuit complexity in terms of the frame potential. This provides a direct link between chaos, complexity, and randomness.

Chaos in the atomic and subatomic world

International Nuclear Information System (INIS)

Nussenzveig, H.M.

1992-01-01

This work discusses the possibility of the existence of chaos in the quantum level. In the macroscopic scale, chaos can be explained by the use of classical mechanics. The problem is to know whether there is any manifestation of chaos in the evolution of a system following the quantum mechanical laws. (A.C.A.S.)

REVISITING EVIDENCE OF CHAOS IN X-RAY LIGHT CURVES: THE CASE OF GRS 1915+105

Energy Technology Data Exchange (ETDEWEB)

Mannattil, Manu; Gupta, Himanshu; Chakraborty, Sagar, E-mail: mmanu@iitk.ac.in, E-mail: hiugupta@iitk.ac.in, E-mail: sagarc@iitk.ac.in [Department of Physics, Indian Institute of Technology Kanpur, Uttar Pradesh 208016 (India)

2016-12-20

Nonlinear time series analysis has been widely used to search for signatures of low-dimensional chaos in light curves emanating from astrophysical bodies. A particularly popular example is the microquasar GRS 1915+105, whose irregular but systematic X-ray variability has been well studied using data acquired by the Rossi X-ray Timing Explorer . With a view to building simpler models of X-ray variability, attempts have been made to classify the light curves of GRS 1915+105 as chaotic or stochastic. Contrary to some of the earlier suggestions, after careful analysis, we find no evidence for chaos or determinism in any of the GRS 1915+105 classes. The dearth of long and stationary data sets representing all the different variability classes of GRS 1915+105 makes it a poor candidate for analysis using nonlinear time series techniques. We conclude that either very exhaustive data analysis with sufficiently long and stationary light curves should be performed, keeping all the pitfalls of nonlinear time series analysis in mind, or alternative schemes of classifying the light curves should be adopted. The generic limitations of the techniques that we point out in the context of GRS 1915+105 affect all similar investigations of light curves from other astrophysical sources.

Quantum chaos: diffusion photoeffect in hydrogen

Energy Technology Data Exchange (ETDEWEB)

Shepelyanskij, D L

1987-05-01

Ionization process in highly excited hydrogen atom in electromagnetic field is presented in the form of an extraordinary photoeffect, in which ionization at the frequency, being much lower than ionization energy, occurs much quicker than single-photon one. Such a quick ionization is explained by dynamic chaos occurence. Question, related to quantum effect influence on chaotic movement of the electron (quantum chaos) is considered. Electron excitation in the chaos area is described by a diffusional equation.

CT Image Reconstruction in a Low Dimensional Manifold

OpenAIRE

Cong, Wenxiang; Wang, Ge; Yang, Qingsong; Hsieh, Jiang; Li, Jia; Lai, Rongjie

2017-01-01

Regularization methods are commonly used in X-ray CT image reconstruction. Different regularization methods reflect the characterization of different prior knowledge of images. In a recent work, a new regularization method called a low-dimensional manifold model (LDMM) is investigated to characterize the low-dimensional patch manifold structure of natural images, where the manifold dimensionality characterizes structural information of an image. In this paper, we propose a CT image reconstruc...

A novel image encryption algorithm based on chaos maps with Markov properties

Science.gov (United States)

Liu, Quan; Li, Pei-yue; Zhang, Ming-chao; Sui, Yong-xin; Yang, Huai-jiang

2015-02-01

In order to construct high complexity, secure and low cost image encryption algorithm, a class of chaos with Markov properties was researched and such algorithm was also proposed. The kind of chaos has higher complexity than the Logistic map and Tent map, which keeps the uniformity and low autocorrelation. An improved couple map lattice based on the chaos with Markov properties is also employed to cover the phase space of the chaos and enlarge the key space, which has better performance than the original one. A novel image encryption algorithm is constructed on the new couple map lattice, which is used as a key stream generator. A true random number is used to disturb the key which can dynamically change the permutation matrix and the key stream. From the experiments, it is known that the key stream can pass SP800-22 test. The novel image encryption can resist CPA and CCA attack and differential attack. The algorithm is sensitive to the initial key and can change the distribution the pixel values of the image. The correlation of the adjacent pixels can also be eliminated. When compared with the algorithm based on Logistic map, it has higher complexity and better uniformity, which is nearer to the true random number. It is also efficient to realize which showed its value in common use.

Meaning Finds a Way: Chaos (Theory) and Composition

Science.gov (United States)

Kyburz, Bonnie Lenore

2004-01-01

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

Chaos theory in geophysics: past, present and future

International Nuclear Information System (INIS)

Sivakumar, B.

2004-01-01

The past two decades of research on chaos theory in geophysics has brought about a significant shift in the way we view geophysical phenomena. Research on chaos theory in geophysics continues to grow at a much faster pace, with applications to a wide variety of geophysical phenomena and geophysical problems. In spite of our success in understanding geophysical phenomena also from a different (i.e. chaotic) perspective, there still seems to be lingering suspicions on the scope of chaos theory in geophysics. The goal of this paper is to present a comprehensive account of the achievements and status of chaos theory in geophysics, and to disseminate the hope and scope for the future. A systematic review of chaos theory in geophysics, covering a wide spectrum of geophysical phenomena studied (e.g. rainfall, river flow, sediment transport, temperature, pressure, tree ring series, etc.), is presented to narrate our past achievements not only in understanding and predicting geophysical phenomena but also in improving the chaos identification and prediction techniques. The present state of chaos research in geophysics (in terms of geophysical phenomena, problems, and chaos methods) and potential for future improvements (in terms of where, why and possibly how) are also highlighted. Our popular views of nature (i.e. stochastic and deterministic), and of geophysical phenomena in particular, are discussed, and the usefulness of chaos theory as a bridge between such views is also put forth

Graphics processing unit accelerated three-dimensional model for the simulation of pulsed low-temperature plasmas

Energy Technology Data Exchange (ETDEWEB)

Fierro, Andrew, E-mail: andrew.fierro@ttu.edu; Dickens, James; Neuber, Andreas [Center for Pulsed Power and Power Electronics, Department of Electrical and Computer Engineering, Texas Tech University, Lubbock, Texas 79409 (United States)

2014-12-15

A 3-dimensional particle-in-cell/Monte Carlo collision simulation that is fully implemented on a graphics processing unit (GPU) is described and used to determine low-temperature plasma characteristics at high reduced electric field, E/n, in nitrogen gas. Details of implementation on the GPU using the NVIDIA Compute Unified Device Architecture framework are discussed with respect to efficient code execution. The software is capable of tracking around 10 × 10{sup 6} particles with dynamic weighting and a total mesh size larger than 10{sup 8} cells. Verification of the simulation is performed by comparing the electron energy distribution function and plasma transport parameters to known Boltzmann Equation (BE) solvers. Under the assumption of a uniform electric field and neglecting the build-up of positive ion space charge, the simulation agrees well with the BE solvers. The model is utilized to calculate plasma characteristics of a pulsed, parallel plate discharge. A photoionization model provides the simulation with additional electrons after the initial seeded electron density has drifted towards the anode. Comparison of the performance benefits between the GPU-implementation versus a CPU-implementation is considered, and a speed-up factor of 13 for a 3D relaxation Poisson solver is obtained. Furthermore, a factor 60 speed-up is realized for parallelization of the electron processes.

Chaos in World Politics: A Reflection

Science.gov (United States)

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

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.

Controllable chaos in hybrid electro-optomechanical systems

Science.gov (United States)

Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

2016-01-01

We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication. PMID:26948505

Controllable chaos in hybrid electro-optomechanical systems.

Science.gov (United States)

Wang, Mei; Lü, Xin-You; Ma, Jin-Yong; Xiong, Hao; Si, Liu-Gang; Wu, Ying

2016-03-07

We investigate the nonlinear dynamics of a hybrid electro-optomechanical system (EOMS) that allows us to realize the controllable opto-mechanical nonlinearity by driving the microwave LC resonator with a tunable electric field. A controllable optical chaos is realized even without changing the optical pumping. The threshold and lifetime of the chaos could be optimized by adjusting the strength, frequency, or phase of the electric field. This study provides a method of manipulating optical chaos with an electric field. It may offer the prospect of exploring the controllable chaos in on-chip optoelectronic devices and its applications in secret communication.

Relativistic quantum chaos-An emergent interdisciplinary field.

Science.gov (United States)

Lai, Ying-Cheng; Xu, Hong-Ya; Huang, Liang; Grebogi, Celso

2018-05-01

Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

Chaos and bifurcations in periodic windows observed in plasmas

International Nuclear Information System (INIS)

Qin, J.; Wang, L.; Yuan, D.P.; Gao, P.; Zhang, B.Z.

1989-01-01

We report the experimental observations of deterministic chaos in a steady-state plasma which is not driven by any extra periodic forces. Two routes to chaos have been found, period-doubling and intermittent chaos. The fine structures in chaos such as periodic windows and bifurcations in windows have also been observed

Experiments on intrinsic and thermally induced chaos in an rf-driven Josephson junction

DEFF Research Database (Denmark)

Davidson, A.; Dueholm, B.; Beasley, M. R.

1986-01-01

We report detailed measurements of low-frequency noise due to microwaves applied to a real Josephson tunnel junction. An intrinsically chaotic region is apparently identified, but the effects of thermal noise are shown to be significant. In particular we show experimental data that we interpret a...... as evidence for thermally activated hopping and thermally affected chaos. The data are only in qualitative accord with recent ideas regarding the effect of thermal noise on intermittent chaos....

Order against chaos in nuclei

International Nuclear Information System (INIS)

Soloviev, V.G.

1995-01-01

Order and chaos and order-to-chaos transition are treated in terms of nuclear wave functions. A quasiparticle-phonon interaction is responsible for the fragmentation of one- and many-quasiparticle and phonon states and for the mixing of closely spaced states. Complete damping of one-quasiparticle states cannot be considered as a transition to chaos due to large many-quasiparticle or quasiparticle-phonon terms in their wave functions. An experimental investigation of the strength distribution of many-quasiparticle and quasiparticle-phonon states should uncover a new region of a regularity in nuclei at intermediate excitation energy. A chaotic behaviour of nuclear states can be shifted to higher excitation energies. ((orig.))

An Improved Chaos Genetic Algorithm for T-Shaped MIMO Radar Antenna Array Optimization

Directory of Open Access Journals (Sweden)

Xin Fu

2014-01-01

Full Text Available In view of the fact that the traditional genetic algorithm easily falls into local optimum in the late iterations, an improved chaos genetic algorithm employed chaos theory and genetic algorithm is presented to optimize the low side-lobe for T-shaped MIMO radar antenna array. The novel two-dimension Cat chaotic map has been put forward to produce its initial population, improving the diversity of individuals. The improved Tent map is presented for groups of individuals of a generation with chaos disturbance. Improved chaotic genetic algorithm optimization model is established. The algorithm presented in this paper not only improved the search precision, but also avoids effectively the problem of local convergence and prematurity. For MIMO radar, the improved chaos genetic algorithm proposed in this paper obtains lower side-lobe level through optimizing the exciting current amplitude. Simulation results show that the algorithm is feasible and effective. Its performance is superior to the traditional genetic algorithm.

Universal signatures of quantum chaos

International Nuclear Information System (INIS)

Aurich, R.; Bolte, J.; Steiner, F.

1994-02-01

We discuss fingerprints of classical chaos in spectra of the corresponding bound quantum systems. A novel quantity to measure quantum chaos in spectra is proposed and a conjecture about its universal statistical behaviour is put forward. Numerical as well as theoretical evidence is provided in favour of the conjecture. (orig.)

Stochastic quantum gravity-(2+1)-dimensional case

International Nuclear Information System (INIS)

Hosoya, Akio

1991-01-01

At first the amazing coincidences are pointed out in quantum field theory in curved space-time and quantum gravity, when they exhibit stochasticity. To explore the origin of them, the (2+1)-dimensional quantum gravity is considered as a toy model. It is shown that the torus universe in the (2+1)-dimensional quantum gravity is a quantum chaos in a rigorous sense. (author). 15 refs

Household chaos and family sleep during infants' first year.

Science.gov (United States)

Whitesell, Corey J; Crosby, Brian; Anders, Thomas F; Teti, Douglas M

2018-05-21

Household chaos has been linked with dysregulated family and individual processes. The present study investigated linkages between household chaos and infant and parent sleep, a self-regulated process impacted by individual, social, and environmental factors. Studies of relations between household chaos and child sleep have focused on older children and teenagers, with little attention given to infants or parent sleep. This study examines these relationships using objective measures of household chaos and sleep while controlling for, respectively, maternal emotional availability at bedtime and martial adjustment, in infant and parent sleep. Multilevel modeling examined mean and variability of sleep duration and fragmentation for infants, mothers, and fathers when infants were 1, 3, 6, 9, and 12 months (N = 167). Results indicated infants in higher chaos homes experienced delays in sleep consolidation patterns, with longer and more variable sleep duration, and greater fragmentation. Parent sleep was also associated with household chaos such that in higher chaos homes, mothers and fathers experienced greater variability in sleep duration, which paralleled infant findings. In lower chaos homes, parents' sleep fragmentation mirrored infants' decreasingly fragmented sleep across the first year and remained lower at all timepoints compared to parents and infants in high chaos homes. Collectively, these findings indicate that after controlling for maternal emotional availability and marital adjustment (respectively) household chaos has a dysregulatory impact on infant and parent sleep. Results are discussed in terms of the potential for chaos-induced poor sleep to dysregulate daytime functioning and, in turn, place parent-infant relationships at risk. (PsycINFO Database Record (c) 2018 APA, all rights reserved).

Learning Low-Dimensional Metrics

OpenAIRE

Jain, Lalit; Mason, Blake; Nowak, Robert

2017-01-01

This paper investigates the theoretical foundations of metric learning, focused on three key questions that are not fully addressed in prior work: 1) we consider learning general low-dimensional (low-rank) metrics as well as sparse metrics; 2) we develop upper and lower (minimax)bounds on the generalization error; 3) we quantify the sample complexity of metric learning in terms of the dimension of the feature space and the dimension/rank of the underlying metric;4) we also bound the accuracy ...

Quantum chaos in the Heisenberg picture

International Nuclear Information System (INIS)

McKellar, B.H.J.; Lancaster, M.; McCaw, J.

2000-01-01

Full text: We explore the possibility of defining quantum chaos in the algebra of quantum mechanical operators. The simple definition of the Lyapunov exponent in terms of a metric on that algebra has the expected properties for the quantum logistic map, as we confirm for the simple spin 1 system. We then show numerically and analytically that the Hamiltonian evolution of finite spin systems does not lead to chaos in this definition, and investigate alternative definitions of quantum chaos in the algebra of operators

Chaos the science of predictable random motion

CERN Document Server

Kautz, Richard

2011-01-01

Based on only elementary mathematics, this engaging account of chaos theory bridges the gap between introductions for the layman and college-level texts. It develops the science of dynamics in terms of small time steps, describes the phenomenon of chaos through simple examples, and concludes with a close look at a homoclinic tangle, the mathematical monster at the heart of chaos. The presentation is enhanced by many figures, animations of chaotic motion (available on a companion CD), and biographical sketches of the pioneers of dynamics and chaos theory. To ensure accessibility to motivated high school students, care has been taken to explain advanced mathematical concepts simply, including exponentials and logarithms, probability, correlation, frequency analysis, fractals, and transfinite numbers. These tools help to resolve the intriguing paradox of motion that is predictable and yet random, while the final chapter explores the various ways chaos theory has been put to practical use.

Computing derivative-based global sensitivity measures using polynomial chaos expansions

International Nuclear Information System (INIS)

Sudret, B.; Mai, C.V.

2015-01-01

In the field of computer experiments sensitivity analysis aims at quantifying the relative importance of each input parameter (or combinations thereof) of a computational model with respect to the model output uncertainty. Variance decomposition methods leading to the well-known Sobol' indices are recognized as accurate techniques, at a rather high computational cost though. The use of polynomial chaos expansions (PCE) to compute Sobol' indices has allowed to alleviate the computational burden though. However, when dealing with large dimensional input vectors, it is good practice to first use screening methods in order to discard unimportant variables. The derivative-based global sensitivity measures (DGSMs) have been developed recently in this respect. In this paper we show how polynomial chaos expansions may be used to compute analytically DGSMs as a mere post-processing. This requires the analytical derivation of derivatives of the orthonormal polynomials which enter PC expansions. Closed-form expressions for Hermite, Legendre and Laguerre polynomial expansions are given. The efficiency of the approach is illustrated on two well-known benchmark problems in sensitivity analysis. - Highlights: • Derivative-based global sensitivity measures (DGSM) have been developed for screening purpose. • Polynomial chaos expansions (PC) are used as a surrogate model of the original computational model. • From a PC expansion the DGSM can be computed analytically. • The paper provides the derivatives of Hermite, Legendre and Laguerre polynomials for this purpose

Resurvey of order and chaos in spinning compact binaries

International Nuclear Information System (INIS)

Wu Xin; Xie Yi

2008-01-01

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

Chaos Theory and Post Modernism

Science.gov (United States)

Snell, Joel

2009-01-01

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…

The three versions of distributional chaos

International Nuclear Information System (INIS)

Balibrea, F.; Smital, J.; Stefankova, M.

2005-01-01

The notion of distributional chaos was introduced by Schweizer and Smital [Trans. Amer. Math. Soc. 344 (1994) 737] for continuous maps of the interval. However, it turns out that, for continuous maps of a compact metric space three mutually nonequivalent versions of distributional chaos, DC1-DC3, can be considered. In this paper we consider the weakest one, DC3. We show that DC3 does not imply chaos in the sense of Li and Yorke. We also show that DC3 is not invariant with respect to topological conjugacy. In other words, there are lower and upper distribution functions Φ xy and Φxy* generated by a continuous map f of a compact metric space (M, ρ) such that Φxy*(t)>Φxy(t) for all t in an interval. However, f on the same space M, but with a metric ρ' generating the same topology as ρ is no more DC3.Recall that, contrary to this, either DC1 or DC2 is topological conjugacy invariant and implies Li and Yorke chaos (cf. [Chaos, Solitons and Fractals 21 (2004) 1125])

Chaotic dynamics and chaos control in nonlinear laser systems

International Nuclear Information System (INIS)

Fang Jinqing; Yao Weiguang

2001-01-01

Chaotic dynamics and chaos control have become a great challenge in nonlinear laser systems and its advances are reviewed mainly based on the ring cavity laser systems. The principle and stability conditions for time-delay feedback control are analyzed and applied to chaos control in the laser systems. Other advanced methods of chaos control, such as weak spatial perturbation and occasional proportional feedback technique, are discussed. Prospects of chaos control for application (such as improvement of laser power and performance, synchronized chaos secure communication and information processing) are pointed out finally

!CHAOS: A cloud of controls

Science.gov (United States)

Angius, S.; Bisegni, C.; Ciuffetti, P.; Di Pirro, G.; Foggetta, L. G.; Galletti, F.; Gargana, R.; Gioscio, E.; Maselli, D.; Mazzitelli, G.; Michelotti, A.; Orrù, R.; Pistoni, M.; Spagnoli, F.; Spigone, D.; Stecchi, A.; Tonto, T.; Tota, M. A.; Catani, L.; Di Giulio, C.; Salina, G.; Buzzi, P.; Checcucci, B.; Lubrano, P.; Piccini, M.; Fattibene, E.; Michelotto, M.; Cavallaro, S. R.; Diana, B. F.; Enrico, F.; Pulvirenti, S.

2016-01-01

The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of aaabstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.

!CHAOS: A cloud of controls

International Nuclear Information System (INIS)

Angius, S.; Bisegni, C.; Ciuffetti, P.

2016-01-01

The paper is aimed to present the !CHAOS open source project aimed to develop a prototype of a national private Cloud Computing infrastructure, devoted to accelerator control systems and large experiments of High Energy Physics (HEP). The !CHAOS project has been financed by MIUR (Italian Ministry of Research and Education) and aims to develop a new concept of control system and data acquisition framework by providing, with a high level of abstraction, all the services needed for controlling and managing a large scientific, or non-scientific, infrastructure. A beta version of the !CHAOS infrastructure will be released at the end of December 2015 and will run on private Cloud infrastructures based on OpenStack.

On CFT and quantum chaos

International Nuclear Information System (INIS)

Turiaci, Gustavo J.; Verlinde, Herman

2016-01-01

We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.

Nuclear spectroscopy and quantum chaos

International Nuclear Information System (INIS)

Sakata, Fumihiko; Marumori, Toshio; Hashimoto, Yukio; Yamamoto, Yoshifumi; Tsukuma, Hidehiko; Iwasawa, Kazuo.

1990-05-01

In this paper, a recent development of INS-TSUKUBA joint research project on large-amplitude collective motion is summerized. The classical theory of nuclear collective dynamics formulated within the time-dependent Hartree-Fock theory is recapitulated and decisive role of the level crossing in the single-particle dynamics on the order-to-chaos transition of collective motion is discussed in detail. Extending the basic idea of the classical theory, we discuss a quantum theory of nuclear collective dynamics which allows us to properly define a concept of quantum chaos for each eigenfunction. By using numerical calculation, we illustrate what the quantum chaos for each eigenfunction means and its relation to usual definition based on the random matrix theory. (author)

Quantum mechanical suppression of chaos

International Nuclear Information System (INIS)

Bluemel, R.; Smilansky, U.

1990-01-01

The relation between determinism and predictability is the central issue in the study of 'deterministic chaos'. Much knowledge has been accumulated in the past 10 years about the chaotic dynamics of macroscopic (classical) systems. The implications of chaos in the microscopic quantum world is examined, in other words, how to reconcile the correspondence principle with the inherent uncertainties which reflect the wave nature of quantum dynamics. Recent atomic physics experiments demonstrate clearly that chaos is relevant to the microscopic world. In particular, such experiments emphasise the urgent need to clarify the genuine quantum mechanism which imposes severe limitations on quantum dynamics, and renders it so very different from its classical counterpart. (author)

On CFT and quantum chaos

Energy Technology Data Exchange (ETDEWEB)

Turiaci, Gustavo J. [Physics Department, Princeton University,Princeton NJ 08544 (United States); Verlinde, Herman [Physics Department, Princeton University,Princeton NJ 08544 (United States); Princeton Center for Theoretical Science, Princeton University,Princeton NJ 08544 (United States)

2016-12-21

We make three observations that help clarify the relation between CFT and quantum chaos. We show that any 1+1-D system in which conformal symmetry is non-linearly realized exhibits two main characteristics of chaos: maximal Lyapunov behavior and a spectrum of Ruelle resonances. We use this insight to identify a lattice model for quantum chaos, built from parafermionic spin variables with an equation of motion given by a Y-system. Finally we point to a relation between the spectrum of Ruelle resonances of a CFT and the analytic properties of OPE coefficients between light and heavy operators. In our model, this spectrum agrees with the quasi-normal modes of the BTZ black hole.

