Showing papers on "Chaotic published in 1995"

Analysis of Observed Chaotic Data

Abstract: Regular Dynamics: Newton to Poincare KAM Theorem | Bifurcations: Routes to Chaos, Stability and Instability | Reconstruction of Phase Space: Regular and Chaotic Motions Observed Chaos | Choosing Time Delays: Chaos as an Information Source Average Mutual Information. | Choosing the Dimension of Reconstructed Phase Space | Invariants of the Motion: Global & Local Lyapunov Exponents Lorenz Model | Modeling Chaos: Local & Global Models Phase Space Models | Signal Separation: Probabilistic Cleaning 'Blind' Signal Separation | Control and Chaos: Parametric Control Examples of Control (including magnetoelastic ribbon, electric circuits, cardiac tissue) | Synchronization of Chaotic Systems: Identical or Dissimilar Systems Chaotic Nonlinear Circuits | Other Example Systems: Laser Intensity Fluctuations Volume Fluctuations of the Great Salt Lake Motion in a Fluid Boundary Layer | Estimating in Chaos: Cramer-Rao Bounds | The Chaos Toolkit: Making 'Physics' out of Chaos

General approach for chaotic synchronization with applications to communication.

Abstract: A general approach for constructing chaotic synchronized dynamical systems is discussed that is based on a decomposition of given systems into active and passive parts. As a possible application the chapter considers an improved encoding method where the information signal is injected into the dynamical system of the transmitter. Furthermore, it highlights how to design in a systematic way high-dimensional synchronized systems that may be used for efficient hyperchaotic encoding of information. Synchronization of periodic signals is a well-known phenomenon in physics, engineering, and many other scientific disciplines.

Chaos Theory and Organization

Abstract: Many authors have stressed the existence of continuous processes of convergence and divergence, stability and instability, evolution and revolution in every organization. This article argues that these processes are embedded in organizational characteristics and in the way organizations are managed. Organizations are presented as nonlinear dynamic systems subject to forces of stability and forces of instability which push them toward chaos. When in a chaotic domain, organizations are likely to exhibit the qualitative properties of chaotic systems. Several of these properties—sensitivity to initial conditions, discreteness of change, attraction to specific configurations, structural invariance at different scales and irreversibility—are used to establish six propositions. First, because of the coupling of counteracting forces, organizations are potentially chaotic. Second, the path from organizational stability to chaos follows a discrete process of change. Third, when the organization is in the chaotic do...

Simulation and Chaotic Behavior of α-Stable Stochastic Processes

Abstract: Preliminary remarks Brownian motion, poisson process, alpha-stable Levy motion computer simulation of alpha-stable random variables stochastic integration spectral representations of stationary processes computer approximations of continuous time processes examples of alpha-stable stochastic modelling convergence of approximate methods chaotic behaviour of stationary processes hierarchy of chaos for stable and ID stationary processes. Appendix - a guide to simulation.

Detection of signals in chaos

Abstract: In this paper, we present a new method for the detection of signals in "noise", which is based on the premise that the "noise" is chaotic with at least one positive Lyapunov exponent. The method is naturally rooted in nonlinear dynamical systems and relies on neural networks for its implementation. We first present an introductory review of chaos. The subject matter selected for this part of the paper is written with emphasis on experimental studies of chaos using a time series. Specifically, we discuss the issues involved in the reconstruction of chaotic dynamics, attractor dimensions, and Lyapunov exponents. We describe procedures for the estimation of the correlation dimension and the largest Lyapunov exponent. The need for an adequate data length is stressed. In the second part of the paper we apply the chaos-based method to a difficult task: the radar detection of a small target in sea clutter. >

Controlling chaos using differential geometric method.

Abstract: We present an effective approach for controlling chaos by using a differential geometric method. It has been shown that the proposed method can control chaotic motion not only to a steady state but also to any desired periodic orbit. The main characteristic of the method is to algebraically transform a nonlinear dynamics into a linear one, so that linear control techniques can be applied. To demonstrate the feasibility of our proposed method, a Lorenz system under different designed requirements is illustrated.