Semiconductor lasers stability, instability and chaos

CERN Document Server

Ohtsubo, Junji

2017-01-01

This book describes the fascinating recent advances made concerning the chaos, stability and instability of semiconductor lasers, and discusses their applications and future prospects in detail. It emphasizes the dynamics in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Applications of semiconductor laser chaos, control and noise, and semiconductor lasers are also demonstrated. Semiconductor lasers with new structures, such as vertical-cavity surface-emitting lasers and broad-area semiconductor lasers, are intriguing and promising devices. Current topics include fast physical number generation using chaotic semiconductor lasers for secure communication, development of chaos, quantum-dot semiconductor lasers and quantum-cascade semiconductor lasers, and vertical-cavity surface-emitting lasers. This fourth edition has been significantly expanded to reflect the latest developments. The fundamental theory of laser chaos and the chaotic dynamics in se...

Homoclinic chaos and energy condition violation

International Nuclear Information System (INIS)

Heinzle, J. Mark; Roehr, Niklas; Uggla, Claes

2006-01-01

In this letter we discuss the connection between so-called homoclinic chaos and the violation of energy conditions in locally rotationally symmetric Bianchi type IX models, where the matter is assumed to be nontilted dust and a positive cosmological constant. We show that homoclinic chaos in these models is an artifact of unphysical assumptions: it requires that there exist solutions with positive matter energy density ρ>0 that evolve through the singularity and beyond as solutions with negative matter energy density ρ<0. Homoclinic chaos is absent when it is assumed that the dust particles always retain their positive mass. In addition, we discuss more general models: for solutions that are not locally rotationally symmetric we demonstrate that the construction of extensions through the singularity, which is required for homoclinic chaos, is not possible in general

Iani Chaos

Science.gov (United States)

2005-01-01

[figure removed for brevity, see original site] Context image for PIA03200 Iani Chaos This VIS image of Iani Chaos shows the layered deposit that occurs on the floor. It appears that the layers were deposited after the chaos was formed. Image information: VIS instrument. Latitude 2.3S, Longitude 342.3E. 17 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.

Semiconductor Lasers Stability, Instability and Chaos

CERN Document Server

Ohtsubo, Junji

2008-01-01

This monograph describes fascinating recent progress in the field of chaos, stability and instability of semiconductor lasers. Applications and future prospects are discussed in detail. The book emphasizes the various dynamics induced in semiconductor lasers by optical and electronic feedback, optical injection, and injection current modulation. Recent results of both theoretical and experimental investigations are presented. Demonstrating applications of semiconductor laser chaos, control and noise, Semiconductor Lasers describes suppression and chaotic secure communications. For those who are interested in optics but not familiar with nonlinear systems, a brief introduction to chaos analysis is presented.

Chua's circuit a paradigm for chaos

CERN Document Server

1993-01-01

For uninitiated researchers, engineers, and scientists interested in a quick entry into the subject of chaos, this book offers a timely collection of 55 carefully selected papers covering almost every aspect of this subject. Because Chua's circuit is endowed with virtually every bifurcation phenomena reported in the extensive literature on chaos, and because it is the only chaotic system which can be easily built by a novice, simulated in a personal computer, and tractable mathematically, it has become a paradigm for chaos, and a vehicle for illustrating this ubiquitous phenomenon. Its supreme

The Strength of Chaos: Accurate Simulation of Resonant Electron Scattering by Many-Electron Ions and Atoms in the Presence of Quantum Chaos

Science.gov (United States)

2017-01-20

AFRL-AFOSR-JP-TR-2017-0012 The Strength of Chaos : accurate simulation of resonant electron scattering by many-electron ions and atoms in the presence...of quantum chaos Igor Bray CURTIN UNIVERSITY OF TECHNOLOGY Final Report 01/20/2017 DISTRIBUTION A: Distribution approved for public release. AF...SUBTITLE The Strength of Chaos : accurate simulation of resonant electron scattering by many- electron ions and atoms in the presence of quantum chaos

CHAOS-BASED ADVANCED ENCRYPTION STANDARD

KAUST Repository

Abdulwahed, Naif B.

2013-05-01

This thesis introduces a new chaos-based Advanced Encryption Standard (AES). The AES is a well-known encryption algorithm that was standardized by U.S National Institute of Standard and Technology (NIST) in 2001. The thesis investigates and explores the behavior of the AES algorithm by replacing two of its original modules, namely the S-Box and the Key Schedule, with two other chaos- based modules. Three chaos systems are considered in designing the new modules which are Lorenz system with multiplication nonlinearity, Chen system with sign modules nonlinearity, and 1D multiscroll system with stair case nonlinearity. The three systems are evaluated on their sensitivity to initial conditions and as Pseudo Random Number Generators (PRNG) after applying a post-processing technique to their output then performing NIST SP. 800-22 statistical tests. The thesis presents a hardware implementation of dynamic S-Boxes for AES that are populated using the three chaos systems. Moreover, a full MATLAB package to analyze the chaos generated S-Boxes based on graphical analysis, Walsh-Hadamard spectrum analysis, and image encryption analysis is developed. Although these S-Boxes are dynamic, meaning they are regenerated whenever the encryption key is changed, the analysis results show that such S-Boxes exhibit good properties like the Strict Avalanche Criterion (SAC) and the nonlinearity and in the application of image encryption. Furthermore, the thesis presents a new Lorenz-chaos-based key expansion for the AES. Many researchers have pointed out that there are some defects in the original key expansion of AES and thus have motivated such chaos-based key expansion proposal. The new proposed key schedule is analyzed and assessed in terms of confusion and diffusion by performing the frequency and SAC test respectively. The obtained results show that the new proposed design is more secure than the original AES key schedule and other proposed designs in the literature. The proposed

Neimark-Sacker bifurcations and evidence of chaos in a discrete dynamical model of walkers

International Nuclear Information System (INIS)

Rahman, Aminur; Blackmore, Denis

2016-01-01

Bouncing droplets on a vibrating fluid bath can exhibit wave-particle behavior, such as being propelled by interacting with its own wave field. These droplets seem to walk across the bath, and thus are dubbed walkers. Experiments have shown that walkers can exhibit exotic dynamical behavior indicative of chaos. While the integro-differential models developed for these systems agree well with the experiments, they are difficult to analyze mathematically. In recent years, simpler discrete dynamical models have been derived and studied numerically. The numerical simulations of these models show evidence of exotic dynamics such as period doubling bifurcations, Neimark–Sacker (N–S) bifurcations, and even chaos. For example, in [1], based on simulations Gilet conjectured the existence of a supercritical N-S bifurcation as the damping factor in his one- dimensional path model. We prove Gilet’s conjecture and more; in fact, both supercritical and subcritical (N-S) bifurcations are produced by separately varying the damping factor and wave-particle coupling for all eigenmode shapes. Then we compare our theoretical results with some previous and new numerical simulations, and find complete qualitative agreement. Furthermore, evidence of chaos is shown by numerically studying a global bifurcation.

Chaos-Introduction to Chaos

Indian Academy of Sciences (India)

It lurks in the fluctuations of stock prices. ... This attracting ellipse, on which the motion ... 'strange' because it is both attracting and chaotic (Box 2). .... the low dimensional state space, wind around forever without intersecting itself or closing on ...

A Chaos Theory Perspective on International Migration

Directory of Open Access Journals (Sweden)

Anca Tănasie

2017-12-01

Full Text Available This paper aims at providing a different approach to international migration analysis, beyond classical models previously proposed by specialized literature. Chaos theory is getting more and more applied into macroeconomics once traditional linear models or even previous dynamic analysis become less suitable. Modern science sees chaos as unpredictable evolution, maybe even disorder. Still, chaos has got its own rules and can describe many dynamic phenomena within our world. Thus, we test whether international migration data falls under the rules of chaos and whether recent developments within the “European migration crisis” (the total daily migration inflows towards the coasts of Italy, by sea, from January 2014 to April 2017 could be described as chaotic.

2nd International Symposium on Chaos, Complexity and Leadership

CERN Document Server

Banerjee, Santo

2015-01-01

These proceedings from the 2013 symposium on "Chaos, complexity and leadership" reflect current research results from all branches of Chaos, Complex Systems and their applications in Management. Included are the diverse results in the fields of applied nonlinear methods, modeling of data and simulations, as well as theoretical achievements of Chaos and Complex Systems. Also highlighted are Leadership and Management applications of Chaos and Complexity Theory.

Prediction based chaos control via a new neural network

International Nuclear Information System (INIS)

Shen Liqun; Wang Mao; Liu Wanyu; Sun Guanghui

2008-01-01

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

Chaotic sedimentation of particle pairs in a vertical channel at low Reynolds number: Multiple states and routes to chaos

Science.gov (United States)

Verjus, Romuald; Guillou, Sylvain; Ezersky, Alexander; Angilella, Jean-Régis

2016-12-01

The sedimentation of a pair of rigid circular particles in a two-dimensional vertical channel containing a Newtonian fluid is investigated numerically, for terminal particle Reynolds numbers (ReT) ranging from 1 to 10, and for a confinement ratio equal to 4. While it is widely admitted that sufficiently inertial pairs should sediment by performing a regular DKT oscillation (Drafting-Kissing-Tumbling), the present analysis shows in contrast that a chaotic regime can also exist for such particles, leading to a much slower sedimentation velocity. It consists of a nearly horizontal pair, corresponding to a maximum effective blockage ratio, and performing a quasiperiodic transition to chaos while increasing the particle weight. For less inertial regimes, the classical oblique doublet structure and its complex behavior (multiple stable states and hysteresis, period-doubling cascade and chaotic attractor) are recovered, in agreement with previous work [Aidun, C. K. and Ding, E.-J., "Dynamics of particle sedimentation in a vertical channel: Period-doubling bifurcation and chaotic state," Phys. Fluids 15, 1612 (2003)]. As a consequence of these various behaviors, the link between the terminal Reynolds number and the non-dimensional driving force is complex: it contains several branches displaying hysteresis as well as various bifurcations. For the range of Reynolds number considered here, a global bifurcation diagram is given.

Chaos in electric drive systems analysis control and application

CERN Document Server

Chau, K T

2011-01-01

In Chaos in Electric Drive Systems: Analysis, Control and Application authors Chau and Wang systematically introduce an emerging technology of electrical engineering that bridges abstract chaos theory and practical electric drives. The authors consolidate all important information in this interdisciplinary technology, including the fundamental concepts, mathematical modeling, theoretical analysis, computer simulation, and hardware implementation. The book provides comprehensive coverage of chaos in electric drive systems with three main parts: analysis, control and application. Corresponding drive systems range from the simplest to the latest types: DC, induction, synchronous reluctance, switched reluctance, and permanent magnet brushless drives.The first book to comprehensively treat chaos in electric drive systemsReviews chaos in various electrical engineering technologies and drive systemsPresents innovative approaches to stabilize and stimulate chaos in typical drivesDiscusses practical application of cha...

Discursive Maps at the Edge of Chaos

Science.gov (United States)

2017-05-25

Discursive Maps at the Edge of Chaos A Monograph by Major Mathieu Primeau Canadian Army, Royal Canadian Engineer School of Advanced Military...Master’s Thesis 3. DATES COVERED (From - To) JUN 2016 – MAY 2017 4. TITLE AND SUBTITLE Discursive Maps at the Edge of Chaos 5a. CONTRACT NUMBER 5b...meaning of boundaries and polarize conflict towards violence. The edge of chaos is the fine line between disorder and coherence. Discursive maps

Exploiting chaos for applications.

Science.gov (United States)

Ditto, William L; Sinha, Sudeshna

2015-09-01

We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.

Exploiting chaos for applications

Energy Technology Data Exchange (ETDEWEB)

Ditto, William L., E-mail: wditto@hawaii.edu [Department of Physics and Astronomy, University of Hawaii at Mānoa, Honolulu, Hawaii 96822 (United States); Sinha, Sudeshna, E-mail: sudeshna@iisermohali.ac.in [Indian Institute of Science Education and Research (IISER), Mohali, Knowledge City, Sector 81, SAS Nagar, PO Manauli 140306, Punjab (India)

2015-09-15

We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.

Chaos, decoherence and quantum cosmology

International Nuclear Information System (INIS)

Calzetta, Esteban

2012-01-01

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

Chaos, Chaos Control and Synchronization of a Gyrostat System

Science.gov (United States)

GE, Z.-M.; LIN, T.-N.

2002-03-01

The dynamic behavior of a gyrostat system subjected to external disturbance is studied in this paper. By applying numerical results, phase diagrams, power spectrum, period-T maps, and Lyapunov exponents are presented to observe periodic and choatic motions. The effect of the parameters changed in the system can be found in the bifurcation and parametric diagrams. For global analysis, the basins of attraction of each attractor of the system are located by employing the modified interpolated cell mapping (MICM) method. Several methods, the delayed feedback control, the addition of constant torque, the addition of periodic force, the addition of periodic impulse torque, injection of dither signal control, adaptive control algorithm (ACA) control and bang-bang control are used to control chaos effectively. Finally, synchronization of chaos in the gyrostat system is studied.

Chaos and its Role in Design and Simulation of Railway Vehicles

DEFF Research Database (Denmark)

True, Hans

1996-01-01

First certain important properties of nonlinear problems are discussed. Thenthe concept of chaos is described. It can only appear in nonlinear systemsand it is very common in the real world. Certain characteristic features ofdeterministic chaos and in relation hereto tests for the existence...... of chaos indynamical systems are presented.\\ Next the relevance of chaos for railwaydynamics is discussed and examples of chaotic oscillations in railwaydynamical model are shown, whereby the distinction between a chaoticattractor and transient chaos is introduces. Some causes of chaos in railwaytechnology...... are discussed. Finally the effects of chaos on field tests andnumerical simulations are discussed....

A-coupled-expanding and distributional chaos

International Nuclear Information System (INIS)

Kim, Cholsan; Ju, Hyonhui; Chen, Minghao; Raith, Peter

2015-01-01

The concept of A-coupled-expanding maps is one of the more natural and useful ideas generalized from the horseshoe map which is commonly known as a criterion of chaos. It is well known that distributional chaos is one of the concepts which reflect strong chaotic behavior. In this paper, we focus on the relationship between A-coupled-expanding and distributional chaos. We prove two theorems which give sufficient conditions for a strictly A-coupled-expanding map to be distributionally chaotic in the senses of two kinds, where A is an m × m irreducible transition matrix

Deterministic Chaos - Complex Chance out of Simple Necessity ...

Indian Academy of Sciences (India)

This is a very lucid and lively book on deterministic chaos. Chaos is very common in nature. However, the understanding and realisation of its potential applications is very recent. Thus this book is a timely addition to the subject. There are several books on chaos and several more are being added every day. In spite of this ...

A simple method of chaos control for a class of chaotic discrete-time systems

International Nuclear Information System (INIS)

Jiang Guoping; Zheng Weixing

2005-01-01

In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called 'odd eigenvalues number limitation' of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system

Chaos M-ary modulation and demodulation method based on Hamilton oscillator and its application in communication.

Science.gov (United States)

Fu, Yongqing; Li, Xingyuan; Li, Yanan; Yang, Wei; Song, Hailiang

2013-03-01

Chaotic communication has aroused general interests in recent years, but its communication effect is not ideal with the restriction of chaos synchronization. In this paper a new chaos M-ary digital modulation and demodulation method is proposed. By using region controllable characteristics of spatiotemporal chaos Hamilton map in phase plane and chaos unique characteristic, which is sensitive to initial value, zone mapping method is proposed. It establishes the map relationship between M-ary digital information and the region of Hamilton map phase plane, thus the M-ary information chaos modulation is realized. In addition, zone partition demodulation method is proposed based on the structure characteristic of Hamilton modulated information, which separates M-ary information from phase trajectory of chaotic Hamilton map, and the theory analysis of zone partition demodulator's boundary range is given. Finally, the communication system based on the two methods is constructed on the personal computer. The simulation shows that in high speed transmission communications and with no chaos synchronization circumstance, the proposed chaotic M-ary modulation and demodulation method has outperformed some conventional M-ary modulation methods, such as quadrature phase shift keying and M-ary pulse amplitude modulation in bit error rate. Besides, it has performance improvement in bandwidth efficiency, transmission efficiency and anti-noise performance, and the system complexity is low and chaos signal is easy to generate.

Chaos concepts, control and constructive use

CERN Document Server

Bolotin, Yurii; Yanovsky, Vladimir

2017-01-01

This book offers a short and concise introduction to the many facets of chaos theory. While the study of chaotic behavior in nonlinear, dynamical systems is a well-established research field with ramifications in all areas of science, there is a lot to be learnt about how chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter for the system under investigation, stochastic resonance being a prime example. The present work stresses the latter aspects and, after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing the relevant algorithms for both Hamiltonian and dissipative systems, among others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance, and a survey of ratchet models. In this second, revised and enlarged edition, two more chapters explore the many interf...

Harnessing quantum transport by transient chaos.

Science.gov (United States)

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

2013-03-01

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

Global chaos synchronization with channel time-delay

International Nuclear Information System (INIS)

Jiang Guoping; Zheng Weixing; Chen Guanrong

2004-01-01

This paper addresses a practical issue in chaos synchronization where there is a time-delay in the receiver as compared with the transmitter. A new synchronization scheme and a general criterion for global chaos synchronization are proposed and developed from the approach of unidirectional linear error feedback coupling with time-delay. The chaotic Chua's circuit is used for illustration, where the coupling parameters are determined according to the criterion under which the global chaos synchronization of the time-delay coupled systems is achieved

Some open questions in 'wave chaos'

International Nuclear Information System (INIS)

Nonnenmacher, Stéphane

2008-01-01

The subject area referred to as 'wave chaos', 'quantum chaos' or 'quantum chaology' has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability, etc. After giving a rough account on 'what is quantum chaos?', I intend to list some pending questions, some of them having been raised a long time ago, some others more recent. The choice of problems (and of references) is of course partial and personal. (open problem)

Nuclear physics, symmetries, and quantum chaos

International Nuclear Information System (INIS)

Bunakov, V.E.

1999-01-01

The reasons why the problem of chaos is of great topical interest in modern physics are briefly summarized, and it is indicated that ambiguities in the concept of quantum chaos present the greatest difficulties in these realms. The theory of random matrices and strength functions are generalized to demonstrate that chaotization of a system is associated with the violation of its symmetries. A criterion of quantum chaoticity is formulated in terms of the spreading width Γ spr . In the classical limit, this criterion reduces to Lyapunov's stability criteria. It is shown that the proposed criterion is applicable to standard problems of the modern theory of dynamical chaos

L'ordre du chaos

CERN Document Server

1989-01-01

Le mouvement brownien ; la mémoire des atomes ; le chaos ; déterminisme et prédictabilité ; déterminisme et chaos ; les phénomènes de physique et les échelles de longueur ; un ordre caché dans la matière désordonnée ; les verres de spin et l'étude des milieux désordonnés ; la convection ; la croissance fractale ; la physique de la matière hétérogène ; la matière ultradivisée.

A new approach for realizing electronic chaos generators

International Nuclear Information System (INIS)

Elwakeel, A.E.

1997-01-01

A dictionary definition of chaos is a 'formless primordial matter, utter confusion' [1]. The study of chaos is part of a larger program of study of so-called strongly nonlinear systems. No strict definition of chaos yet exists, however, nonrandom complicated motions that exhibit a very rapid growth of errors and that, despite perfect determinism, inhibit any ability to render accurate long-term prediction are usually termed chaotic. In other words, chaos may be referred to as deterministic randomness since it is the phenomenon where deterministic laws, are sometimes extremely simple, show random (or random-like) behaviours while random (or random-like) motions happen to follow strict deterministic laws. The sense of order in chaos can be usually observed in the space of dimensions where time is not a dimension, while the sense of randomness is usually evident when time is incorporated. 10 refs., 29 figs

Particle ratios, quarks, and Chao-Yang statistics

Energy Technology Data Exchange (ETDEWEB)

Chew, C K; Low, G B; Lo, S Y [Nanyang Univ. (Singapore). Dept. of Physics; Phua, K K [Argonne National Lab., IL (USA)

1980-01-01

By introducing quarks into Chao-Yang statistics for 'violent' collisions, particle ratios are obtained which are consistent with the Chao-Yang results. The present method can also be extended to baryon-meson and baryon-antibaryon ratios.

Devil's staircase and the absence of chaos in the dc- and ac-driven overdamped Frenkel-Kontorova model

Science.gov (United States)

Sokolović, I.; Mali, P.; Odavić, J.; Radošević, S.; Medvedeva, S. Yu.; Botha, A. E.; Shukrinov, Yu. M.; Tekić, J.

2017-08-01

The devil's staircase structure arising from the complete mode locking of an entirely nonchaotic system, the overdamped dc+ac driven Frenkel-Kontorova model with deformable substrate potential, was observed. Even though no chaos was found, a hierarchical ordering of the Shapiro steps was made possible through the use of a previously introduced continued fraction formula. The absence of chaos, deduced here from Lyapunov exponent analyses, can be attributed to the overdamped character and the Middleton no-passing rule. A comparative analysis of a one-dimensional stack of Josephson junctions confirmed the disappearance of chaos with increasing dissipation. Other common dynamic features were also identified through this comparison. A detailed analysis of the amplitude dependence of the Shapiro steps revealed that only for the case of a purely sinusoidal substrate potential did the relative sizes of the steps follow a Farey sequence. For nonsinusoidal (deformed) potentials, the symmetry of the Stern-Brocot tree, depicting all members of particular Farey sequence, was seen to be increasingly broken, with certain steps being more prominent and their relative sizes not following the Farey rule.

Geometric chaos indicators and computations of the spherical hypertube manifolds of the spatial circular restricted three-body problem

Science.gov (United States)

Guzzo, Massimiliano; Lega, Elena

2018-06-01

The circular restricted three-body problem has five relative equilibria L1 ,L2, . . . ,L5. The invariant stable-unstable manifolds of the center manifolds originating at the partially hyperbolic equilibria L1 ,L2 have been identified as the separatrices for the motions which transit between the regions of the phase-space which are internal or external with respect to the two massive bodies. While the stable and unstable manifolds of the planar problem have been extensively studied both theoretically and numerically, the spatial case has not been as deeply investigated. This paper is devoted to the global computation of these manifolds in the spatial case with a suitable finite time chaos indicator. The definition of the chaos indicator is not trivial, since the mandatory use of the regularizing Kustaanheimo-Stiefel variables may introduce discontinuities in the finite time chaos indicators. From the study of such discontinuities, we define geometric chaos indicators which are globally defined and smooth, and whose ridges sharply approximate the stable and unstable manifolds of the center manifolds of L1 ,L2. We illustrate the method for the Sun-Jupiter mass ratio, and represent the topology of the asymptotic manifolds using sections and three-dimensional representations.

Approximate motion integrals and the quantum chaos problem

International Nuclear Information System (INIS)

Bunakov, V.E.; Ivanov, I.B.

2001-01-01

One discusses the problem of occurrence and seek for the motion integrals in the stationary quantum mechanics and its relation to the quantum chaos. One studies decomposition of quantum numbers and derives the criterion of chaos. To seek the motion integrals one applies the convergence method. One derived the approximate integrals in the Hennone-Hales problem. One discusses the problem of compatibility of chaos and integrability [ru

Chaos-based wireless communication resisting multipath effects

Science.gov (United States)

Yao, Jun-Liang; Li, Chen; Ren, Hai-Peng; Grebogi, Celso

2017-09-01

In additive white Gaussian noise channel, chaos has been shown to be the optimal coherent communication waveform in the sense of using a very simple matched filter to maximize the signal-to-noise ratio. Recently, Lyapunov exponent spectrum of the chaotic signals after being transmitted through a wireless channel has been shown to be unaltered, paving the way for wireless communication using chaos. In wireless communication systems, inter-symbol interference caused by multipath propagation is one of the main obstacles to achieve high bit transmission rate and low bit-error rate (BER). How to resist the multipath effect is a fundamental problem in a chaos-based wireless communication system (CWCS). In this paper, a CWCS is built to transmit chaotic signals generated by a hybrid dynamical system and then to filter the received signals by using the corresponding matched filter to decrease the noise effect and to detect the binary information. We find that the multipath effect can be effectively resisted by regrouping the return map of the received signal and by setting the corresponding threshold based on the available information. We show that the optimal threshold is a function of the channel parameters and of the information symbols. Practically, the channel parameters are time-variant, and the future information symbols are unavailable. In this case, a suboptimal threshold is proposed, and the BER using the suboptimal threshold is derived analytically. Simulation results show that the CWCS achieves a remarkable competitive performance even under inaccurate channel parameters.

Spatial chaos of trapped Bose-Einstein condensate in one-dimensional weak optical lattice potential

International Nuclear Information System (INIS)

Chong Guishu; Hai Wenhua; Xie Qiongtao

2004-01-01

The spatially chaotic attractor in an elongated cloud of Bose-Einstein condensed atoms perturbed by a weak optical lattice potential is studied. The analytical insolvability and numerical incomputability of the atomic number density are revealed by a perturbed solution that illustrates the unpredictability of the deterministic chaos. Although this could lead the nonphysical explosion and unboundedness to the numerical solution, the theoretical analysis offers a criterion to avoid them. Moreover, the velocity field is investigated that exhibits the superfluid property of the chaotic system

Replication of chaos in neural networks, economics and physics

CERN Document Server

Akhmet, Marat

2016-01-01

This book presents detailed descriptions of chaos for continuous-time systems. It is the first-ever book to consider chaos as an input for differential and hybrid equations. Chaotic sets and chaotic functions are used as inputs for systems with attractors: equilibrium points, cycles and tori. The findings strongly suggest that chaos theory can proceed from the theory of differential equations to a higher level than previously thought. The approach selected is conducive to the in-depth analysis of different types of chaos. The appearance of deterministic chaos in neural networks, economics and mechanical systems is discussed theoretically and supported by simulations. As such, the book offers a valuable resource for mathematicians, physicists, engineers and economists studying nonlinear chaotic dynamics.

Nuclear physics and ideas of quantum chaos

International Nuclear Information System (INIS)

Zelevinsky, V.G.

2002-01-01

The field nowadays called 'many-body quantum chaos' was started in 1939 with the article by I.I. Gurevich studying the regularities of nuclear spectra. The field has been extensively developed recently, both mathematically and in application to mesoscopic systems and quantum fields. We argue that nuclear physics and the theory of quantum chaos are mutually beneficial. Many ideas of quantum chaos grew up from the factual material of nuclear physics; this enrichment still continues to take place. On the other hand, many phenomena in nuclear structure and reactions, as well as the general problem of statistical physics of finite strongly interacting systems, can be understood much deeper with the help of ideas and methods borrowed from the field of quantum chaos. A brief review of the selected topics related to the recent development is presented

Quantum confinement effects in low-dimensional systems

Indian Academy of Sciences (India)

2015-06-03

Jun 3, 2015 ... Quantum confinement effects in low-dimensional systems. Figure 5. (a) Various cuts of the three-dimensional data showing energy vs. momen- tum dispersion relations for Ag film of 17 ML thickness on Ge(111). (b) Photo- emission intensity maps along ¯M– ¯ – ¯K direction. (c) Substrate bands replotted ...

Chaos based encryption system for encrypting electroencephalogram signals.

Science.gov (United States)

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

2014-05-01

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.

Chaos from simple models to complex systems

CERN Document Server

Cencini, Massimo; Vulpiani, Angelo

2010-01-01

Chaos: from simple models to complex systems aims to guide science and engineering students through chaos and nonlinear dynamics from classical examples to the most recent fields of research. The first part, intended for undergraduate and graduate students, is a gentle and self-contained introduction to the concepts and main tools for the characterization of deterministic chaotic systems, with emphasis to statistical approaches. The second part can be used as a reference by researchers as it focuses on more advanced topics including the characterization of chaos with tools of information theor

Towards CHAOS-5 - How can Swarm contribute?

DEFF Research Database (Denmark)

Finlay, Chris; Olsen, Nils; Tøffner-Clausen, Lars

2014-01-01

The launch of ESA's satellite trio Swarm in November 2013 opens an exciting new chapter in the observation and monitoring of Earth's magnetic field from space. We report preliminary results from an extension of the CHAOS series of geomagnetic field models to include both scalar and vector field...... observations from the three Swarm satellites, along with the most recent quasi-definitive ground observatory data. The fit of this new update CHAOS field model to the Swarm observations will be presented in detail providing useful insight the initial Swarm data. Enhancements of the CHAOS modelling scheme...

Controlling chaos in a pendulum equation with ultra-subharmonic resonances

International Nuclear Information System (INIS)

Yang Jianping; Jing Zhujun

2009-01-01

Analytical and numerical results concerning control of chaos in a pendulum equation with parametric and external excitations are given by using Melnikov methods. We give the necessary conditions of chaos control with ultra-subharmonic resonances (i.e. Ω/ω=p/q,q>1,p,q are prime), where homoclinic chaos or heteroclinic chaos can be inhibited. Numerical simulations show that chaotic behavior can be converted to period-nq (n element of Z + ) orbits by adjusting amplitude and phase-difference of parametric excitation, and the distribution of maximum Lyapunov exponents in parameter-plane (Ψ,β) gives the regions in which chaos can be controlled.

Ray and wave chaos in underwater acoustic waveguides

International Nuclear Information System (INIS)

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

2012-01-01

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

Doubly excited helium. From strong correlation to chaos

International Nuclear Information System (INIS)

Jiang, Yuhai

2006-03-01

In the present dissertation, the double excitation states of helium including the autoionization decay of these states were studied experimentally and theoretically in a broad energy region, which includes the transition from strong correlation below the low single ionization thresholds (SIT) to the region of quantum chaos at energies very close to the double-ionization threshold. Two kind of experiments were performed, namely total-ion-yield measurements with the aim to observe total cross sections (TCS) and electron time-of-flight (TOF) measurements to obtain partial cross sections (PCS) as well as angular distribution parameters (ADP). Both types of measurements were performed at the third generation synchrotron radiation facility BESSY II in Berlin. The TCSs were recorded up to the SIT I 15 , and they were found to be in in excellent agreement with state-of-the-art complex-rotation calculations performed recently by D. Delande. These experimental and theoretical data on the TCSs were analyzed in order to study quantum chaos in doubly excited helium, and interesting signatures of quantum chaos were found. The TOF technique allowed to measure PCSs and ADPs in the energy regions from I 5 to I 9 and I 7 , respectively. These experimental data provide a critical assessment of theoretical models that can be used to explore the dynamics of strong correlation as well as quantum chaos in helium. In the theoretical part of this dissertation, the n- and l-specific PCSs and ADPs below I 4 were calculated employing the R-matrix method. The present theoretical results agree well with a recent experimental study of l-specific PCSs below I 4 by J.R. Harries et al. An analysis of patterns in the PCSs and ADPs on the basis of the present experimental and theoretical l-specific data allowed to improve the present understanding of autoionization decay dynamics in this two-electron atom. (orig.)

Chaos desynchronization in strongly coupled systems

International Nuclear Information System (INIS)

Wu Ye; Liu Weiqing; Xiao, Jinghua; Zhan Meng

2007-01-01

The dynamics of chaos desynchronization in strongly coupled oscillator systems is studied. We find a new bifurcation from synchronous chaotic state, chaotic short wave bifurcation, i.e. a chaotic desynchronization attractor is new born in the systems due to chaos desynchronization. In comparison with the usual periodic short wave bifurcation, very rich but distinct phenomena are observed

Galloping instability to chaos of cables

CERN Document Server

Luo, Albert C J

2017-01-01

This book provides students and researchers with a systematic solution for fluid-induced structural vibrations, galloping instability and the chaos of cables. They will also gain a better understanding of stable and unstable periodic motions and chaos in fluid-induced structural vibrations. Further, the results presented here will help engineers effectively design and analyze fluid-induced vibrations.

Control of chaos in a three-well duffing system

International Nuclear Information System (INIS)

Yang Jianping; Jing Zhujun

2009-01-01

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 Chacon et al. [Chacon R. General results on chaos suppression for biharmonically driven dissipative systems. Phys Lett A 1999;257:293-300, Chacon R, Palmero F, Balibrea F. Taming chaos in a driven Josephson Junction. Int J Bifurc Chaos 2001;11(7):1897-909, Chacon R. Role of ultrasubharmonic resonances in taming chaos by weak harmonic perturbations. Europhys Lett 2001;54(2):148C153]. We theoretically give the parameter-space region and intervals of initial phase difference for primary and subharmonic resonance and the necessary condition for the superharmonic and supersubharmonic resonance, where homoclinic chaos or heteroclinic chaos can be suppressed. Numerical simulations show the consistency and difference with theoretical analysis and the chaotic behavior can be converted to periodic orbits by adjusting amplitude and phase-difference of inhibiting excitation. Moreover, we consider the influence of parametric frequency on maximum Lyapunov exponent (LE) for different phase-differences, and give the distribution of maximum Lyapunov exponents in parameter-plane, which indicates the regions of non-chaotic states (non-positive LE) and chaotic states (positive LE).

CHAOS: An SDN-Based Moving Target Defense System

Directory of Open Access Journals (Sweden)

Yuan Shi

2017-01-01

Full Text Available Moving target defense (MTD has provided a dynamic and proactive network defense to reduce or move the attack surface that is available for exploitation. However, traditional network is difficult to realize dynamic and active security defense effectively and comprehensively. Software-defined networking (SDN points out a brand-new path for building dynamic and proactive defense system. In this paper, we propose CHAOS, an SDN-based MTD system. Utilizing the programmability and flexibility of SDN, CHAOS obfuscates the attack surface including host mutation obfuscation, ports obfuscation, and obfuscation based on decoy servers, thereby enhancing the unpredictability of the networking environment. We propose the Chaos Tower Obfuscation (CTO method, which uses the Chaos Tower Structure (CTS to depict the hierarchy of all the hosts in an intranet and define expected connection and unexpected connection. Moreover, we develop fast CTO algorithms to achieve a different degree of obfuscation for the hosts in each layer. We design and implement CHAOS as an application of SDN controller. Our approach makes it very easy to realize moving target defense in networks. Our experimental results show that a network protected by CHAOS is capable of decreasing the percentage of information disclosure effectively to guarantee the normal flow of traffic.

Magnetoresistance oscillations of two-dimensional electron systems in lateral superlattices with structured unit cells

Science.gov (United States)

Gerhardts, Rolf R.

2015-11-01

Model calculations for commensurability oscillations of the low-field magnetoresistance of two-dimensional electron systems (2DES) in lateral superlattices, consisting of unit cells with an internal structure, are compared with recent experiments. The relevant harmonics of the effective modulation potential depend not only on the geometrical structure of the modulated unit cell, but also strongly on the nature of the modulation. While higher harmonics of an electrostatically generated surface modulation are exponentially damped at the position of the 2DES about 90 nm below the surface, no such damping appears for strain-induced modulation generated, e.g., by the deposition of stripes of calixarene resist on the surface before cooling down the sample.

A New Technique in saving Fingerprint with low volume by using Chaos Game and Fractal Theory

Directory of Open Access Journals (Sweden)

Maryam Ashourzadeh

2010-12-01

Full Text Available Fingerprint is one of the simplest and most reliable biometric features of human for identification. In this study by using fractal theory and by the assistance of Chaos Game a new fractal is made from fingerprint. While making the new fractal by using Chaos Game mechanism some parameters, which can be used in identification process, can be deciphered. For this purpose, a fractal is made for each fingerprint, we save 10 parameters for every fingerprint, which have necessary information for identity, as said before. So we save 10 decimal parameters with 0.02 accuracy instead of saving the picture of a fingerprint or some parts of it. Now we improve the great volume of fingerprint pictures by using this model which employs fractal for knowing the personality

Path and semimartingale properties of chaos processes

DEFF Research Database (Denmark)

Basse-O'Connor, Andreas; Graversen, Svend-Erik

2010-01-01

The present paper characterizes various properties of chaos processes which in particular include processes where all time variables admit a Wiener chaos expansion of a fixed finite order. The main focus is on the semimartingale property, p-variation and continuity. The general results obtained...

Quantum Phenomena in Low-Dimensional Systems

OpenAIRE

Geller, Michael R.

2001-01-01

A brief summary of the physics of low-dimensional quantum systems is given. The material should be accessible to advanced physics undergraduate students. References to recent review articles and books are provided when possible.

Controlling beam halo-chaos via backstepping design

International Nuclear Information System (INIS)

Gao Yuan; Kong Feng

2008-01-01

A backstepping control method is proposed for controlling beam halo-chaos in the periodic focusing channels (PFCs) of high-current ion accelerator. The analysis and numerical results show that the method, via adjusting an exterior magnetic field, is effective to control beam halo chaos with five types of initial distribution ion beams, all statistical quantities of the beam halo-chaos are largely reduced, and the uniformity of ion beam is improved. This control method has an important value of application, for the exterior magnetic field can be easily adjusted in the periodical magnetic focusing channels in experiment

Global sensitivity analysis using low-rank tensor approximations

International Nuclear Information System (INIS)

Konakli, Katerina; Sudret, Bruno

2016-01-01

In the context of global sensitivity analysis, the Sobol' indices constitute a powerful tool for assessing the relative significance of the uncertain input parameters of a model. We herein introduce a novel approach for evaluating these indices at low computational cost, by post-processing the coefficients of polynomial meta-models belonging to the class of low-rank tensor approximations. Meta-models of this class can be particularly efficient in representing responses of high-dimensional models, because the number of unknowns in their general functional form grows only linearly with the input dimension. The proposed approach is validated in example applications, where the Sobol' indices derived from the meta-model coefficients are compared to reference indices, the latter obtained by exact analytical solutions or Monte-Carlo simulation with extremely large samples. Moreover, low-rank tensor approximations are confronted to the popular polynomial chaos expansion meta-models in case studies that involve analytical rank-one functions and finite-element models pertinent to structural mechanics and heat conduction. In the examined applications, indices based on the novel approach tend to converge faster to the reference solution with increasing size of the experimental design used to build the meta-model. - Highlights: • A new method is proposed for global sensitivity analysis of high-dimensional models. • Low-rank tensor approximations (LRA) are used as a meta-modeling technique. • Analytical formulas for the Sobol' indices in terms of LRA coefficients are derived. • The accuracy and efficiency of the approach is illustrated in application examples. • LRA-based indices are compared to indices based on polynomial chaos expansions.

Chaos in the Solar System

Science.gov (United States)

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

2001-01-01

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!

Hyperbolic Chaos A Physicist’s View

CERN Document Server

Kuznetsov, Sergey P

2012-01-01

"Hyperbolic Chaos: A Physicist’s View” presents recent progress on uniformly hyperbolic attractors in dynamical systems from a physical rather than mathematical perspective (e.g. the Plykin attractor, the Smale – Williams solenoid). The structurally stable attractors manifest strong stochastic properties, but are insensitive to variation of functions and parameters in the dynamical systems. Based on these characteristics of hyperbolic chaos, this monograph shows how to find hyperbolic chaotic attractors in physical systems and how to design a physical systems that possess hyperbolic chaos.   This book is designed as a reference work for university professors and researchers in the fields of physics, mechanics, and engineering.   Dr. Sergey P. Kuznetsov is a professor at the Department of Nonlinear Processes, Saratov State University, Russia.  

An empirical study on identifying critical success factors on chaos management

Directory of Open Access Journals (Sweden)

Naser Azad

2012-08-01

Full Text Available Chaos management is one of the most necessary efforts on managing business units. Many organizations fail to cope with undesirable circumstances, which may happen without any prior notice and as a result, they may face with significant financial losses. In this paper, we present an empirical study to determine critical success factors, which could help handle any possible chaos in organizations. The proposed study of this paper is implemented for a set of travel agencies located in Tehran, Iran. Chronbach alpha is calculated as 0.821, which is well above the minimum desirable level. In addition, we have also performed factor analysis, which yields a KMO value of 0.576 with the level of significance of 0.000. The results indicate that there are six important factors including effective management strategy, internal environmental factors, creative and innovative attitudes, external environmental factors and top level management thoughts.

Chaos: Choto delat?

Science.gov (United States)

Campbell, David

1987-11-01

I provide 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.

Low-Dimensional Organic-Inorganic Halide Perovskite: Structure, Properties, and Applications.

Science.gov (United States)

Misra, Ravi K; Cohen, Bat-El; Iagher, Lior; Etgar, Lioz

2017-10-09

Three-dimensional (3 D) perovskite has attracted a lot of attention owing to its success in photovoltaic (PV) solar cells. However, one of its major crucial issues lies in its stability, which has limited its commercialization. An important property of organic-inorganic perovskite is the possibility of forming a layered material by using long organic cations that do not fit into the octahedral cage. These long organic cations act as a "barrier" that "caps" 3 D perovskite to form the layered material. Controlling the number of perovskite layers could provide a confined structure with chemical and physical properties that are different from those of 3 D perovskite. This opens up a whole new batch of interesting materials with huge potential for optoelectronic applications. This Minireview presents the synthesis, properties, and structural orientation of low-dimensional perovskite. It also discusses the progress of low-dimensional perovskite in PV solar cells, which, to date, have performance comparable to that of 3 D perovskite but with enhanced stability. Finally, the use of low-dimensional perovskite in light-emitting diodes (LEDs) and photodetectors is discussed. The low-dimensional perovskites are promising candidates for LED devices, mainly because of their high radiative recombination as a result of the confined low-dimensional quantum well. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.

Model for Shock Wave Chaos

KAUST Repository

Kasimov, Aslan R.

2013-03-08

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

From chaos to order methodologies, perspectives and applications

CERN Document Server

Chen Guan Rong

1998-01-01

Chaos control has become a fast-developing interdisciplinary research field in recent years. This book is for engineers and applied scientists who want to have a broad understanding of the emerging field of chaos control. It describes fundamental concepts, outlines representative techniques, provides case studies, and highlights recent developments, putting the reader at the forefront of current research.Important topics presented in the book include: Fundamentals of nonlinear dynamical systems, essential for understanding and developing chaos control methods.; Parametric variation and paramet

Philosophical perspectives on quantum chaos: Models and interpretations

Science.gov (United States)

Bokulich, Alisa Nicole

2001-09-01

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

Future device applications of low-dimensional carbon superlattice structures

Science.gov (United States)

Bhattacharyya, Somnath

2005-03-01

We observe superior transport properties in low-dimensional amorphous carbon (a-C) and superlattice structures fabricated by a number of different techniques. Low temperature conductivity of these materials is explained using argument based on the crossover of dimensionality of weak localization and electron-electron interactions along with a change of sign of the magneto-resistance. These trends are significantly different from many other well characterized ordered or oriented carbon structures, and, show direct evidence of high correlation length, mobility and an effect of the dimensionality in low-dimensional a-C films. We show routes to prepare bespoke features by tuning the phase relaxation time in order to make high-speed devices over large areas. The artificially grown multi-layer superlattice structures of diamond-like amorphous carbon films show high-frequency resonance and quantum conductance suggesting sufficiently high values of phase coherence length in the present disordered a-C system that could lead to fast switching multi-valued logic.

True quantum chaos? An instructive example

International Nuclear Information System (INIS)

Berry, M.V.

1992-01-01

Any chaotic classical system can be transformed into a quantum system that preserves the chaos, because the classical Liouville equation involving 2Ν phase-space variables q ,p has the form of a 'Schroedinger equation' with 'coordinates' Q=[q,p]. The feature of this quantum system that allows chaos to persist is linarity of the Hamiltonian' in the 2Ν 'momentum' operators conjugate to Q. (orig.)

Random matrices and chaos in nuclear physics: Nuclear structure

International Nuclear Information System (INIS)

Weidenmueller, H. A.; Mitchell, G. E.

2009-01-01

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

Wave of chaos in a diffusive system: Generating realistic patterns of patchiness in plankton-fish dynamics

International Nuclear Information System (INIS)

Upadhyay, Ranjit Kumar; Kumari, Nitu; Rai, Vikas

2009-01-01

We show that wave of chaos (WOC) can generate two-dimensional time-independent spatial patterns which can be a potential candidate for understanding planktonic patchiness observed in marine environments. These spatio-temporal patterns were obtained in computer simulations of a minimal model of phytoplankton-zooplankton dynamics driven by forces of diffusion. We also attempt to figure out the average lifetimes of these non-linear non-equilibrium patterns. These spatial patterns serve as a realistic model for patchiness found in aquatic systems (e.g., marine and oceanic). Additionally, spatio-temporal chaos produced by bi-directional WOCs is robust to changes in key parameters of the system; e.g., intra-specific competition among individuals of phytoplankton and the rate of fish predation. The ideas contained in the present paper may find applications in diverse fields of human endeavor.

Universality in quantum chaos and the one-parameter scaling theory.

Science.gov (United States)

García-García, Antonio M; Wang, Jiao

2008-02-22

The one-parameter scaling theory is adapted to the context of quantum chaos. We define a generalized dimensionless conductance, g, semiclassically and then study Anderson localization corrections by renormalization group techniques. This analysis permits a characterization of the universality classes associated to a metal (g-->infinity), an insulator (g-->0), and the metal-insulator transition (g-->g(c)) in quantum chaos provided that the classical phase space is not mixed. According to our results the universality class related to the metallic limit includes all the systems in which the Bohigas-Giannoni-Schmit conjecture holds but automatically excludes those in which dynamical localization effects are important. The universality class related to the metal-insulator transition is characterized by classical superdiffusion or a fractal spectrum in low dimensions (d < or = 2). Several examples are discussed in detail.

Some remarks on chaos in topological dynamics

Directory of Open Access Journals (Sweden)

Huoyung Wang

2011-10-01

Full Text Available Bau-Sen Du introduced a notion of chaos which is stronger than Li-Yorke sensitivity. A TDS (X, f is called chaotic if there is a positive e such that for any x and any nonempty open set V of X there is a point y in V such that the pair (x, y is proximal but not e-asymptotic. In this article, we show that a TDS (T, f is transitive but not mixing if and only if (T, f is Li-Yorke sensitive but not chaotic, where T is a tree. Moreover, we compare such chaos with other notions of chaos.

Quantum chaos induced by nonadiabatic coupling in wave-packet dynamics

International Nuclear Information System (INIS)

Higuchi, Hisashi; Takatsuka, Kazuo

2002-01-01

The effect of nonadiabatic coupling due to breakdown of the Born-Oppenheimer approximation on chaos is investigated. A couple of measures (indicators) that detect the extent of chaos in wave-packet dynamics on coupled potential functions are devised. Using them, we show that chaos is indeed induced by a nonadiabatic coupling in individual time-dependent wave-packet dynamics. This chaos is genuinely of quantum nature, since it arises from bifurcation and merging of a wave packet at the quasicrossing region of two coupled potential functions

Chaos control using sliding-mode theory

International Nuclear Information System (INIS)

Nazzal, Jamal M.; Natsheh, Ammar N.

2007-01-01

Chaos control means to design a controller that is able to mitigating or eliminating the chaos behavior of nonlinear systems that experiencing such phenomenon. In this paper, a nonlinear Sliding-Mode Controller (SMC) is presented. Two nonlinear chaotic systems are chosen to be our case study in this paper, the well known Chua's circuit and Lorenz system. The study shows the effectiveness of the designed nonlinear Sliding-Mode Controller

Polynomiography and Chaos

Science.gov (United States)

Kalantari, Bahman

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

Chaos in blood flow control in genetic and renovascular hypertensive rats

DEFF Research Database (Denmark)

Yip, K P; Holstein-Rathlou, N H; Marsh, D J

1991-01-01

Hydrostatic pressure and flow in renal proximal tubules oscillate at 30-40 mHz in normotensive rats anesthetized with halothane. The oscillations originate in tubuloglomerular feedback, a mechanism that provides local blood flow regulation. Instead of oscillations, spontaneously hypertensive rats...... (SHR) have aperiodic tubular pressure fluctuations; the pattern is suggestive of deterministic chaos. Normal rats made hypertensive by clipping one renal artery had similar aperiodic tubular pressure fluctuations in the unclipped kidney, and the fraction of rats with irregular fluctuations increased...... with time after the application of the renal artery clip. Statistical measures of deterministic chaos were applied to tubular pressure data. The correlation dimension, a measure of the dimension of the phase space attractor generating the time series, indicated the presence of a low-dimension strange...

Dielectric spectroscopy studies of low-disorder and low-dimensional materials

OpenAIRE

Tripathi, Pragya

2016-01-01

In this thesis we employ dielectric spectroscopy (in different implementations) to study the dielectric properties of different materials ranging from completely disordered supercooled liquids to low-disorder solids with only ratcheting reorientational motions, to low-dimensional systems such as thin films or needle-like crystals. The probed material properties include the electrical conductivity, the space-charge processes due to sample heterogeneities, molecular dynamics, hydrogen-bond dyna...

Collision analysis of one kind of chaos-based hash function

International Nuclear Information System (INIS)

Xiao Di; Peng Wenbing; Liao Xiaofeng; Xiang Tao

2010-01-01

In the last decade, various chaos-based hash functions have been proposed. Nevertheless, the corresponding analyses of them lag far behind. In this Letter, we firstly take a chaos-based hash function proposed very recently in Amin, Faragallah and Abd El-Latif (2009) as a sample to analyze its computational collision problem, and then generalize the construction method of one kind of chaos-based hash function and summarize some attentions to avoid the collision problem. It is beneficial to the hash function design based on chaos in the future.

Congenital high airway obstruction syndrome (CHAOS) associated with cervical myelomeningocele.

Science.gov (United States)

Adin, Mehmet Emin

2017-10-01

Congenital high airway obstruction syndrome (CHAOS) is a rare and potentially fatal entity resulting from complete or near complete developmental airway obstruction. Although most reported cases of CHAOS are sporadic, the condition may also be associated with certain syndromes and a variety of cervical masses. Meningocele and myelomeningocele have not yet been reported in association with CHAOS. We describe the typical constellation of sonographic findings in a case of early diagnosis of CHAOS associated with cervical myelomeningocele. © 2016 Wiley Periodicals, Inc. J Clin Ultrasound 45:507-510, 2017. © 2016 Wiley Periodicals, Inc.

Chaos analysis and chaotic EMI suppression of DC-DC converters

CERN Document Server

Zhang, Bo

2014-01-01

Introduces chaos theory, its analytical methods and the means to apply chaos to the switching power supply design DC-DC converters are typical switching systems which have plenty of nonlinear behaviors, such as bifurcation and chaos. The nonlinear behaviors of DC-DC converters have been studied heavily over the past 20 years, yet researchers are still unsure of the practical application of bifurcations and chaos in switching converters. The electromagnetic interference (EMI), which resulted from the high rates of changes of voltage and current, has become a major design criterion in DC-DC co

Colloquium: Random matrices and chaos in nuclear spectra

International Nuclear Information System (INIS)

Papenbrock, T.; Weidenmueller, H. A.

2007-01-01

Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model (a mean-field theory) plus a residual interaction. The question is answered using a statistical approach (the two-body random ensemble): The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification

A qualitative numerical study of high dimensional dynamical systems

Science.gov (United States)

Albers, David James

Since Poincare, the father of modern mathematical dynamical systems, much effort has been exerted to achieve a qualitative understanding of the physical world via a qualitative understanding of the functions we use to model the physical world. In this thesis, we construct a numerical framework suitable for a qualitative, statistical study of dynamical systems using the space of artificial neural networks. We analyze the dynamics along intervals in parameter space, separating the set of neural networks into roughly four regions: the fixed point to the first bifurcation; the route to chaos; the chaotic region; and a transition region between chaos and finite-state neural networks. The study is primarily with respect to high-dimensional dynamical systems. We make the following general conclusions as the dimension of the dynamical system is increased: the probability of the first bifurcation being of type Neimark-Sacker is greater than ninety-percent; the most probable route to chaos is via a cascade of bifurcations of high-period periodic orbits, quasi-periodic orbits, and 2-tori; there exists an interval of parameter space such that hyperbolicity is violated on a countable, Lebesgue measure 0, "increasingly dense" subset; chaos is much more likely to persist with respect to parameter perturbation in the chaotic region of parameter space as the dimension is increased; moreover, as the number of positive Lyapunov exponents is increased, the likelihood that any significant portion of these positive exponents can be perturbed away decreases with increasing dimension. The maximum Kaplan-Yorke dimension and the maximum number of positive Lyapunov exponents increases linearly with dimension. The probability of a dynamical system being chaotic increases exponentially with dimension. The results with respect to the first bifurcation and the route to chaos comment on previous results of Newhouse, Ruelle, Takens, Broer, Chenciner, and Iooss. Moreover, results regarding the high-dimensional

Using sparse polynomial chaos expansions for the global sensitivity analysis of groundwater lifetime expectancy in a multi-layered hydrogeological model

International Nuclear Information System (INIS)

Deman, G.; Konakli, K.; Sudret, B.; Kerrou, J.; Perrochet, P.; Benabderrahmane, H.

2016-01-01

The study makes use of polynomial chaos expansions to compute Sobol' indices within the frame of a global sensitivity analysis of hydro-dispersive parameters in a simplified vertical cross-section of a segment of the subsurface of the Paris Basin. Applying conservative ranges, the uncertainty in 78 input variables is propagated upon the mean lifetime expectancy of water molecules departing from a specific location within a highly confining layer situated in the middle of the model domain. Lifetime expectancy is a hydrogeological performance measure pertinent to safety analysis with respect to subsurface contaminants, such as radionuclides. The sensitivity analysis indicates that the variability in the mean lifetime expectancy can be sufficiently explained by the uncertainty in the petrofacies, i.e. the sets of porosity and hydraulic conductivity, of only a few layers of the model. The obtained results provide guidance regarding the uncertainty modeling in future investigations employing detailed numerical models of the subsurface of the Paris Basin. Moreover, the study demonstrates the high efficiency of sparse polynomial chaos expansions in computing Sobol' indices for high-dimensional models. - Highlights: • Global sensitivity analysis of a 2D 15-layer groundwater flow model is conducted. • A high-dimensional random input comprising 78 parameters is considered. • The variability in the mean lifetime expectancy for the central layer is examined. • Sparse polynomial chaos expansions are used to compute Sobol' sensitivity indices. • The petrofacies of a few layers can sufficiently explain the response variance.

Quantum Bound to Chaos and the Semiclassical Limit

Science.gov (United States)

Kurchan, Jorge

2018-06-01

We discuss the quantum bound on chaos in the context of the free propagation of a particle in an arbitrarily curved surface at low temperatures. The semiclassical calculation of the Lyapunov exponent can be performed in much the same way as the corresponding one for the `Loschmidt echo'. The bound appears here as the impossibility to scatter a wave, by effect of the curvature, over characteristic lengths smaller than the deBroglie wavelength.

Hamiltonian Chaos and Fractional Dynamics

International Nuclear Information System (INIS)

Combescure, M

2005-01-01

This book provides an introduction and discussion of the main issues in the current understanding of classical Hamiltonian chaos, and of its fractional space-time structure. It also develops the most complex and open problems in this context, and provides a set of possible applications of these notions to some fundamental questions of dynamics: complexity and entropy of systems, foundation of classical statistical physics on the basis of chaos theory, and so on. Starting with an introduction of the basic principles of the Hamiltonian theory of chaos, the book covers many topics that can be found elsewhere in the literature, but which are collected here for the readers' convenience. In the last three parts, the author develops topics which are not typically included in the standard textbooks; among them are: - the failure of the traditional description of chaotic dynamics in terms of diffusion equations; - he fractional kinematics, its foundation and renormalization group analysis; - 'pseudo-chaos', i.e. kinetics of systems with weak mixing and zero Lyapunov exponents; - directional complexity and entropy. The purpose of this book is to provide researchers and students in physics, mathematics and engineering with an overview of many aspects of chaos and fractality in Hamiltonian dynamical systems. In my opinion it achieves this aim, at least provided researchers and students (mainly those involved in mathematical physics) can complement this reading with comprehensive material from more specialized sources which are provided as references and 'further reading'. Each section contains introductory pedagogical material, often illustrated by figures coming from several numerical simulations which give the feeling of what's going on, and thus is very useful to the reader who is not very familiar with the topics presented. Some problems are included at the end of most sections to help the reader to go deeper into the subject. My one regret is that the book does not

Chaos in nuclei: Theory and experiment

Science.gov (United States)

Muñoz, L.; Molina, R. A.; Gómez, J. M. G.

2018-05-01

During the last three decades the quest for chaos in nuclei has been quite intensive, both with theoretical calculations using nuclear models and with detailed analyses of experimental data. In this paper we outline the concept and characteristics of quantum chaos in two different approaches, the random matrix theory fluctuations and the time series fluctuations. Then we discuss the theoretical and experimental evidence of chaos in nuclei. Theoretical calculations, especially shell-model calculations, have shown a strongly chaotic behavior of bound states in regions of high level density. The analysis of experimental data has shown a strongly chaotic behavior of nuclear resonances just above the one-nucleon emission threshold. For bound states, combining experimental data of a large number of nuclei, a tendency towards chaotic motion is observed in spherical nuclei, while deformed nuclei exhibit a more regular behavior associated to the collective motion. On the other hand, it had never been possible to observe chaos in the experimental bound energy levels of any single nucleus. However, the complete experimental spectrum of the first 151 states up to excitation energies of 6.20 MeV in the 208Pb nucleus have been recently identified and the analysis of its spectral fluctuations clearly shows the existence of chaotic motion.

Stochastic chaos in a Duffing oscillator and its control

International Nuclear Information System (INIS)

Wu Cunli; Lei Youming; Fang Tong

2006-01-01

Stochastic chaos discussed here means a kind of chaotic responses in a Duffing oscillator with bounded random parameters under harmonic excitations. A system with random parameters is usually called a stochastic system. The modifier 'stochastic' here implies dependent on some random parameter. As the system itself is stochastic, so is the response, even under harmonic excitations alone. In this paper stochastic chaos and its control are verified by the top Lyapunov exponent of the system. A non-feedback control strategy is adopted here by adding an adjustable noisy phase to the harmonic excitation, so that the control can be realized by adjusting the noise level. It is found that by this control strategy stochastic chaos can be tamed down to the small neighborhood of a periodic trajectory or an equilibrium state. In the analysis the stochastic Duffing oscillator is first transformed into an equivalent deterministic nonlinear system by the Gegenbauer polynomial approximation, so that the problem of controlling stochastic chaos can be reduced into the problem of controlling deterministic chaos in the equivalent system. Then the top Lyapunov exponent of the equivalent system is obtained by Wolf's method to examine the chaotic behavior of the response. Numerical simulations show that the random phase control strategy is an effective way to control stochastic chaos

Suppression of chaos at slow variables by rapidly mixing fast dynamics through linear energy-preserving coupling

Science.gov (United States)

Abramov, R. V.

2011-12-01

Chaotic multiscale dynamical systems are common in many areas of science, one of the examples being the interaction of the low-frequency dynamics in the atmosphere with the fast turbulent weather dynamics. One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger chaotic system would result in general increase of chaos at the slow variables.

Handbook of Chaos Control

CERN Document Server

Schuster, H G

2008-01-01

This long-awaited revised second edition of the standard reference on the subject has been considerably expanded to include such recent developments as novel control schemes, control of chaotic space-time patterns, control of noisy nonlinear systems, and communication with chaos, as well as promising new directions in research. The contributions from leading international scientists active in the field provide a comprehensive overview of our current level of knowledge on chaos control and its applications in physics, chemistry, biology, medicine, and engineering. In addition, they show the overlap with the traditional field of control theory in the engineering community.An interdisciplinary approach of interest to scientists and engineers working in a number of areas

Chaos Theory as a Model for Managing Issues and Crises.

Science.gov (United States)

Murphy, Priscilla

1996-01-01

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…

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

Science.gov (United States)

Willhauck, Susan

2010-01-01

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…

Chaos in the fractional order Chen system and its control

International Nuclear Information System (INIS)

Li Chunguang; Chen Guanrong

2004-01-01

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

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

Science.gov (United States)

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

2010-01-01

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

Experimental study of chaos synchronization in the Belousov-Zhabotinsky chemical system

International Nuclear Information System (INIS)

Li Yanni; Chen Lan; Cai Zunsheng; Zhao Xuezhuang

2004-01-01

Employing self-adaptive parameter regulation scheme, chaos synchronization in the Belousov-Zhabotinsky-CSTR chemical system has been studied experimentally. By optimizing the combination of regulation parameters, the trend of chaos synchronization is observed and the prediction of chaos synchronization from numerical simulation is thus verified by the experiment. In addition, the difference of sensitivity to noise with the mass coupling scheme and the self-adaptive parameter regulation scheme in chaos synchronization has also been discussed

Scaling properties of localized quantum chaos

International Nuclear Information System (INIS)

Izrailev, F.M.

1991-01-01

Statistical properties of spectra and eigenfunctions are studied for the model of quantum chaos in the presence of dynamical localization. The main attention is paid to the scaling properties of localization length and level spacing distribution in the intermediate region between Poissonian and Wigner-Dyson statistics. It is shown that main features of such localized quantum chaos are well described by the introduced ensemble of band random matrices. 28 refs.; 7 figs

Individual chaos implies collective chaos for weakly mixing discrete dynamical systems

International Nuclear Information System (INIS)

Liao Gongfu; Ma Xianfeng; Wang Lidong

2007-01-01

Let X be a metric space (X,f) a discrete dynamical system, where f:X->X is a continuous function. Let f-bar denote the natural extension of f to the space of all non-empty compact subsets of X endowed with Hausdorff metric induced by d. In this paper we investigate some dynamical properties of f and f-bar . It is proved that f is weakly mixing (mixing) if and only if f-bar is weakly mixing (mixing, respectively). From this, we deduce that weak-mixing of f implies transitivity of f-bar , further, if f is mixing or weakly mixing, then chaoticity of f (individual chaos) implies chaoticity of f-bar (collective chaos) and if X is a closed interval then f-bar is chaotic (in the sense of Devaney) if and only if f is weakly mixing

Doubly excited helium. From strong correlation to chaos

Energy Technology Data Exchange (ETDEWEB)

Jiang, Yuhai

2006-03-15

In the present dissertation, the double excitation states of helium including the autoionization decay of these states were studied experimentally and theoretically in a broad energy region, which includes the transition from strong correlation below the low single ionization thresholds (SIT) to the region of quantum chaos at energies very close to the double-ionization threshold. Two kind of experiments were performed, namely total-ion-yield measurements with the aim to observe total cross sections (TCS) and electron time-of-flight (TOF) measurements to obtain partial cross sections (PCS) as well as angular distribution parameters (ADP). Both types of measurements were performed at the third generation synchrotron radiation facility BESSY II in Berlin. The TCSs were recorded up to the SIT I{sub 15}, and they were found to be in in excellent agreement with state-of-the-art complex-rotation calculations performed recently by D. Delande. These experimental and theoretical data on the TCSs were analyzed in order to study quantum chaos in doubly excited helium, and interesting signatures of quantum chaos were found. The TOF technique allowed to measure PCSs and ADPs in the energy regions from I{sub 5} to I{sub 9} and I{sub 7}, respectively. These experimental data provide a critical assessment of theoretical models that can be used to explore the dynamics of strong correlation as well as quantum chaos in helium. In the theoretical part of this dissertation, the n- and l-specific PCSs and ADPs below I{sub 4} were calculated employing the R-matrix method. The present theoretical results agree well with a recent experimental study of l-specific PCSs below I{sub 4} by J.R. Harries et al. An analysis of patterns in the PCSs and ADPs on the basis of the present experimental and theoretical l-specific data allowed to improve the present understanding of autoionization decay dynamics in this two-electron atom. (orig.)

Calculating topological entropy for transient chaos with an application to communicating with chaos

International Nuclear Information System (INIS)

Jacobs, J.; Ott, E.; Hunt, B.R.

1998-01-01

Recent work on communicating with chaos provides a practical motivation for being able to determine numerically the topological entropy for chaotic invariant sets. In this paper we discuss numerical methods for evaluating topological entropy. To assess the accuracy and convergence of the methods, we test them in situations where the topological entropy is known independently. We also discuss the entropy of invariant chaotic saddles formed by those points in a given attractor that never visit some forbidden 'gap' region. Such gaps have been proposed as a means of providing noise immunity in schemes for communication with chaos, and we discuss the dependence of the topological entropy on the size of the gap. copyright 1998 The American Physical Society

The Chaos of Katrina

National Research Council Canada - National Science Library

Morris, Jr, Gerald W

2007-01-01

.... The study investigates whether chaos theory, part of complexity science, can extract information from Katrina contracting data to help managers make better logistics decisions during disaster relief operations...

Low-mode truncation methods in the sine-Gordon equation

International Nuclear Information System (INIS)

Xiong Chuyu.

1991-01-01

In this dissertation, the author studies the chaotic and coherent motions (i.e., low-dimensional chaotic attractor) in some near integrable partial differential equations, particularly the sine-Gordon equation and the nonlinear Schroedinger equation. In order to study the motions, he uses low mode truncation methods to reduce these partial differential equations to some truncated models (low-dimensional ordinary differential equations). By applying many methods available to low-dimensional ordinary differential equations, he can understand the low-dimensional chaotic attractor of PDE's much better. However, there are two important questions one needs to answer: (1) How many modes is good enough for the low mode truncated models to capture the dynamics uniformly? (2) Is the chaotic attractor in a low mode truncated model close to the chaotic attractor in the original PDE? And how close is? He has developed two groups of powerful methods to help to answer these two questions. They are the computation methods of continuation and local bifurcation, and local Lyapunov exponents and Lyapunov exponents. Using these methods, he concludes that the 2N-nls ODE is a good model for the sine-Gordon equation and the nonlinear Schroedinger equation provided one chooses a 'good' basis and uses 'enough' modes (where 'enough' depends on the parameters of the system but is small for the parameter studied here). Therefore, one can use 2N-nls ODE to study the chaos of PDE's in more depth

Chaos and reliability in balanced spiking networks with temporal drive.

Science.gov (United States)

Lajoie, Guillaume; Lin, Kevin K; Shea-Brown, Eric

2013-05-01

Biological information processing is often carried out by complex networks of interconnected dynamical units. A basic question about such networks is that of reliability: If the same signal is presented many times with the network in different initial states, will the system entrain to the signal in a repeatable way? Reliability is of particular interest in neuroscience, where large, complex networks of excitatory and inhibitory cells are ubiquitous. These networks are known to autonomously produce strongly chaotic dynamics-an obvious threat to reliability. Here, we show that such chaos persists in the presence of weak and strong stimuli, but that even in the presence of chaos, intermittent periods of highly reliable spiking often coexist with unreliable activity. We elucidate the local dynamical mechanisms involved in this intermittent reliability, and investigate the relationship between this phenomenon and certain time-dependent attractors arising from the dynamics. A conclusion is that chaotic dynamics do not have to be an obstacle to precise spike responses, a fact with implications for signal coding in large networks.

Design of High-Security USB Flash Drives Based on Chaos Authentication

Directory of Open Access Journals (Sweden)

Teh-Lu Liao

2018-05-01

Full Text Available This paper aims to propose a novel design of high-security USB flash drives with the chaos authentication. A chaos authentication approach with the non-linear encryption and decryption function design is newly proposed and realized based on the controller design of chaos synchronization. To complete the design of high-security USB flash drives, first, we introduce six parameters into the original Henon map to adjust and obtain richer chaotic state responses. Then a discrete sliding mode scheme is proposed to solve the synchronization problem of discrete hyperchaotic Henon maps. The proposed sliding mode controller can ensure the synchronization of the master-slave Henon maps. The selection of the switching surface and the existence of the sliding motion are also addressed. Finally, the obtained results are applied to design a new high-security USB flash drive with chaos authentication. We built discrete hyperchaotic Henon maps in the smartphone (master and microcontroller (slave, respectively. The Bluetooth module is used to communicate between the master and the slave to achieve chaos synchronization such that the same random and dynamical chaos signal can be simultaneously obtained at both the USB flash drive and smartphone, and pass the chaos authentication. When users need to access data in the flash drive, they can easily enable the encryption APP in the smartphone (master for chaos authentication. After completing the chaos synchronization and authentication, the ARM-based microcontroller allows the computer to access the data in the high-security USB flash drive.

Chaos: A Topic for Interdisciplinary Education in Physics

Science.gov (United States)

Bae, Saebyok

2009-01-01

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

Controlling chaos faster

International Nuclear Information System (INIS)

Bick, Christian; Kolodziejski, Christoph; Timme, Marc

2014-01-01

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

Fascination of chaos

International Nuclear Information System (INIS)

Loskutov, Alexander

2010-01-01

This review introduces most of the concepts used in the study of chaotic phenomena in nonlinear systems and has as its objective to summarize the current understanding of results from the theory of chaotic dynamical systems and to describe the original ideas underlying the study of deterministic chaos. The presentation relies on informal analysis, with abstract mathematical ideas visualized geometrically or by examples from physics. Hyperbolic dynamics, homoclinic trajectories and tangencies, wild hyperbolic sets, and different types of attractors which appear in dynamical systems are considered. The key aspects of ergodic theory are discussed, and the basic statistical properties of chaotic dynamical systems are described. The fundamental difference between stochastic dynamics and deterministic chaos is explained. The review concludes with an investigation of the possibility of studying complex systems on the basis of the analysis of registered signals, i.e. the generated time series. (reviews of topical problems)

Controlling chaos faster.

Science.gov (United States)

Bick, Christian; Kolodziejski, Christoph; Timme, Marc

2014-09-01

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.

Controlling chaos faster

Energy Technology Data Exchange (ETDEWEB)

Bick, Christian [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Bernstein Center for Computational Neuroscience (BCCN), 37077 Göttingen (Germany); Institute for Mathematics, Georg–August–Universität Göttingen, 37073 Göttingen (Germany); Kolodziejski, Christoph [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); III. Physical Institute—Biophysics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany); Timme, Marc [Network Dynamics, Max Planck Institute for Dynamics and Self-Organization (MPIDS), 37077 Göttingen (Germany); Institute for Nonlinear Dynamics, Georg–August–Universität Göttingen, 37077 Göttingen (Germany)

2014-09-01

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.

Deterministic chaos in the processor load

International Nuclear Information System (INIS)

Halbiniak, Zbigniew; Jozwiak, Ireneusz J.

2007-01-01

In this article we present the results of research whose purpose was to identify the phenomenon of deterministic chaos in the processor load. We analysed the time series of the processor load during efficiency tests of database software. Our research was done on a Sparc Alpha processor working on the UNIX Sun Solaris 5.7 operating system. The conducted analyses proved the presence of the deterministic chaos phenomenon in the processor load in this particular case

One-dimensional low spatial frequency LIPSS with rotating orientation on fused silica

Energy Technology Data Exchange (ETDEWEB)

Schwarz, Simon, E-mail: simon.schwarz@h-ab.de; Rung, Stefan; Hellmann, Ralf

2017-07-31

Highlights: • Generation of one-dimensional low spatial frequency LIPSS on transparent material. • Varying the angle of incidence results in a rotation of the one-dimensional LSFL. • Rotation angle of LSFL decreases with increasing the applied fluence. • Orientation of the LSFL is mirror-inverted when reversing the scanning direction. - Abstract: We report on the generation of one-dimensional low spatial frequency LIPSS on transparent material. The influence of the applied laser fluence and angle of incidence on the periodicity, orientation and quality of the one-dimensional low spatial frequency LIPSS is investigated, facilitating the generation of highly uniform LIPSS alongside a line. Most strikingly, however, we observe a previously unreported effect of a pronounced rotation of the one-dimensional low spatial frequency LIPSS for varying angle of incidence upon inclined laser irradiation.

Digital Communication Devices Based on Nonlinear Dynamics and Chaos

National Research Council Canada - National Science Library

Larson, Lawrence

2003-01-01

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

Household chaos, sociodemographic risk, coparenting, and parent-infant relations during infants' first year.

Science.gov (United States)

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

2015-04-01

Household chaos is a construct often overlooked in studies of human development, despite its theoretical links with the integrity of individual well-being, family processes, and child development. The present longitudinal study examined relations between household chaos and well-established correlates of chaos (sociodemographic risk, major life events, and personal distress) and several constructs that, to date, are theoretically linked with chaos but never before assessed as correlates (quality of coparenting and emotional availability with infants at bedtime). In addressing this aim, we introduce a new measure of household chaos (the Descriptive In-home Survey of Chaos--Observer ReporteD, or DISCORD), wholly reliant on independent observer report, which draws from household chaos theory and prior empirical work but extends the measurement of chaos to include information about families' compliance with a home visiting protocol. Household chaos was significantly associated with socioeconomic risk, negative life events, less favorable coparenting, and less emotionally available bedtime parenting, but not with personal distress. These findings emphasize the need to examine household chaos as a direct and indirect influence on child and family outcomes, as a moderator of intervention attempts to improving parenting and child development, and as a target of intervention in its own right. (c) 2015 APA, all rights reserved).

Chaos and fractals. Applications to nuclear engineering

International Nuclear Information System (INIS)

Clausse, A.; Delmastro, D.F.

1990-01-01

This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es

Chaos and order in models of black hole pairs

International Nuclear Information System (INIS)

Levin, Janna

2006-01-01

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

Navigating Through Chaos: Charge Nurses and Patient Safety.

Science.gov (United States)

Cathro, Heather

2016-04-01

The aim of this study was to explore actions and the processes charge nurses (CNs) implement to keep patients safe and generate an emerging theory to inform CN job descriptions, orientation, and training to promote patient safety in practice. Healthcare workers must provide a safe environment for patients. CNs are the frontline leaders on most hospital units and can function as gatekeepers for safe patient care. This grounded theory study utilized purposive sampling of CNs on medical-surgical units in a 400-bed metropolitan hospital. Data collection consisted of 11 interviews and 6 observations. The emerging theory was navigating through chaos: CNs balancing multiple roles, maintaining a watchful eye, and working with and leading the healthcare team to keep patients safe. CNs have knowledge of patients, staff, and complex healthcare environments, putting them in opportune positions to influence patient safety.

Chaos as an intermittently forced linear system.

Science.gov (United States)

Brunton, Steven L; Brunton, Bingni W; Proctor, Joshua L; Kaiser, Eurika; Kutz, J Nathan

2017-05-30

Understanding the interplay of order and disorder in chaos is a central challenge in modern quantitative science. Approximate linear representations of nonlinear dynamics have long been sought, driving considerable interest in Koopman theory. We present a universal, data-driven decomposition of chaos as an intermittently forced linear system. This work combines delay embedding and Koopman theory to decompose chaotic dynamics into a linear model in the leading delay coordinates with forcing by low-energy delay coordinates; this is called the Hankel alternative view of Koopman (HAVOK) analysis. This analysis is applied to the Lorenz system and real-world examples including Earth's magnetic field reversal and measles outbreaks. In each case, forcing statistics are non-Gaussian, with long tails corresponding to rare intermittent forcing that precedes switching and bursting phenomena. The forcing activity demarcates coherent phase space regions where the dynamics are approximately linear from those that are strongly nonlinear.The huge amount of data generated in fields like neuroscience or finance calls for effective strategies that mine data to reveal underlying dynamics. Here Brunton et al.develop a data-driven technique to analyze chaotic systems and predict their dynamics in terms of a forced linear model.

Crisis route to chaos in semiconductor lasers subjected to external optical feedback

Science.gov (United States)

Wishon, Michael J.; Locquet, Alexandre; Chang, C. Y.; Choi, D.; Citrin, D. S.

2018-03-01

Semiconductor lasers subjected to optical feedback have been intensively used as archetypical testbeds for high-speed (sub-ns) and high-dimensional nonlinear dynamics. By simultaneously extracting all the dynamical variables, we demonstrate that for larger current, the commonly named "quasiperiodic" route is in fact based on mixed external-cavity solutions that lock the oscillation frequency of the intensity, voltage, and separation in optical frequency through a mechanism involving successive rejections along the unstable manifold of an antimode. We show that chaos emerges from a crisis resulting from the inability to maintain locking as the unstable manifold becomes inaccessible.

Reduced Wiener Chaos representation of random fields via basis adaptation and projection

Energy Technology Data Exchange (ETDEWEB)

Tsilifis, Panagiotis, E-mail: tsilifis@usc.edu [Department of Mathematics, University of Southern California, Los Angeles, CA 90089 (United States); Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089 (United States); Ghanem, Roger G., E-mail: ghanem@usc.edu [Department of Civil Engineering, University of Southern California, Los Angeles, CA 90089 (United States)

2017-07-15

A new characterization of random fields appearing in physical models is presented that is based on their well-known Homogeneous Chaos expansions. We take advantage of the adaptation capabilities of these expansions where the core idea is to rotate the basis of the underlying Gaussian Hilbert space, in order to achieve reduced functional representations that concentrate the induced probability measure in a lower dimensional subspace. For a smooth family of rotations along the domain of interest, the uncorrelated Gaussian inputs are transformed into a Gaussian process, thus introducing a mesoscale that captures intermediate characteristics of the quantity of interest.

Inelastic light scattering by low-lying excitations of electrons in low-dimensional semiconductors

Energy Technology Data Exchange (ETDEWEB)

Pellegrini, V. [NEST CNR-INFM and Scuola Normale Superiore, Pisa (Italy); Pinczuk, A. [Department of Physics, Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027 (United States); Bell Laboratories, Lucent Technologies, Murray Hill, New Jersey (United States)

2006-11-15

The low-dimensional electron systems that reside in artificial semiconductor heterostructures of great perfection are a contemporary materials base for explorations of collective phenomena. Studies of low-lying elementary excitations by inelastic light scattering offer insights on properties such energetics, interactions and spin magnetization. We review here recent light scattering results obtained from two-dimensional (2D) quantum fluids in semiconductor heterostructures under extreme conditions of low temperature and large magnetic field, where the quantum Hall phases are archetypes of novel behaviors. We also consider recent light scattering experiments that have probed the excitation spectra of few-electron states in semiconductor quantum dots. (copyright 2006 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

Chaotic operation and chaos control of travelling wave ultrasonic motor.

Science.gov (United States)

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

2013-08-01

The travelling wave ultrasonic motor, which is a nonlinear dynamic system, has complex chaotic phenomenon with some certain choices of system parameters and external inputs, and its chaotic characteristics have not been studied until now. In this paper, the preliminary study of the chaos phenomenon in ultrasonic motor driving system has been done. The experiment of speed closed-loop control is designed to obtain several groups of time sampling data sequence of the amplitude of driving voltage, and phase-space reconstruction is used to analyze the chaos characteristics of these time sequences. The largest Lyapunov index is calculated and the result is positive, which shows that the travelling wave ultrasonic motor has chaotic characteristics in a certain working condition Then, the nonlinear characteristics of travelling wave ultrasonic motor are analyzed which includes Lyapunov exponent map, the bifurcation diagram and the locus of voltage relative to speed based on the nonlinear chaos model of a travelling wave ultrasonic motor. After that, two kinds of adaptive delay feedback controllers are designed in this paper to control and suppress chaos in USM speed control system. Simulation results show that the method can control unstable periodic orbits, suppress chaos in USM control system. Proportion-delayed feedback controller was designed following and arithmetic of fuzzy logic was used to adaptively adjust the delay time online. Simulation results show that this method could fast and effectively change the chaos movement into periodic or fixed-point movement and make the system enter into stable state from chaos state. Finally the chaos behavior was controlled. Copyright © 2013 Elsevier B.V. All rights reserved.

User-Driven Chaos

DEFF Research Database (Denmark)

Lykke, Marianne; Lund, Haakon; Skov, Mette

2016-01-01

CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500,000 broadcasts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings...

Fabrication, Characterization, Properties, and Applications of Low-Dimensional BiFeO3 Nanostructures

Directory of Open Access Journals (Sweden)

Heng Wu

2014-01-01

Full Text Available Low-dimensional BiFeO3 nanostructures (e.g., nanocrystals, nanowires, nanotubes, and nanoislands have received considerable attention due to their novel size-dependent properties and outstanding multiferroic properties at room temperature. In recent years, much progress has been made both in fabrications and (microstructural, electrical, and magnetic in characterizations of BiFeO3 low-dimensional nanostructures. An overview of the state of art in BiFeO3 low-dimensional nanostructures is presented. First, we review the fabrications of high-quality BiFeO3 low-dimensional nanostructures via a variety of techniques, and then the structural characterizations and physical properties of the BiFeO3 low-dimensional nanostructures are summarized. Their potential applications in the next-generation magnetoelectric random access memories and photovoltaic devices are also discussed. Finally, we conclude this review by providing our perspectives to the future researches of BiFeO3 low-dimensional nanostructures and some key problems are also outlined.

Does chaos theory have major implications for philosophy of medicine?

Science.gov (United States)

Holm, S

2002-12-01

In the literature it is sometimes claimed that chaos theory, non-linear dynamics, and the theory of fractals have major implications for philosophy of medicine, especially for our analysis of the concept of disease and the concept of causation. This paper gives a brief introduction to the concepts underlying chaos theory and non-linear dynamics. It is then shown that chaos theory has only very minimal implications for the analysis of the concept of disease and the concept of causation, mainly because the mathematics of chaotic processes entail that these processes are fully deterministic. The practical unpredictability of chaotic processes, caused by their extreme sensitivity to initial conditions, may raise practical problems in diagnosis, prognosis, and treatment, but it raises no major theoretical problems. The relation between chaos theory and the problem of free will is discussed, and it is shown that chaos theory may remove the problem of predictability of decisions, but does not solve the problem of free will. Chaos theory may thus be very important for our understanding of physiological processes, and specific disease entities, without having any major implications for philosophy of medicine.

Quantum manifestations of chaos

International Nuclear Information System (INIS)

Borondo, F.; Benito, R.M.

1998-01-01

The correspondence between classical and quantum mechanics is considered both in the regular and chaotic regimes, and the main results regarding the quantum manifestations of chaos are reviewed. (Author) 16 refs

Nonlinear dynamics and chaos in a fractional-order financial system

International Nuclear Information System (INIS)

Chen Weiching

2008-01-01

This study examines the two most attractive characteristics, memory and chaos, in simulations of financial systems. A fractional-order financial system is proposed in this study. It is a generalization of a dynamic financial model recently reported in the literature. The fractional-order financial system displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions. It has been found that chaos exists in fractional-order financial systems with orders less than 3. In this study, the lowest order at which this system yielded chaos was 2.35. Period doubling and intermittency routes to chaos in the fractional-order financial system were found

Chaos synchronization of a new chaotic system via nonlinear control

International Nuclear Information System (INIS)

Zhang Qunjiao; Lu Junan

2008-01-01

This paper investigates chaos synchronization of a new chaotic system [Lue J, Chen G, Cheng D. A new chaotic system and beyond: the generalized Lorenz-like system. Int J Bifurcat Chaos 2004;14:1507-37]. Two kinds of novel nonlinear controllers are designed based on the Lyapunov stability theory. It can be viewed as an improvement to the existing results of reference [Park JH. Chaos synchronization of a chaotic system via nonlinear control. Chaos, Solitons and Fractals 2005;25:579-84] because we use less controllers but realize a global and exponential asymptotical synchronization. Numerical simulations are provided to show the effectiveness and advantage of this method

Chaos in charged AdS black hole extended phase space

Science.gov (United States)

Chabab, M.; El Moumni, H.; Iraoui, S.; Masmar, K.; Zhizeh, S.

2018-06-01

We present an analytical study of chaos in a charged black hole in the extended phase space in the context of the Poincare-Melnikov theory. Along with some background on dynamical systems, we compute the relevant Melnikov function and find its zeros. Then we analyse these zeros either to identify the temporal chaos in the spinodal region, or to observe spatial chaos in the small/large black hole equilibrium configuration. As a byproduct, we derive a constraint on the Black hole' charge required to produce chaotic behaviour. To the best of our knowledge, this is the first endeavour to understand the correlation between chaos and phase picture in black holes.

The chaos and order in nuclear molecular dynamics; Chaos i porzadek w jadrowej dynamice molekularnej

Energy Technology Data Exchange (ETDEWEB)

Srokowski, T. [Institute of Nuclear Physics, Cracow (Poland)

1995-12-31

The subject of the presented report is role of chaos in scattering processes in the frame of molecular dynamics. In this model, it is assumed that scattering particles (nuclei) consist of not-interacted components as alpha particles or {sup 12}C, {sup 16}O and {sup 20}Ne clusters. The results show such effects as dynamical in stabilities and fractal structure as well as compound nuclei decay and heavy-ion fusion. The goal of the report is to make the reader more familiar with the chaos model and its application to nuclear phenomena. 157 refs, 40 figs.

Chaos control applied to heart rhythm dynamics

Energy Technology Data Exchange (ETDEWEB)

Borem Ferreira, Bianca, E-mail: biaborem@gmail.com [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil); Souza de Paula, Aline, E-mail: alinedepaula@unb.br [Universidade de Brasi' lia, Department of Mechanical Engineering, 70.910.900 Brasilia, DF (Brazil); Amorim Savi, Marcelo, E-mail: savi@mecanica.ufrj.br [Universidade Federal do Rio de Janeiro, COPPE, Department of Mechanical Engineering, P.O. Box 68.503, 21.941.972 Rio de Janeiro, RJ (Brazil)

2011-08-15

Highlights: > A natural cardiac pacemaker is modeled by a modified Van der Pol oscillator. > Responses related to normal and chaotic, pathological functioning of the heart are investigated. > Chaos control methods are applied to avoid pathological behaviors of heart dynamics. > Different approaches are treated: stabilization of unstable periodic orbits and chaos suppression. - Abstract: The dynamics of cardiovascular rhythms have been widely studied due to the key aspects of the heart in the physiology of living beings. Cardiac rhythms can be either periodic or chaotic, being respectively related to normal and pathological physiological functioning. In this regard, chaos control methods may be useful to promote the stabilization of unstable periodic orbits using small perturbations. In this article, the extended time-delayed feedback control method is applied to a natural cardiac pacemaker described by a mathematical model. The model consists of a modified Van der Pol equation that reproduces the behavior of this pacemaker. Results show the ability of the chaos control strategy to control the system response performing either the stabilization of unstable periodic orbits or the suppression of chaotic response, avoiding behaviors associated with critical cardiac pathologies.

Low-dimensional chaotic attractors in drift wave turbulence

International Nuclear Information System (INIS)

Persson, M.; Nordman, H.

1991-01-01

Simulation results of toroidal η i -mode turbulence are analyzed using mathematical tools of nonlinear dynamics. Low-dimensional chaotic attractors are found in the strongly nonlinear regime while in the weakly interacting regime the dynamics is high dimensional. In both regimes, the solutions are found to display sensitive dependence on initial conditions, characterized by a positive largest Liapunov exponent. (au)

Chaos and Christianity: A Response to Butz and a Biblical Alternative.

Science.gov (United States)

Watts, Richard E.; Trusty, Jerry

1997-01-01

M.R. Butz's position regarding chaos theory and Christianity is reviewed. The compatibility of biblical theology and the sciences is discussed. Parallels between chaos theory and the philosophical perspective of Soren Kierkegaard are explored. A biblical model is offered for counselors in assisting Christian clients in embracing chaos. (Author/EMK)

Metadata in CHAOS

DEFF Research Database (Denmark)

Lykke, Marianne; Skov, Mette; Lund, Haakon

CHAOS (Cultural Heritage Archive Open System) provides streaming access to more than 500.000 broad-casts by the Danish Broadcast Corporation from 1931 and onwards. The archive is part of the LARM project with the purpose of enabling researchers to search, annotate, and interact with recordings...

Quantum Fluctuations of Low Dimensional Bose-Einstein ...

African Journals Online (AJOL)

Tadesse

that low dimensional quantum gases exhibit not only highly fascinating .... 2009; Marquardt and Girvin, 2009; Law, 1995; Vitali et al., 2007). ... ideal playground to test correlations between light and mesoscopic objects, to understand the.

Effect of smoothing on robust chaos.

Science.gov (United States)

Deshpande, Amogh; Chen, Qingfei; Wang, Yan; Lai, Ying-Cheng; Do, Younghae

2010-08-01

In piecewise-smooth dynamical systems, situations can arise where the asymptotic attractors of the system in an open parameter interval are all chaotic (e.g., no periodic windows). This is the phenomenon of robust chaos. Previous works have established that robust chaos can occur through the mechanism of border-collision bifurcation, where border is the phase-space region where discontinuities in the derivatives of the dynamical equations occur. We investigate the effect of smoothing on robust chaos and find that periodic windows can arise when a small amount of smoothness is present. We introduce a parameter of smoothing and find that the measure of the periodic windows in the parameter space scales linearly with the parameter, regardless of the details of the smoothing function. Numerical support and a heuristic theory are provided to establish the scaling relation. Experimental evidence of periodic windows in a supposedly piecewise linear dynamical system, which has been implemented as an electronic circuit, is also provided.

Chaos Concepts, Control and Constructive Use

CERN Document Server

Bolotin, Yurii; Yanovsky, Vladimir

2009-01-01

The study of chaotic behaviour in nonlinear, dynamical systems is now a well established research domain with ramifications into all fields of sciences, spanning a vast range of applications, from celestial mechanics, via climate change, to the functioning of brownian motors in cells. A more recent discovery is that chaos can be controlled and, under appropriate conditions, can actually be constructive in the sense of becoming a control parameter itself for the system under investigation, stochastic resonance being a prime example. The present work is putting emphasis on the latter aspects, and after recalling the paradigm changes introduced by the concept of chaos, leads the reader skillfully through the basics of chaos control by detailing relevant algorithms for both Hamiltonian and dissipative systems amongst others. The main part of the book is then devoted to the issue of synchronization in chaotic systems, an introduction to stochastic resonance and a survey of ratchet models. This short and concise pr...

Chaos-based hash function (CBHF) for cryptographic applications

International Nuclear Information System (INIS)

Amin, Mohamed; Faragallah, Osama S.; Abd El-Latif, Ahmed A.

2009-01-01

As the core of cryptography, hash is the basic technique for information security. Many of the hash functions generate the message digest through a randomizing process of the original message. Subsequently, a chaos system also generates a random behavior, but at the same time a chaos system is completely deterministic. In this paper, an algorithm for one-way hash function construction based on chaos theory is introduced. Theoretical analysis and computer simulation indicate that the algorithm can satisfy all performance requirements of hash function in an efficient and flexible manner and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.

Chaos-based hash function (CBHF) for cryptographic applications

Energy Technology Data Exchange (ETDEWEB)

Amin, Mohamed [Dept. of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511 (Egypt)], E-mail: mamin04@yahoo.com; Faragallah, Osama S. [Dept. of Computer Science and Engineering, Faculty of Electronic Engineering, Menoufia University, Menouf 32952 (Egypt)], E-mail: osam_sal@yahoo.com; Abd El-Latif, Ahmed A. [Dept. of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El-Koom 32511 (Egypt)], E-mail: ahmed_rahiem@yahoo.com

2009-10-30

As the core of cryptography, hash is the basic technique for information security. Many of the hash functions generate the message digest through a randomizing process of the original message. Subsequently, a chaos system also generates a random behavior, but at the same time a chaos system is completely deterministic. In this paper, an algorithm for one-way hash function construction based on chaos theory is introduced. Theoretical analysis and computer simulation indicate that the algorithm can satisfy all performance requirements of hash function in an efficient and flexible manner and secure against birthday attacks or meet-in-the-middle attacks, which is good choice for data integrity or authentication.

Chaos and the (un)predictability of evolution in a changing environment.

Science.gov (United States)

Rego-Costa, Artur; Débarre, Florence; Chevin, Luis-Miguel

2018-02-01

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency-dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco-evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability. © 2017 The Author(s). Evolution © 2017 The Society for the Study of Evolution.

Chaos-induced resonant effects and its control

International Nuclear Information System (INIS)

Zambrano, Samuel; Casado, Jose M.; Sanjuan, Miguel A.F.

2007-01-01

This Letter shows that a suitable chaotic signal can induce resonant effects analogous to those observed in presence of noise in a bistable system under periodic forcing. By constructing groups of chaotic and random perturbations with similar one-time statistics we show that in some cases chaos and noise induce indistinguishable resonant effects. This reinforces the conjecture by which in some situations where noise is supposed to play a key role maybe chaos is the key ingredient. Here we also show that the presence of a chaotic signal as the perturbation leading to a resonance opens new control perspectives based on our ability to stabilize chaos in different periodic orbits. A discussion of the possible implications of these facts is also presented at the end of the Letter

Chaos, complexity, and random matrices

Science.gov (United States)

Cotler, Jordan; Hunter-Jones, Nicholas; Liu, Junyu; Yoshida, Beni

2017-11-01

Chaos and complexity entail an entropic and computational obstruction to describing a system, and thus are intrinsically difficult to characterize. In this paper, we consider time evolution by Gaussian Unitary Ensemble (GUE) Hamiltonians and analytically compute out-of-time-ordered correlation functions (OTOCs) and frame potentials to quantify scrambling, Haar-randomness, and circuit complexity. While our random matrix analysis gives a qualitatively correct prediction of the late-time behavior of chaotic systems, we find unphysical behavior at early times including an O(1) scrambling time and the apparent breakdown of spatial and temporal locality. The salient feature of GUE Hamiltonians which gives us computational traction is the Haar-invariance of the ensemble, meaning that the ensemble-averaged dynamics look the same in any basis. Motivated by this property of the GUE, we introduce k-invariance as a precise definition of what it means for the dynamics of a quantum system to be described by random matrix theory. We envision that the dynamical onset of approximate k-invariance will be a useful tool for capturing the transition from early-time chaos, as seen by OTOCs, to late-time chaos, as seen by random matrix theory.

Scientific data interpolation with low dimensional manifold model

Science.gov (United States)

Zhu, Wei; Wang, Bao; Barnard, Richard; Hauck, Cory D.; Jenko, Frank; Osher, Stanley

2018-01-01

We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

Scientific data interpolation with low dimensional manifold model

International Nuclear Information System (INIS)

Zhu, Wei; Wang, Bao; Barnard, Richard C.; Hauck, Cory D.

2017-01-01

Here, we propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace–Beltrami operator in the Euler–Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings.

Modified projective synchronization with complex scaling factors of uncertain real chaos and complex chaos

International Nuclear Information System (INIS)

Zhang Fang-Fang; Liu Shu-Tang; Yu Wei-Yong

2013-01-01

To increase the variety and security of communication, we present the definitions of modified projective synchronization with complex scaling factors (CMPS) of real chaotic systems and complex chaotic systems, where complex scaling factors establish a link between real chaos and complex chaos. Considering all situations of unknown parameters and pseudo-gradient condition, we design adaptive CMPS schemes based on the speed-gradient method for the real drive chaotic system and complex response chaotic system and for the complex drive chaotic system and the real response chaotic system, respectively. The convergence factors and dynamical control strength are added to regulate the convergence speed and increase robustness. Numerical simulations verify the feasibility and effectiveness of the presented schemes. (general)

Some new surprises in chaos.

Science.gov (United States)

Bunimovich, Leonid A; Vela-Arevalo, Luz V

2015-09-01

"Chaos is found in greatest abundance wherever order is being sought.It always defeats order, because it is better organized"Terry PratchettA brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.

Extension of spatiotemporal chaos in glow discharge-semiconductor systems.

Science.gov (United States)

Akhmet, Marat; Rafatov, Ismail; Fen, Mehmet Onur

2014-12-01

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528-4535 (1996)] 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 [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).].

"I Had Seen Order and Chaos, but Had Thought They Were Different." The Challenges of the Chaos Theory for Career Development

Science.gov (United States)

Pryor, Robert; Bright, Jim

2004-01-01

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…

Applying Chaos Theory to Lesson Planning and Delivery

Science.gov (United States)

Cvetek, Slavko

2008-01-01

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

Chaos game representation of the D st index and prediction of geomagnetic storm events

International Nuclear Information System (INIS)

Yu, Z.G.; Anh, V.V.; Wanliss, J.A.; Watson, S.M.

2007-01-01

This paper proposes a two-dimensional chaos game representation (CGR) for the D st index. The CGR provides an effective method to characterize the multifractality of the D st time series. The probability measure of this representation is then modeled as a recurrent iterated function system in fractal theory, which leads to an algorithm for prediction of a storm event. We present an analysis and modeling of the D st time series over the period 1963-2003. The numerical results obtained indicate that the method is useful in predicting storm events one day ahead

The Chaos Theory of Careers: A User's Guide

Science.gov (United States)

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

2005-01-01

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

Ligand combination strategy for the preparation of novel low-dimensional and open-framework metal cluster materials

Science.gov (United States)

Anokhina, Ekaterina V.

Low-dimensional and open-framework materials containing transition metals have a wide range of applications in redox catalysis, solid-state batteries, and electronic and magnetic devices. This dissertation reports on research carried out with the goal to develop a strategy for the preparation of low-dimensional and open-framework materials using octahedral metal clusters as building blocks. Our approach takes its roots from crystal engineering principles where the desired framework topologies are achieved through building block design. The key idea of this work is to induce directional bonding preferences in the cluster units using a combination of ligands with a large difference in charge density. This investigation led to the preparation and characterization of a new family of niobium oxychloride cluster compounds with original structure types exhibiting 1ow-dimensional or open-framework character. Most of these materials have framework topologies unprecedented in compounds containing octahedral clusters. Comparative analysis of their structural features indicates that the novel cluster connectivity patterns in these systems are the result of complex interplay between the effects of anisotropic ligand arrangement in the cluster unit and optimization of ligand-counterion electrostatic interactions. The important role played by these factors sets niobium oxychloride systems apart from cluster compounds with one ligand type or statistical ligand distribution where the main structure-determining factor is the total number of ligands. These results provide a blueprint for expanding the ligand combination strategy to other transition metal cluster systems and for the future rational design of cluster-based materials.

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

International Nuclear Information System (INIS)

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

2013-01-01

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

Patterns in chaos

International Nuclear Information System (INIS)

Chirikov, B.V.

1990-01-01

Classification of chaotic patterns in classical Hamiltonian systems is given as a series of levels with increasing disorder. Hamiltonian dynamics is presented, including the renormalization chaos, based upon the fairly simple resonant theory. First estimates for the critical structure and related statistical anomalies in arbitrary dimensions are discussed. 49 refs

Onset of chaos and dc current-voltage characteristics of rf-driven Josephson junctions in the low-frequency regime

International Nuclear Information System (INIS)

Chi, C.C.; Vanneste, C.

1990-01-01

A comprehensive picture of the dc current-voltage (I-V) characteristics of rf-driven Josephson junctions in the low-frequency regime is presented. The boundary of the low-frequency regime is roughly defined by the junction characteristic frequency for overdamped junctions, and by the inverse of the junction damping time for underdamped junctions. An adiabatic model valid for the low-frequency regime is used to describe the overall shapes of the I-V curves, which is in good agreement with both the numerical simulations and the experimental results. For underdamped junctions, the Shapiro steps are the prominent features on the I-V curves if the rf frequency is sufficiently below the boundary. As the rf frequency is increased towards the boundary, large negatively-going tails on top of the Shapiro steps are observed both experimentally and numerically. Numerical simulations using the resistively- and capacitively-shunted-junction model (RCSJ model) reveal that the negatively-going tail is a signature of the low-frequency boundary of the junction chaotic regime. With use of the adiabatic model and the existence of plasma oscillations for underdamped junctions, the onset of chaos and its effect on the Shapiro steps can be fully explained. The high-frequency limit of the adiabatic model and the chaotic behavior of the Josephson junctions beyond the low-frequency regime are also briefly discussed

Household Chaos and Children’s Cognitive and Socio-Emotional Development in Early Childhood: Does Childcare Play a Buffering Role?

Science.gov (United States)

Berry, Daniel; Blair, Clancy; Willoughby, Michael; Garrett-Peters, Patricia; Vernon-Feagans, Lynne; Mills-Koonce, W. Roger

2018-01-01

Evidence suggests that household chaos is associated with less optimal child outcomes. Yet, there is an increasing indication that children’s experiences in childcare may buffer them against the detrimental effects of such environments. Our study aims were to test: (1) whether children’s experiences in childcare mitigated relations between household chaos and children’s cognitive and social development, and (2) whether these (conditional) chaos effects were mediated by links between chaos and executive functioning. Using data from The Family Life Project (n = 1,235)—a population-based sample of families from low-income, rural contexts—our findings indicated that household disorganization in early childhood was predictive of worse cognitive and social outcomes at approximately age five. However, these relations were substantially attenuated for children attending greater childcare hours. Subsequent models indicated that the conditional associations between household disorganization and less optimal outcomes at age five were mediated by conditional links between disorganization and less optimal executive functioning. PMID:29720785

Detecting Chaos from Agricultural Product Price Time Series

Directory of Open Access Journals (Sweden)

Xin Su

2014-12-01

Full Text Available Analysis of the characteristics of agricultural product price volatility and trend forecasting are necessary to formulate and implement agricultural price control policies. Taking wholesale cabbage prices as an example, a multiple test methodology has been adopted to identify the nonlinearity, fractality, and chaos of the data. The approaches used include the R/S analysis, the BDS test, the power spectra, the recurrence plot, the largest Lyapunov exponent, the Kolmogorov entropy, and the correlation dimension. The results show that there is chaos in agricultural wholesale price data, which provides a good theoretical basis for selecting reasonable forecasting models as prediction techniques based on chaos theory can be applied to forecasting agricultural prices.

Chaos, strange attractors, and fractal basin boundaries

International Nuclear Information System (INIS)

Grebogi, C.

1989-01-01

Even simple mathematical models of physical systems are often observed to exhibit rather complex time evolution. Upon observation, one often has the feeling that such complex time evolutions could, for most practical purposes, be best characterized by statistical properties rather than by detailed knowledge of the exact process. In such situations, the time evolution is often labeled chaotic or turbulent. The study of chaotic dynamics has recently undergone explosive growth. Motivation for this comes partly from the fact that chaotic dynamics is being found to be of fundamental importance in many branches of science and engineering. Examples illustrating the wide-ranging applications of chaotic dynamics to scientific and engineering problems are the following: fluid dynamics, biology, ecology, meteorology, optics, electronics, mechanical engineerings, physiology, economics, chemistry, accelerator technology, thermonuclear fusion, celestial mechanics, and oceanography. The common element in all of the above topics is that they involve nonlinearity in some way. Indeed chaos is expected to be common whenever nonlinearity plays a role. Since nonlinearity is inherent in so much of science and engineering, an understanding of chaos is essential. Given the varied nature of applications where chaos is important, it is natural that researchers in a broad range of fields have become interested in and have contributed to recent developments in chaos

Chaos theory: A fascinating concept for oncologists

International Nuclear Information System (INIS)

Denis, F.; Letellier, C.

2012-01-01

The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. (authors)

Chaos synchronization of coupled hyperchaotic system

International Nuclear Information System (INIS)

Yang Lixin; Chu Yandong; Zhang Jiangang; Li Xianfeng

2009-01-01

Chaos synchronization, as an important topic, has become an active research subject in nonlinear science. Over the past two decades, chaos synchronization between nonlinear systems has been extensively studied, and many types of synchronization have been announced. This paper introduces synchronization of coupled hyperchaotic system, based on the Lapunov stability theory, asymptotic stability of the system is guaranteed by means of Lapunov function. The numerical simulation was provided in order to show the effectiveness of this method for the synchronization of the chaotic hyperchaotic Chen system and Rossler system.

Synthesis, Properties, and Applications of Low-Dimensional Carbon-Related Nanomaterials

Directory of Open Access Journals (Sweden)

Ali Mostofizadeh

2011-01-01

Full Text Available In recent years, many theoretical and experimental studies have been carried out to develop one of the most interesting aspects of the science and nanotechnology which is called carbon-related nanomaterials. The goal of this paper is to provide a review of some of the most exciting and important developments in the synthesis, properties, and applications of low-dimensional carbon nanomaterials. Carbon nanomaterials are formed in various structural features using several different processing methods. The synthesis techniques used to produce specific kinds of low-dimensional carbon nanomaterials such as zero-dimensional carbon nanomaterials (including fullerene, carbon-encapsulated metal nanoparticles, nanodiamond, and onion-like carbons, one-dimensional carbon nanomaterials (including carbon nanofibers and carbon nanotubes, and two-dimensional carbon nanomaterials (including graphene and carbon nanowalls are discussed in this paper. Subsequently, the paper deals with an overview of the properties of the mainly important products as well as some important applications and the future outlooks of these advanced nanomaterials.

Polynomial chaos functions and stochastic differential equations

International Nuclear Information System (INIS)

Williams, M.M.R.

2006-01-01

The Karhunen-Loeve procedure and the associated polynomial chaos expansion have been employed to solve a simple first order stochastic differential equation which is typical of transport problems. Because the equation has an analytical solution, it provides a useful test of the efficacy of polynomial chaos. We find that the convergence is very rapid in some cases but that the increased complexity associated with many random variables can lead to very long computational times. The work is illustrated by exact and approximate solutions for the mean, variance and the probability distribution itself. The usefulness of a white noise approximation is also assessed. Extensive numerical results are given which highlight the weaknesses and strengths of polynomial chaos. The general conclusion is that the method is promising but requires further detailed study by application to a practical problem in transport theory

Extension of spatiotemporal chaos in glow discharge-semiconductor systems

International Nuclear Information System (INIS)

Akhmet, Marat; Fen, Mehmet Onur; Rafatov, Ismail

2014-01-01

Generation of chaos in response systems is discovered numerically through specially designed unidirectional coupling of two glow discharge-semiconductor systems. By utilizing the auxiliary system approach, [H. D. I. Abarbanel, N. F. Rulkov, and M. M. Sushchik, Phys. Rev. E 53, 4528–4535 (1996)] 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 [D. D. Šijačić U. Ebert, and I. Rafatov, Phys. Rev. E 70, 056220 (2004).

Switching control of linear systems for generating chaos

International Nuclear Information System (INIS)

Liu Xinzhi; Teo, Kok-Lay; Zhang Hongtao; Chen Guanrong

2006-01-01

In this paper, a new switching method is developed, which can be applied to generating different types of chaos or chaos-like dynamics from two or more linear systems. A numerical simulation is given to illustrate the generated chaotic dynamic behavior of the systems with some variable parameters. Finally, a circuit is built to realize various chaotic dynamical behaviors

Neural chaos and schizophrenia

Czech Academy of Sciences Publication Activity Database

Bob, P.; Chládek, Jan; Šusta, M.; Glaslová, K.; Jagla, F.; Kukleta, M.

2007-01-01

Roč. 26, č. 4 (2007), s. 298-305 ISSN 0231-5882 Institutional research plan: CEZ:AV0Z20650511 Keywords : EDA * Lyapunov exponent * schizophrenia * chaos Subject RIV: FL - Psychiatry, Sexuology Impact factor: 1.286, year: 2007

Chaos control of Chen chaotic dynamical system

International Nuclear Information System (INIS)

Yassen, M.T.

2003-01-01

This paper is devoted to study the problem of controlling chaos in Chen chaotic dynamical system. Two different methods of control, feedback and nonfeedback methods are used to suppress chaos to unstable equilibria or unstable periodic orbits (UPO). The Lyapunov direct method and Routh-Hurwitz criteria are used to study the conditions of the asymptotic stability of the steady states of the controlled system. Numerical simulations are presented to show these results

Topographic variations in chaos on Europa: Implications for diapiric formation

Science.gov (United States)

Schenk, Paul M.; Pappalardo, Robert T.

2004-01-01

Disrupted terrain, or chaos, on Europa, might have formed through melting of a floating ice shell from a subsurface ocean [Cam et al., 1998; Greenberg et al., 19991, or breakup by diapirs rising from the warm lower portion of the ice shell [Head and Pappalardo, 1999; Collins et al., 20001. Each model makes specific and testable predictions for topographic expression within chaos and relative to surrounding terrains on local and regional scales. High-resolution stereo-controlled photoclinometric topography indicates that chaos topography, including the archetypal Conamara Chaos region, is uneven and commonly higher than surrounding plains by up to 250 m. Elevated and undulating topography is more consistent with diapiric uplift of deep material in a relatively thick ice shell, rather than melt-through and refreezing of regionally or globally thin ice by a subsurface ocean. Vertical and horizontal scales of topographic doming in Conamara Chaos are consistent with a total ice shell thickness >15 km. Contact between Europa's ocean and surface may most likely be indirectly via diapirism or convection.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics.

Science.gov (United States)

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-10-17

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law.

A new type of cascading synchronization for halo-chaos and its potential for communication applications

International Nuclear Information System (INIS)

Fang Jinqing; Yu Xinghuo

2004-01-01

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

Neutron scattering studies of low dimensional magnetic systems

DEFF Research Database (Denmark)

Hansen, Ursula Bengård

investigated at low temperaturesand in a longitudinal magnetic eld using neutron spectroscopy. Here we observe thehybridisation of the magnon bound states, inherent to the low dimensional nature ofCoCl2 · 2D2O.At higher temperature, signatures which can be attributed to Magnetic Bloch Oscillationsis observed...

Controlling Mackey-Glass chaos

Science.gov (United States)

Kiss, Gábor; Röst, Gergely

2017-11-01

The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

Chaos in quantum channels

Energy Technology Data Exchange (ETDEWEB)

Hosur, Pavan; Qi, Xiao-Liang [Department of Physics, Stanford University,476 Lomita Mall, Stanford, California 94305 (United States); Roberts, Daniel A. [Center for Theoretical Physics and Department of Physics, Massachusetts Institute of Technology,77 Massachusetts Ave, Cambridge, Massachusetts 02139 (United States); Yoshida, Beni [Perimeter Institute for Theoretical Physics,31 Caroline Street North, Waterloo, Ontario N2L 2Y5 (Canada); Walter Burke Institute for Theoretical Physics, California Institute of Technology,1200 E California Blvd, Pasadena CA 91125 (United States)

2016-02-01

We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.

Controlling Mackey-Glass chaos.

Science.gov (United States)

Kiss, Gábor; Röst, Gergely

2017-11-01

The Mackey-Glass equation is the representative example of delay induced chaotic behavior. Here, we propose various control mechanisms so that otherwise erratic solutions are forced to converge to the positive equilibrium or to a periodic orbit oscillating around that equilibrium. We take advantage of some recent results of the delay differential literature, when a sufficiently large domain of the phase space has been shown to be attractive and invariant, where the system is governed by monotone delayed feedback and chaos is not possible due to some Poincaré-Bendixson type results. We systematically investigate what control mechanisms are suitable to drive the system into such a situation and prove that constant perturbation, proportional feedback control, Pyragas control, and state dependent delay control can all be efficient to control Mackey-Glass chaos with properly chosen control parameters.

Spatiotemporal chaos from bursting dynamics

International Nuclear Information System (INIS)

Berenstein, Igal; De Decker, Yannick

2015-01-01

In this paper, we study the emergence of spatiotemporal chaos from mixed-mode oscillations, by using an extended Oregonator model. We show that bursting dynamics consisting of fast/slow mixed mode oscillations along a single attractor can lead to spatiotemporal chaotic dynamics, although the spatially homogeneous solution is itself non-chaotic. This behavior is observed far from the Hopf bifurcation and takes the form of a spatiotemporal intermittency where the system locally alternates between the fast and the slow phases of the mixed mode oscillations. We expect this form of spatiotemporal chaos to be generic for models in which one or several slow variables are coupled to activator-inhibitor type of oscillators

A quantum correction to chaos

International Nuclear Information System (INIS)

Fitzpatrick, A. Liam; Kaplan, Jared

2016-01-01

We use results on Virasoro conformal blocks to study chaotic dynamics in CFT_2 at large central charge c. The Lyapunov exponent λ_L, which is a diagnostic for the early onset of chaos, receives 1/c corrections that may be interpreted as λ_L=((2π)/β)(1+(12/c)). However, out of time order correlators receive other equally important 1/c suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on λ_L that emerges at large c, focusing on CFT_2 and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.

Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

International Nuclear Information System (INIS)

Konakli, Katerina; Sudret, Bruno

2016-01-01

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely the exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input

Polynomial meta-models with canonical low-rank approximations: Numerical insights and comparison to sparse polynomial chaos expansions

Energy Technology Data Exchange (ETDEWEB)

Konakli, Katerina, E-mail: konakli@ibk.baug.ethz.ch; Sudret, Bruno

2016-09-15

The growing need for uncertainty analysis of complex computational models has led to an expanding use of meta-models across engineering and sciences. The efficiency of meta-modeling techniques relies on their ability to provide statistically-equivalent analytical representations based on relatively few evaluations of the original model. Polynomial chaos expansions (PCE) have proven a powerful tool for developing meta-models in a wide range of applications; the key idea thereof is to expand the model response onto a basis made of multivariate polynomials obtained as tensor products of appropriate univariate polynomials. The classical PCE approach nevertheless faces the “curse of dimensionality”, namely the exponential increase of the basis size with increasing input dimension. To address this limitation, the sparse PCE technique has been proposed, in which the expansion is carried out on only a few relevant basis terms that are automatically selected by a suitable algorithm. An alternative for developing meta-models with polynomial functions in high-dimensional problems is offered by the newly emerged low-rank approximations (LRA) approach. By exploiting the tensor–product structure of the multivariate basis, LRA can provide polynomial representations in highly compressed formats. Through extensive numerical investigations, we herein first shed light on issues relating to the construction of canonical LRA with a particular greedy algorithm involving a sequential updating of the polynomial coefficients along separate dimensions. Specifically, we examine the selection of optimal rank, stopping criteria in the updating of the polynomial coefficients and error estimation. In the sequel, we confront canonical LRA to sparse PCE in structural-mechanics and heat-conduction applications based on finite-element solutions. Canonical LRA exhibit smaller errors than sparse PCE in cases when the number of available model evaluations is small with respect to the input

Controlling the optical field chaos in storage ring free-electron lasers

International Nuclear Information System (INIS)

Wang Wenjie

1995-01-01

The controlling of optical field chaos in a storage ring free-electron laser oscillator is discussed by using a phenomenal model. A novel method (which is called the 'beating method') of controlling chaos in a nonlinear dynamical system described by non-autonomous ordinary differential equations was developed. The result of theoretical analysis and numerical simulation shows that the optical field chaos in a storage ring free-electron laser oscillator can be suppressed and a periodic laser intensity can be obtained when a weak periodic control field is added to the optical cavity. The validity of this method of eliminating chaos is confirmed by the fact that the leading Lyapunov characteristic exponent of the system changes from a positive real number to a negative one. A further research is carried out, and it is found that only when the period of the control field equals to an integral multiple of that of the gain modulation in the optical cavity can the optical field chaos be suppressed. This means that the 'beating method' of controlling chaos is a kind of resonant method. A way to determine the 'best beating position' in the phase trajectory has also been obtained

Low-dimensional carbon and MXene-based electrochemical capacitor electrodes.

Science.gov (United States)

Yoon, Yeoheung; Lee, Keunsik; Lee, Hyoyoung

2016-04-29

Due to their unique structure and outstanding intrinsic physical properties such as extraordinarily high electrical conductivity, large surface area, and various chemical functionalities, low-dimension-based materials exhibit great potential for application in electrochemical capacitors (ECs). The electrical properties of electrochemical capacitors are determined by the electrode materials. Because energy charge storage is a surface process, the surface properties of the electrode materials greatly influence the electrochemical performance of the cell. Recently, graphene, a single layer of sp(2)-bonded carbon atoms arrayed into two-dimensional carbon nanomaterial, has attracted wide interest as an electrode material for electrochemical capacitor applications due to its unique properties, including a high electrical conductivity and large surface area. Several low-dimensional materials with large surface areas and high conductivity such as onion-like carbons (OLCs), carbide-derived carbons (CDCs), carbon nanotubes (CNTs), graphene, metal hydroxide, transition metal dichalcogenides (TMDs), and most recently MXene, have been developed for electrochemical capacitors. Therefore, it is useful to understand the current issues of low-dimensional materials and their device applications.

Low-dimensional carbon and MXene-based electrochemical capacitor electrodes

International Nuclear Information System (INIS)

Yoon, Yeoheung; Lee, Hyoyoung; Lee, Keunsik

2016-01-01

Due to their unique structure and outstanding intrinsic physical properties such as extraordinarily high electrical conductivity, large surface area, and various chemical functionalities, low-dimension-based materials exhibit great potential for application in electrochemical capacitors (ECs). The electrical properties of electrochemical capacitors are determined by the electrode materials. Because energy charge storage is a surface process, the surface properties of the electrode materials greatly influence the electrochemical performance of the cell. Recently, graphene, a single layer of sp 2 -bonded carbon atoms arrayed into two-dimensional carbon nanomaterial, has attracted wide interest as an electrode material for electrochemical capacitor applications due to its unique properties, including a high electrical conductivity and large surface area. Several low-dimensional materials with large surface areas and high conductivity such as onion-like carbons (OLCs), carbide-derived carbons (CDCs), carbon nanotubes (CNTs), graphene, metal hydroxide, transition metal dichalcogenides (TMDs), and most recently MXene, have been developed for electrochemical capacitors. Therefore, it is useful to understand the current issues of low-dimensional materials and their device applications. (topical review)

Controlling chaos in the current-driven ion acoustic instability

International Nuclear Information System (INIS)

Fukuyama, T.; Taniguchi, K.; Kawai, Y.

2002-01-01

Control of intermittent chaos caused by the current-driven ion acoustic instability is attempted and the controlling mechanism is investigated. When a small negative dc voltage is applied to the chaotic system as a perturbation, the system changes from a chaotic state to a periodic state while maintaining the instability, indicating that the chaotic state caused by the ion acoustic instability is well controlled by applying a small negative dc voltage. A hysteresis structure is observed on the V-I curve of the mesh grid to which the negative dc voltage to control is applied. Furthermore, when a negative dc voltage is applied to the state which shows a laminar structure existing under same experimental conditions, the system becomes chaotic via a bifurcation. Driven-chaos is excited when a negative dc voltage is applied to the laminar state. Applying a small negative dc voltage leads to controlling intermittent chaos while exciting driven-chaos

Workshop on low-dimensional quantum field theory and its applications

International Nuclear Information System (INIS)

Yamamoto, Hisashi

1990-02-01

The workshop on 'Low-Dimensional Quantum Field Theory and its Applications' was held at INS on December 18 - 20, 1989 with about seventy participants. Some pedagogical reviews and the latest results were delivered on the recent topics related to both solid-state and particle physics. Among them are quantum Hall effect, high T c superconductivity and related topics in low-dimensional quantum field theory. Many active discussions were made on these issues. (J.P.N.)

Chaos Modelling with Computers

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 1; Issue 5. Chaos Modelling with Computers Unpredicatable Behaviour of Deterministic Systems. Balakrishnan Ramasamy T S K V Iyer. General Article Volume 1 Issue 5 May 1996 pp 29-39 ...

Fully digital 1-D, 2-D and 3-D multiscroll chaos as hardware pseudo random number generators

KAUST Repository

Mansingka, Abhinav S.

2012-10-07

This paper introduces the first fully digital implementation of 1-D, 2-D and 3-D multiscroll chaos using the sawtooth nonlinearity in a 3rd order ODE with the Euler approximation. Systems indicate chaotic behaviour through phase space boundedness and positive Lyapunov exponent. Low-significance bits form a PRNG and pass all tests in the NIST SP. 800-22 suite without post-processing. Real-time control of the number of scrolls allows distinct output streams with 2-D and 3-D multiscroll chaos enabling greater controllability. The proposed PRNGs are experimentally verified on a Xilinx Virtex 4 FPGA with logic utilization less than 1.25%, throughput up to 5.25 Gbits/s and up to 512 distinct output streams with low cross-correlation.

THEORY OF SECULAR CHAOS AND MERCURY'S ORBIT

International Nuclear Information System (INIS)

Lithwick, Yoram; Wu Yanqin

2011-01-01

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 ∼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.

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

Science.gov (United States)

Fulai, Wang

2012-12-01

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.

Efficient Bayesian inference of subsurface flow models using nested sampling and sparse polynomial chaos surrogates

KAUST Repository

Elsheikh, Ahmed H.

2014-02-01

An efficient Bayesian calibration method based on the nested sampling (NS) algorithm and non-intrusive polynomial chaos method is presented. Nested sampling is a Bayesian sampling algorithm that builds a discrete representation of the posterior distributions by iteratively re-focusing a set of samples to high likelihood regions. NS allows representing the posterior probability density function (PDF) with a smaller number of samples and reduces the curse of dimensionality effects. The main difficulty of the NS algorithm is in the constrained sampling step which is commonly performed using a random walk Markov Chain Monte-Carlo (MCMC) algorithm. In this work, we perform a two-stage sampling using a polynomial chaos response surface to filter out rejected samples in the Markov Chain Monte-Carlo method. The combined use of nested sampling and the two-stage MCMC based on approximate response surfaces provides significant computational gains in terms of the number of simulation runs. The proposed algorithm is applied for calibration and model selection of subsurface flow models. © 2013.

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

International Nuclear Information System (INIS)

Ree, S.; Reichl, L.E.

1999-01-01

We study classical and quantum dynamics of a particle in a circular billiard with a straight cut. Classically, this system can be integrable, nonintegrable with soft chaos, or nonintegrable with hard chaos as we vary the size of the cut. We plot Poincaracute e surfaces of section to study chaos. Quantum mechanically, we look at Husimi plots, and also use the quantum web, the technique primarily used in spin systems so far, to try to see differences in quantum manifestations of soft and hard chaos. copyright 1999 The American Physical Society

Chaos controlling problems for circuit systems with Josephson junction

International Nuclear Information System (INIS)

Gou, X-F; Wang, X; Xie, J-L

2008-01-01

The complex dynamical characters of the Josephson junction circuit system are studied and the tunnel effect is considered. The dynamical equation of the system is established. The route from periodic motion to chaos is illustrated using bifurcation diagram. An adscititious coupling controller is constructed to control the chaos

A New Generation of Luminescent Materials Based on Low-Dimensional Perovskites

KAUST Repository

Pan, Jun

2017-06-02

Low-dimensional perovskites with high luminescence properties are promising materials for optoelectronic applications. In this article, properties of two emerging types of low-dimensional perovskites are discussed, including perovskite quantum dots CsPbX3 (X = Cl, Br or I) and zero-dimensional perovskite Cs4PbBr6. Moreover, their application for light down conversion in LCD backlighting systems and in visible light communication are also presented. With their superior optical properties, we believe that further development of these materials will potentially open more prospective applications, especially for optoelectronics devices.

Is the K-quantum number conserved in the order-to-chaos transittion region?

DEFF Research Database (Denmark)

Benzoni...[], G.; Døssing, T.; Herskind, B.

2005-01-01

To study the order-to-chaos transition in nuclei we investigate the validity of the K-quantum number in the excited rapidly rotating 163Er nucleus, analyzing the variance and covariance of the spectrum fluctuations of ¿-cascades feeding into low-K and high-K bands. The data are compared...

How does the Xenopus laevis embryonic cell cycle avoid spatial chaos?

Science.gov (United States)

Gelens, Lendert; Huang, Kerwyn Casey; Ferrell, James E.

2015-01-01

Summary Theoretical studies have shown that a deterministic biochemical oscillator can become chaotic when operating over a sufficiently large volume, and have suggested that the Xenopus laevis cell cycle oscillator operates close to such a chaotic regime. To experimentally test this hypothesis, we decreased the speed of the post-fertilization calcium wave, which had been predicted to generate chaos. However, cell divisions were found to develop normally and eggs developed into normal tadpoles. Motivated by these experiments, we carried out modeling studies to understand the prerequisites for the predicted spatial chaos. We showed that this type of spatial chaos requires oscillatory reaction dynamics with short pulse duration, and postulated that the mitotic exit in Xenopus laevis is likely slow enough to avoid chaos. In systems with shorter pulses, chaos may be an important hazard, as in cardiac arrhythmias, or a useful feature, as in the pigmentation of certain mollusk shells. PMID:26212326

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

Science.gov (United States)

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

2011-01-01

Household chaos has been linked to poorer cognitive, behavioral, and self-regulatory outcomes in young children, but the mechanisms responsible remain largely unknown. Using a diverse sample of families in Chicago, the present study tests for the independent contributions made by five indicators of household chaos: noise, crowding, family instability, lack of routine, and television usually on. Chaos was measured at age 2; outcomes measured at age 5 tap receptive vocabulary, attention and behavior problems, and effortful control. Results show that controlling for all other measures of chaos, children with a lack of routine scored lower on receptive vocabulary and delayed gratification, while children whose television was generally on scored higher on aggression and attention problems. The provision of learning materials mediated a small part of the association between television and receptive vocabulary. Family instability, crowding, and noise did not predict any outcomes once other measures of chaos were controlled. PMID:22919120

[Chaos theory: a fascinating concept for oncologists].

Science.gov (United States)

Denis, F; Letellier, C

2012-05-01

The oncologist is confronted daily by questions related to the fact that any patient presents a specific evolution for his cancer: he is challenged by very different, unexpected and often unpredictable outcomes, in some of his patients. The mathematical approach used today to describe this evolution has recourse to statistics and probability laws: such an approach does not ultimately apply to one particular patient, but to a given more or less heterogeneous population. This approach therefore poorly characterizes the dynamics of this disease and does not allow to state whether a patient is cured, to predict if he will relapse and when this could occur, and in what form, nor to predict the response to treatment and, in particular, to radiation therapy. Chaos theory, not well known by oncologists, could allow a better understanding of these issues. Developed to investigate complex systems producing behaviours that cannot be predicted due to a great sensitivity to initial conditions, chaos theory is rich of suitable concepts for a new approach of cancer dynamics. This article is three-fold: to provide a brief introduction to chaos theory, to clarify the main connecting points between chaos and carcinogenesis and to point out few promising research perspectives, especially in radiotherapy. Copyright © 2012 Société française de radiothérapie oncologique (SFRO). Published by Elsevier SAS. All rights reserved.

Chaos on hyperspace

Czech Academy of Sciences Publication Activity Database

Beran, Zdeněk; Čelikovský, Sergej

2013-01-01

Roč. 23, č. 5 (2013), 1350084-1-1350084-9 ISSN 0218-1274 R&D Projects: GA ČR GA13-20433S Institutional support: RVO:67985556 Keywords : Hyperspace * chaos * shadowing * Bernoulli shift Subject RIV: BC - Control Systems Theory Impact factor: 1.017, year: 2013 http://library.utia.cas.cz/separaty/2013/TR/beran-0392926.pdf

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

Science.gov (United States)

Akmansoy, Vesile; Kartal, Sadik

2014-01-01

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…

Error function attack of chaos synchronization based encryption schemes.

Science.gov (United States)

Wang, Xingang; Zhan, Meng; Lai, C-H; Gang, Hu

2004-03-01

Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor. Copyright 2004 American Institute of Physics.

Transient chaos - a resolution of breakdown of quantum-classical correspondence in optomechanics

Science.gov (United States)

Wang, Guanglei; Lai, Ying-Cheng; Grebogi, Celso

2016-01-01

Recently, the phenomenon of quantum-classical correspondence breakdown was uncovered in optomechanics, where in the classical regime the system exhibits chaos but in the corresponding quantum regime the motion is regular - there appears to be no signature of classical chaos whatsoever in the corresponding quantum system, generating a paradox. We find that transient chaos, besides being a physically meaningful phenomenon by itself, provides a resolution. Using the method of quantum state diffusion to simulate the system dynamics subject to continuous homodyne detection, we uncover transient chaos associated with quantum trajectories. The transient behavior is consistent with chaos in the classical limit, while the long term evolution of the quantum system is regular. Transient chaos thus serves as a bridge for the quantum-classical transition (QCT). Strikingly, as the system transitions from the quantum to the classical regime, the average chaotic transient lifetime increases dramatically (faster than the Ehrenfest time characterizing the QCT for isolated quantum systems). We develop a physical theory to explain the scaling law. PMID:27748418

Relations between distributional, Li-Yorke and ω chaos

International Nuclear Information System (INIS)

Guirao, Juan Luis Garcia; Lampart, Marek

2006-01-01

The forcing relations between notions of distributional, Li-Yorke and ω chaos were studied by many authors. In this paper we summarize all known connections between these three different types of chaos and fulfill the results for general compact metric spaces by the construction of a selfmap on a compact perfect set which is ω chaotic, not distributionally chaotic and has zero topological entropy

Chaos and the classical limit of quantum systems

Energy Technology Data Exchange (ETDEWEB)

Hogg, T; Huberman, B A [Xerox Palo Alto Research Center, CA (USA)

1984-10-01

The authors discuss the question of whether experiments can be designed to test the existence of quantum chaos. In particular, they show that high energies are not sufficient to guarantee that an initially localized wave packet will behave classically for long times. Computer simulations illustrating these ideas are presented and the question whether experiments can be designed to observe quantum chaos is commented on.

Relations between distributional, Li-Yorke and {omega} chaos

Energy Technology Data Exchange (ETDEWEB)

Guirao, Juan Luis Garcia [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, C/Paseo Alfonso XIII, 30203-Cartagena (Region de Murcia) (Spain)]. E-mail: juan.garcia@upct.es; Lampart, Marek [Mathematical Institute at Opava, Silesian University at Opava, Na Rybnicku 1, 746 01 Opava (Czech Republic)]. E-mail: marek.lampart@math.slu.cz

2006-05-15

The forcing relations between notions of distributional, Li-Yorke and {omega} chaos were studied by many authors. In this paper we summarize all known connections between these three different types of chaos and fulfill the results for general compact metric spaces by the construction of a selfmap on a compact perfect set which is {omega} chaotic, not distributionally chaotic and has zero topological entropy.

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

Science.gov (United States)

Duffy, Jean Ann

2000-01-01

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

Low dimensional neutron moderators for enhanced source brightness

DEFF Research Database (Denmark)

Mezei, Ferenc; Zanini, Luca; Takibayev, Alan

2014-01-01

In a recent numerical optimization study we have found that liquid para-hydrogen coupled cold neutron moderators deliver 3–5 times higher cold neutron brightness at a spallation neutron source if they take the form of a flat, quasi 2-dimensional disc, in contrast to the conventional more voluminous...... for cold neutrons. This model leads to the conclusions that the optimal shape for high brightness para-hydrogen neutron moderators is the quasi 1-dimensional tube and these low dimensional moderators can also deliver much enhanced cold neutron brightness in fission reactor neutron sources, compared...... to the much more voluminous liquid D2 or H2 moderators currently used. Neutronic simulation calculations confirm both of these theoretical conclusions....

A quantum correction to chaos

Energy Technology Data Exchange (ETDEWEB)

Fitzpatrick, A. Liam [Department of Physics, Boston University,590 Commonwealth Avenue, Boston, MA 02215 (United States); Kaplan, Jared [Department of Physics and Astronomy, Johns Hopkins University,3400 N. Charles St, Baltimore, MD 21218 (United States)

2016-05-12

We use results on Virasoro conformal blocks to study chaotic dynamics in CFT{sub 2} at large central charge c. The Lyapunov exponent λ{sub L}, which is a diagnostic for the early onset of chaos, receives 1/c corrections that may be interpreted as λ{sub L}=((2π)/β)(1+(12/c)). However, out of time order correlators receive other equally important 1/c suppressed contributions that do not have such a simple interpretation. We revisit the proof of a bound on λ{sub L} that emerges at large c, focusing on CFT{sub 2} and explaining why our results do not conflict with the analysis leading to the bound. We also comment on relationships between chaos, scattering, causality, and bulk locality.

The transition to chaos conservative classical systems and quantum manifestations

CERN Document Server

Reichl, Linda E

2004-01-01

This book provides a thorough and comprehensive discussion of classical and quantum chaos theory for bounded systems and for scattering processes Specific discussions include • Noether’s theorem, integrability, KAM theory, and a definition of chaotic behavior • Area-preserving maps, quantum billiards, semiclassical quantization, chaotic scattering, scaling in classical and quantum dynamics, dynamic localization, dynamic tunneling, effects of chaos in periodically driven systems and stochastic systems • Random matrix theory and supersymmetry The book is divided into several parts Chapters 2 through 4 deal with the dynamics of nonlinear conservative classical systems Chapter 5 and several appendices give a thorough grounding in random matrix theory and supersymmetry techniques Chapters 6 and 7 discuss the manifestations of chaos in bounded quantum systems and open quantum systems respectively Chapter 8 focuses on the semiclassical description of quantum systems with underlying classical chaos, and Chapt...

Low dimensional field theories and condensed matter physics

International Nuclear Information System (INIS)

Nagaoka, Yosuke

1992-01-01

This issue is devoted to the Proceedings of the Fourth Yukawa International Seminar (YKIS '91) on Low Dimensional Field Theories and Condensed Matter Physics, which was held on July 28 to August 3 in Kyoto. In recent years there have been great experimental discoveries in the field of condensed matter physics: the quantum Hall effect and the high temperature superconductivity. Theoretical effort to clarify mechanisms of these phenomena revealed that they are deeply related to the basic problem of many-body systems with strong correlation. On the other hand, there have been important developments in field theory in low dimensions: the conformal field theory, the Chern-Simons gauge theory, etc. It was found that these theories work as a powerful method of approach to the problems in condensed matter physics. YKIS '91 was devoted to the study of common problems in low dimensional field theories and condensed matter physics. The 17 of the presented papers are collected in this issue. (J.P.N.)

Many-Body Quantum Chaos and Entanglement in a Quantum Ratchet

Science.gov (United States)

Valdez, Marc Andrew; Shchedrin, Gavriil; Heimsoth, Martin; Creffield, Charles E.; Sols, Fernando; Carr, Lincoln D.

2018-06-01

We uncover signatures of quantum chaos in the many-body dynamics of a Bose-Einstein condensate-based quantum ratchet in a toroidal trap. We propose measures including entanglement, condensate depletion, and spreading over a fixed basis in many-body Hilbert space, which quantitatively identify the region in which quantum chaotic many-body dynamics occurs, where random matrix theory is limited or inaccessible. With these tools, we show that many-body quantum chaos is neither highly entangled nor delocalized in the Hilbert space, contrary to conventionally expected signatures of quantum chaos.

Improved particle swarm optimization combined with chaos

International Nuclear Information System (INIS)

Liu Bo; Wang Ling; Jin Yihui; Tang Fang; Huang Dexian

2005-01-01

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 technique through individual improvement plus population cooperation and competition, hybrid particle swarm optimization algorithm is proposed by incorporating chaos. Firstly, adaptive inertia weight factor (AIWF) is introduced in PSO to efficiently balance the exploration and exploitation abilities. Secondly, PSO with AIWF and chaos are hybridized to form a chaotic PSO (CPSO), which reasonably combines the population-based evolutionary searching ability of PSO and chaotic searching behavior. Simulation results and comparisons with the standard PSO and several meta-heuristics show that the CPSO can effectively enhance the searching efficiency and greatly improve the searching quality

Entanglement as a signature of quantum chaos.

Science.gov (United States)

Wang, Xiaoguang; Ghose, Shohini; Sanders, Barry C; Hu, Bambi

2004-01-01

We explore the dynamics of entanglement in classically chaotic systems by considering a multiqubit system that behaves collectively as a spin system obeying the dynamics of the quantum kicked top. In the classical limit, the kicked top exhibits both regular and chaotic dynamics depending on the strength of the chaoticity parameter kappa in the Hamiltonian. We show that the entanglement of the multiqubit system, considered for both the bipartite and the pairwise entanglement, yields a signature of quantum chaos. Whereas bipartite entanglement is enhanced in the chaotic region, pairwise entanglement is suppressed. Furthermore, we define a time-averaged entangling power and show that this entangling power changes markedly as kappa moves the system from being predominantly regular to being predominantly chaotic, thus sharply identifying the edge of chaos. When this entangling power is averaged over all states, it yields a signature of global chaos. The qualitative behavior of this global entangling power is similar to that of the classical Lyapunov exponent.

Nonlinear dynamics and quantum chaos an introduction

CERN Document Server

Wimberger, Sandro

2014-01-01

The field of nonlinear dynamics and chaos has grown very much over the last few decades and is becoming more and more relevant in different disciplines. This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. It provides a thorough and modern introduction to the concepts of Hamiltonian dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It covers a wide range of topics usually not found in similar books. Motivations of the respective subjects and a clear presentation eases the understanding. The book is based on lectures on classical and quantum chaos held by the author at Heidelberg University. It contains exercises and worked examples, which makes it ideal for an introductory course for students as well as for researchers starting to work in the field.

Dynamics and chaos control of gyrostat satellite

International Nuclear Information System (INIS)

Aslanov, Vladimir; Yudintsev, Vadim

2012-01-01

Highlights: ► Free dual-spin gyrostat with a small rotor asymmetry is considered. ► Equations in Andoyer-Deprit canonical dimensionless variables are obtained. ► Phase space heteroclinic and homoclinic trajectories are written in closed form. ► Modified Melnikov function is used to construct the control that eliminates chaos. - Abstract: We consider the chaotic motion of the free gyrostat consisting of a platform with a triaxial inertia ellipsoid and a rotor with a small asymmetry with respect to the axis of rotation. Dimensionless equations of motion of the system with perturbations caused by small asymmetries of the rotor are written in Andoyer-Deprit variables. These perturbations lead to separatrix chaos. For gyrostats with different ratios of moments of inertia heteroclinic and homoclinic trajectories are written in closed-form. These trajectories are used for constructing modified Melnikov function, which is used for determine the control that eliminates separatrix chaos. Melnikov function and phase space trajectory are built to show the effectiveness of the control.

Quantum Effects in the Thermoelectric Power Factor of Low-Dimensional Semiconductors.

Science.gov (United States)

Hung, Nguyen T; Hasdeo, Eddwi H; Nugraha, Ahmad R T; Dresselhaus, Mildred S; Saito, Riichiro

2016-07-15

We theoretically investigate the interplay between the confinement length L and the thermal de Broglie wavelength Λ to optimize the thermoelectric power factor of semiconducting materials. An analytical formula for the power factor is derived based on the one-band model assuming nondegenerate semiconductors to describe quantum effects on the power factor of the low-dimensional semiconductors. The power factor is enhanced for one- and two-dimensional semiconductors when L is smaller than Λ of the semiconductors. In this case, the low-dimensional semiconductors having L smaller than their Λ will give a better thermoelectric performance compared to their bulk counterpart. On the other hand, when L is larger than Λ, bulk semiconductors may give a higher power factor compared to the lower dimensional ones.

Controlling chaos and synchronization for new chaotic system using linear feedback control

International Nuclear Information System (INIS)

Yassen, M.T.

2005-01-01

This paper is devoted to study the problem of controlling chaos for new chaotic dynamical system (four-scroll dynamical system). Linear feedback control is used to suppress chaos to unstable equilibria and to achieve chaos synchronization of two identical four-scroll systems. Routh-Hurwitz criteria is used to study the conditions of the asymptotic stability of the equilibrium points of the controlled system. The sufficient conditions for achieving synchronization of two identical four-scroll systems are derived by using Lyapunov stability theorem. Numerical simulations are presented to demonstrate the effectiveness of the proposed chaos control and synchronization schemes

A study of low-dimensional inhomogeneous systems

International Nuclear Information System (INIS)

Arredondo Leon, Yesenia

2009-01-01

While the properties of homogeneous one-dimensional systems, even with disorder, are relatively well-understood, very little is known about the properties of strongly interacting inhomogeneous systems. Their high-energy physics is determined by the underlying chemistry which, in the atomic scale, introduces Coulomb correlations and local potentials. On the other hand, at large length scales, the physics has to be described by the Tomonaga-Luttinger liquid (TLL) model. In order to establish a connection between the low-energy TLL and the quasi-one-dimensional systems synthesized in the laboratory, we investigate the density-density correlation function in inhomogeneous one-dimensional systems in the asymptotic region. To investigate homogeneous as well as inhomogeneous systems, we use the density-matrix renormalization group (DMRG) method. We present results for ground state properties, such as the density-density correlation function and the parameter K c , which characterizes its decay at large distances. (orig.)

A study of low-dimensional inhomogeneous systems

Energy Technology Data Exchange (ETDEWEB)

Arredondo Leon, Yesenia

2009-01-15

While the properties of homogeneous one-dimensional systems, even with disorder, are relatively well-understood, very little is known about the properties of strongly interacting inhomogeneous systems. Their high-energy physics is determined by the underlying chemistry which, in the atomic scale, introduces Coulomb correlations and local potentials. On the other hand, at large length scales, the physics has to be described by the Tomonaga-Luttinger liquid (TLL) model. In order to establish a connection between the low-energy TLL and the quasi-one-dimensional systems synthesized in the laboratory, we investigate the density-density correlation function in inhomogeneous one-dimensional systems in the asymptotic region. To investigate homogeneous as well as inhomogeneous systems, we use the density-matrix renormalization group (DMRG) method. We present results for ground state properties, such as the density-density correlation function and the parameter K{sub c}, which characterizes its decay at large distances. (orig.)

Dynamical transitions in large systems of mean field-coupled Landau-Stuart oscillators: Extensive chaos and cluster states.

Science.gov (United States)

Ku, Wai Lim; Girvan, Michelle; Ott, Edward

2015-12-01

In this paper, we study dynamical systems in which a large number N of identical Landau-Stuart oscillators are globally coupled via a mean-field. Previously, it has been observed that this type of system can exhibit a variety of different dynamical behaviors. These behaviors include time periodic cluster states in which each oscillator is in one of a small number of groups for which all oscillators in each group have the same state which is different from group to group, as well as a behavior in which all oscillators have different states and the macroscopic dynamics of the mean field is chaotic. We argue that this second type of behavior is "extensive" in the sense that the chaotic attractor in the full phase space of the system has a fractal dimension that scales linearly with N and that the number of positive Lyapunov exponents of the attractor also scales linearly with N. An important focus of this paper is the transition between cluster states and extensive chaos as the system is subjected to slow adiabatic parameter change. We observe discontinuous transitions between the cluster states (which correspond to low dimensional dynamics) and the extensively chaotic states. Furthermore, examining the cluster state, as the system approaches the discontinuous transition to extensive chaos, we find that the oscillator population distribution between the clusters continually evolves so that the cluster state is always marginally stable. This behavior is used to reveal the mechanism of the discontinuous transition. We also apply the Kaplan-Yorke formula to study the fractal structure of the extensively chaotic attractors.

Are low-dimensional dynamics typical in magnetically confined plasmas?

International Nuclear Information System (INIS)

Ball, R.; Dewar, R.L.

2000-01-01

Full text: Since 1988 there have been many serious attempts to construct low-dimensional dynamical systems that model L-H transitions and associated oscillatory phenomena in magnetically confined plasmas. Such models usually consist of coupled ordinary differential equations in a few dynamical state variables and several parameters that represent physical properties or external controls. The advantages of a unified, low-dimensional approach to modelling plasma behaviour are multifold. Most importantly, the qualitative analysis of nonlinear ODE and algebraic systems is supported by a substantial body of theory. The toolkits of singularity and stability theory are well-developed and accessible, and contain the right tools for the job of charting the state and parameter space. One of the driving forces behind the development of low-dimensional dynamical models is the predictive potential of a parameter map. For example, a model that talks of the shape and extent of hysteresis in the L-H transition would help engineers who are interested in controlling access to H-mode. We can express this problem another way: given the enormous number of variables and parameters that could be varied around a hysteretic regime, it would be cheaper to know in advance which ones actually do influence the quality and quantity of the hysteresis. The quest for a low-dimensional state space that contains the qualitative dynamics of L-H transitions also introduces other problems. We need to identify the essential (few) dynamical variables and the essential (few) independent parameter groups, clarify the mechanisms for the feedback that is modelled by nonlinear terms, and identify symmetries in the physics. Before jumping the gun on these questions the fundamental issue should be addressed of whether a confined plasma, having many important length and time scales, steep gradients, strong anisotropy, and an uncountable multiplicity of states, can indeed exhibit low-dimensional dynamics. In this

Intermittency route to chaos in a biochemical system.

Science.gov (United States)

De la Fuente, I M; Martinez, L; Veguillas, J

1996-01-01

The numerical analysis of a glycolytic model performed through the construction of a system of three differential-delay equations reveals a phenomenon of intermittency route to chaos. In our biochemical system, the consideration of delay time variations under constant input flux as well as frequency variations of the periodic substrate input flux allows us, in both cases, to observe a type of transition to chaos different from the 'Feigenbaum route'.

Chaos synchronization of the fractional-order Chen's system

International Nuclear Information System (INIS)

Zhu Hao; Zhou Shangbo; He Zhongshi

2009-01-01

In this paper, based on the stability theorem of linear fractional systems, a necessary condition is given to check the chaos synchronization of fractional systems with incommensurate order. Chaos synchronization is studied by utilizing the Pecora-Carroll (PC) method and the coupling method. The necessary condition can also be used as a tool to confirm results of a numerical simulation. Numerical simulation results show the effectiveness of the necessary condition.

Aram Chaos Rocks

Science.gov (United States)

2005-01-01

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

Chaos and Structures in Nonlinear Plasmas

Science.gov (United States)

Chen, James

In recent decades, the concepts and applications of chaos, complexity, and nonlinear dynamics have profoundly influenced scientific as well as literary thinking. Some aspects of these concepts are used in almost all of the geophysical disciplines. Chaos and Structures in Nonlinear Plasmas, written by two respected plasma physicists, focuses on nonlinear phenomena in laboratory and space plasmas, which are rich in nonlinear and complex collective effects. Chaos is treated only insofar as it relates to some aspects of nonlinear plasma physics.At the outset, the authors note that plasma physics research has made fundamental contributions to modern nonlinear sciences. For example, the Poincare surface of section technique was extensively used in studies of stochastic field lines in magnetically confined plasmas and turbulence. More generally, nonlinearity in plasma waves and wave-wave and wave-particle interactions critically determines the propagation of energy through a plasma medium. The book also makes it clear that the importance of understanding nonlinear waves goes beyond plasma physics, extending to such diverse fields as solid state physics, fluid dynamics, atmospheric physics, and optics. In space physics, non-linear plasma physics is essential for interpreting in situ as well as remote-sensing data.

Chaos and its control in an impulsive differential system

International Nuclear Information System (INIS)

Jiang Guirong; Lu Qishao; Qian Linning

2007-01-01

In this paper, the existence of chaos and its control in an autonomous impulsive differential system are discussed both theoretically and numerically. The existence of a snap-back repeller, as well as the chaos in the sense of Li-Yorke, is proved based on the qualitative analysis using the Poincare map and the Lambert W-function. Moreover, the existence of the period-3 periodic window embedded in the chaotic region is also demonstrated. An algorithm of chaos control to stabilize the unstable periodic solutions is proposed. Detailed numerical results of chaotic attractors and stabilization of unstable periodic orbits by the impulsive effects, which are illustrated by an example, are in good agreement with the theoretical analysis

Study of intermittent bifurcations and chaos in boost PFC converters by nonlinear discrete models

International Nuclear Information System (INIS)

Zhang Hao; Ma Xikui; Xue Bianling; Liu Weizeng

2005-01-01

This paper mainly deals with nonlinear phenomena like intermittent bifurcations and chaos in boost PFC converters under peak-current control mode. Two nonlinear models in the form of discrete maps are derived to describe precisely the nonlinear dynamics of boost PFC converters from two points of view, i.e., low- and high-frequency regimes. Based on the presented discrete models, both the evolution of intermittent behavior and the periodicity of intermittency are investigated in detail from the fast and slow-scale aspects, respectively. Numerical results show that the occurrence of intermittent bifurcations and chaos with half one line period is one of the most distinguished dynamical characteristics. Finally, we make some instructive conclusions, which prove to be helpful in improving the performances of practical circuits

Suppression of chaos at slow variables by rapidly mixing fast dynamics

Science.gov (United States)

Abramov, R.

2012-04-01

One of the key questions about chaotic multiscale systems is how the fast dynamics affects chaos at the slow variables, and, therefore, impacts uncertainty and predictability of the slow dynamics. Here we demonstrate that the linear slow-fast coupling with the total energy conservation property promotes the suppression of chaos at the slow variables through the rapid mixing at the fast variables, both theoretically and through numerical simulations. A suitable mathematical framework is developed, connecting the slow dynamics on the tangent subspaces to the infinite-time linear response of the mean state to a constant external forcing at the fast variables. Additionally, it is shown that the uncoupled dynamics for the slow variables may remain chaotic while the complete multiscale system loses chaos and becomes completely predictable at the slow variables through increasing chaos and turbulence at the fast variables. This result contradicts the common sense intuition, where, naturally, one would think that coupling a slow weakly chaotic system with another much faster and much stronger mixing system would result in general increase of chaos at the slow variables.

Quantum chaos: entropy signatures

International Nuclear Information System (INIS)

Miller, P.A.; Sarkar, S.; Zarum, R.

1998-01-01

A definition of quantum chaos is given in terms of entropy production rates for a quantum system coupled weakly to a reservoir. This allows the treatment of classical and quantum chaos on the same footing. In the quantum theory the entropy considered is the von Neumann entropy and in classical systems it is the Gibbs entropy. The rate of change of the coarse-grained Gibbs entropy of the classical system with time is given by the Kolmogorov-Sinai (KS) entropy. The relation between KS entropy and the rate of change of von Neumann entropy is investigated for the kicked rotator. For a system which is classically chaotic there is a linear relationship between these two entropies. Moreover it is possible to construct contour plots for the local KS entropy and compare it with the corresponding plots for the rate of change of von Neumann entropy. The quantitative and qualitative similarities of these plots are discussed for the standard map (kicked rotor) and the generalised cat maps. (author)

Chaos detection and predictability

CERN Document Server

Gottwald, Georg; Laskar, Jacques

2016-01-01

Distinguishing chaoticity from regularity in deterministic dynamical systems and specifying the subspace of the phase space in which instabilities are expected to occur is of utmost importance in as disparate areas as astronomy, particle physics and climate dynamics.   To address these issues there exists a plethora of methods for chaos detection and predictability. The most commonly employed technique for investigating chaotic dynamics, i.e. the computation of Lyapunov exponents, however, may suffer a number of problems and drawbacks, for example when applied to noisy experimental data.   In the last two decades, several novel methods have been developed for the fast and reliable determination of the regular or chaotic nature of orbits, aimed at overcoming the shortcomings of more traditional techniques. This set of lecture notes and tutorial reviews serves as an introduction to and overview of modern chaos detection and predictability techniques for graduate students and non-specialists.   The book cover...

Research on a family of n-scroll chaos generators

International Nuclear Information System (INIS)

Zhang, G; Yang, S-Z; He, L-F

2008-01-01

This paper studies a family of n-scroll chaos generators using a modified Chua's circuit. A mathematic model of the generators is established, the relationship between equilibrium points and scrolls is also analyzed, and a general theorem for generation of n-scroll chaos attractors is given. Numerical simulation is illustrated, showing excellent agreement with our theoretical predictions

Parrondo’s paradox for chaos control and anticontrol of fractional-order systems

International Nuclear Information System (INIS)

Danca, Marius-F; Tang, Wallace K S

2016-01-01

We present the generalized forms of Parrondo’s paradox existing in fractional-order nonlinear systems. The generalization is implemented by applying a parameter switching (PS) algorithm to the corresponding initial value problems associated with the fractional-order nonlinear systems. The PS algorithm switches a system parameter within a specific set of N ≥ 2 values when solving the system with some numerical integration method. It is proven that any attractor of the concerned system can be approximated numerically. By replacing the words “winning” and “loosing” in the classical Parrondo’s paradox with “order” and “chaos', respectively, the PS algorithm leads to the generalized Parrondo’s paradox: chaos 1 + chaos 2 + ··· + chaos N = order and order 1 + order 2 + ··· + order N = chaos. Finally, the concept is well demonstrated with the results based on the fractional-order Chen system. (paper)

Application of chaos theory to the particle dynamics of asymmetry-induced transport

Science.gov (United States)

Eggleston, D. L.

2018-03-01

The techniques of chaos theory are employed in an effort to better understand the complex single-particle dynamics of asymmetry-induced transport in non-neutral plasmas. The dynamical equations are re-conceptualized as describing time-independent trajectories in a four-dimensional space consisting of the radius r, rotating frame angle ψ, axial position z, and axial velocity v. Results include the identification of an integral of the motion, fixed-point analysis of the dynamical equations, the construction and interpretation of Poincaré sections to visualize the dynamics, and, for the case of chaotic motion, numerical calculation of the largest Lyapunov exponent. Chaotic cases are shown to be associated with the overlap of resonance islands formed by the applied asymmetry.

De Moivre's formula: are Sands' H-functions the same as Chao's?

International Nuclear Information System (INIS)

Nishikawa, P

2012-01-01

It has often been said that there is no clear extension of the Courant-Snyder theory to coupled dynamics. In particular, one never sees an extension of the symplectic de Moivre type formula beyond one degree of freedom. In the process of analysing the existence and meaning of such a formula, I discovered quite accidentally that Sands' formalism, if expressed in terms of Ripken-like lattice functions germane to the full three dimensional oscillator, gives the exact same result as the more accurate Chao theory. This semi-serious paper displays this elegant connection. It is based in the lattice functions of Ripken as extended by Forest. We review Forest's derivation from the point of view de Moivre's formula extended to three degrees of freedom.

Order out of chaos in atomic nuclei

Energy Technology Data Exchange (ETDEWEB)

Rotter, I

1988-07-01

The transition from the resonance reaction mechanism at low level density to the direct reaction mechanism at high level density is investigated by means of numerical results obtained from microscopic calculations for nucleon-induced reactions. The transition takes place rather sharply at GAMMA approx. = D-bar. Here, two types of motion of the nucleons exist simultaneously: a motion in long-living states which are near equilibrium and a motion in short-living states which are far from equilibrium. A formation of order out of chaos takes place only in the open quantum mechanical nuclear system. It is caused by quantum fluctuations via the continuum.

A series of new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation

International Nuclear Information System (INIS)

Yong Chen; Qi Wang

2005-01-01

In this paper, we extend the algebraic method proposed by Fan (Chaos, Solitons and Fractals 20 (2004) 609) and the improved extended tanh method by Yomba (Chaos, Solitons and Fractals 20 (2004) 1135) to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations (NPDE). Some new soliton-like solutions and double-like periodic solutions of a (2 + 1)-dimensional dispersive long wave equation are obtained

A history of chaos theory.

Science.gov (United States)

Oestreicher, Christian

2007-01-01

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.

A history of chaos theory

Science.gov (United States)

Oestreicher, Christian

2007-01-01

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

Next-order spin-orbit contributions to chaos in compact binaries

International Nuclear Information System (INIS)

Wang Yuzhao; Wu Xin

2011-01-01

This paper is mainly devoted to numerically investigating the effects of the next-order spin-orbit interactions including the 2.5 post-Newtonian order term of the equations of motion and the second post-Newtonian order terms of the spin precession equations on chaos in the conservative Lagrangian dynamics of a spinning compact binary system. It is shown sufficiently through individual orbit simulations, the dependence of the invariant fast Lyapunov indicators on the variations of initial spin angles and the phase space scans for chaos, that the next-order spin-orbit contributions do play an important role in the amplification of chaos.

PREFACE: Dynamics of low-dimensional systems Dynamics of low-dimensional systems

Science.gov (United States)

Bernasconi, M.; Miret-Artés, S.; Toennies, J. P.

2012-03-01

With the development of techniques for high-resolution inelastic helium atom scattering (HAS), electron scattering (EELS) and neutron spin echo spectroscopy, it has become possible, within approximately the last thirty years, to measure the dispersion curves of surface phonons in insulators, semiconductors and metals. In recent years, the advent of new experimental techniques such as 3He spin-echo spectroscopy, scanning inelastic electron tunnel spectroscopy, inelastic x-ray scattering spectroscopy and inelastic photoemission have extended surface phonon spectroscopy to a variety of systems. These include ultra-thin metal films, adsorbates at surface and elementary processes where surface phonons play an important role. Other important directions have been actively pursued in the past decade: the dynamics of stepped surfaces and clusters grown on metal surfaces, due to their relevance in many dynamical and chemical processes at surfaces, including heterogeneous catalysis; clusters; diffusion etc. The role of surface effects in these processes has been conjectured since the early days of surface dynamics, although only now is the availability of ab initio approaches providing those conjectures with a microscopic basis. Last but not least, the investigation of non-adiabatic effects, originating for instance from the hybridization (avoided crossing) of the surface phonons branches with the quasi 1D electron-hole excitation branch, is also a challenging new direction. Furthermore, other elementary oscillations such as surface plasmons are being actively investigated. The aforementioned experimental breakthroughs have been accompanied by advances in the theoretical study of atom-surface interaction. In particular, in the past decade first principles calculations based on density functional perturbation theory have boosted the theoretical study of the dynamics of low-dimensional systems. Phonon dispersion relations of clean surfaces, the dynamics of adsorbates, and the

Control and synchronization of chaos in nonlinear systems and prospects for application. Pt.1

International Nuclear Information System (INIS)

Fang Jinqing

1996-01-01

Main progress in one challenging subject of nonlinear science--control and synchronization of chaos in nonlinear systems are reviewed systematically, including recent advance in controlling and synchronizing hyperchaos. Current methods and principles of schemes of chaos control and synchronization are classified and summarized in detail. Potential prospects for application are commented both in theory and experiment. The whole review is divided into two parts. In the first one, subject on the mechanism and method of chaos control are analyzed and discussed extensively. In the second one, the synchronization of non-chaos, chaos, hyperchaos and their control and application are described. Main trends for development of the subject is mentioned. (101 refs.)

A cubic map chaos criterion theorem with applications in generalized synchronization based pseudorandom number generator and image encryption.

Science.gov (United States)

Yang, Xiuping; Min, Lequan; Wang, Xue

2015-05-01

This paper sets up a chaos criterion theorem on a kind of cubic polynomial discrete maps. Using this theorem, Zhou-Song's chaos criterion theorem on quadratic polynomial discrete maps and generalized synchronization (GS) theorem construct an eight-dimensional chaotic GS system. Numerical simulations have been carried out to verify the effectiveness of theoretical results. The chaotic GS system is used to design a chaos-based pseudorandom number generator (CPRNG). Using FIPS 140-2 test suit/Generalized FIPS 140-2, test suit tests the randomness of two 1000 key streams consisting of 20 000 bits generated by the CPRNG, respectively. The results show that there are 99.9%/98.5% key streams to have passed the FIPS 140-2 test suit/Generalized FIPS 140-2 test. Numerical simulations show that the different keystreams have an average 50.001% same codes. The key space of the CPRNG is larger than 2(1345). As an application of the CPRNG, this study gives an image encryption example. Experimental results show that the linear coefficients between the plaintext and the ciphertext and the decrypted ciphertexts via the 100 key streams with perturbed keys are less than 0.00428. The result suggests that the decrypted texts via the keystreams generated via perturbed keys of the CPRNG are almost completely independent on the original image text, and brute attacks are needed to break the cryptographic system.