Desynchronization by periodic orbits.

Abstract: Synchronous chaotic behavior is often interrupted by bursts of desynchronized behavior. We investigate the role of unstable periodic orbits in bursting events and show that they serve as sources of local transverse instability within a synchronous chaotic attractor. Analysis of bursts in both model and experimental studies of two coupled R\"ossler-like oscillators reveals the importance of unstable periodic orbits in bursting events.

An application of deterministic chaotic maps to model packet traffic

Abstract: We investigate the application of deterministic chaotic maps to model traffic sources in packet based networks, motivated in part by recent measurement studies which indicate the presence of significant statistical features in packet traffic more characteristic of fractal processes than conventional stochastic processes. We describe one approach whereby traffic sources can be modeled by chaotic maps, and illustrate the traffic characteristics that can be generated by analyzing several classes of maps. We outline a potential performance analysis approach based on chaotic maps that can be used to assess the traffic significance of fractal properties. We show that low order nonlinear maps can capture several of the fractal properties observed in actual data, and show that the source characteristics observed in actual traffic can lead to heavy-tailed queue length distributions. It is our conclusion that while there are considerable analytical difficulties, chaotic maps may allow accurate, yet concise, models of packet traffic, with some potential for transient and steady state analysis.

Gaussian orthogonal ensemble statistics in a microwave stadium billiard with chaotic dynamics: Porter-Thomas distribution and algebraic decay of time correlations.

Abstract: The complete set of resonance parameters for 950 resonances of a superconducting microwave cavity connected to three antennas has been measured. This cavity simulates the quantum mechanics of a particle in a Bunimovich stadium. The partial widths are found to follow a Porter-Thomas distribution. The Fourier transforms of the $S$-matrix autocorrelation functions decay algebraically (nonexponentially) in time. These results agree perfectly with the predictions of random-matrix theory. They constitute one of the most stringent tests ever of this expected connection between chaotic dynamics and randommatrix theory.

Stochastic models of chaotic systems

Abstract: Nonlinear dynamical systems, although strictly deterministic, often exhibit chaotic behavior which appears to be random. The determination of the probabilistic properties of such systems is, in general, an open problem. Closure approximations for moment expansion methods have been unsatisfactory. More successful has been approximation on the dynamics level by the use of linear stochastic models that attempt to generate the probabilistic properties of the original nonlinear chaotic system as closely as possible. Examples are reviewed of this approach to simple nonlinear systems, to turbulence, and to large-eddy simulation. A stochastic model that simulates the transient energy spectrum of the global atmosphere is developed.

Maximum-likelihood estimation of a class of chaotic signals

Abstract: The chaotic sequences corresponding to tent map dynamics are potentially attractive in a range of engineering applications. Optimal estimation algorithms for signal filtering, prediction, and smoothing in the presence of white Gaussian noise are derived for this class of sequences based on the method of maximum likelihood. The resulting algorithms are highly nonlinear but have convenient recursive implementations that are efficient both in terms of computation and storage. Performance evaluations are also included and compared with the associated Cramer-Rao bounds. >

Chaos applied to fluid mixing

Abstract: Chaotic advection in perspective, H. Aref invariant manifold templates for chaotic advection, D. Beigie et al quantification of mixing in aperiodic chaotic flows, M. Liu et al Hamiltonian formulation of the equations of streamlines in three-dimensional steady flows, K. Bajer orientation dynamics and stretching of particles in unsteady, three-dimensional fluid flows - unsteady attractors, A.J. Szeri and L.G. Leal interaction of chaotic advection and diffusion, S.W. Jones resonant and chaotic advection in a curved pipe, P.E. Hydon application of chaotic advection to heat transfer, Hsueh-Chia Chang and M. Sen interacting two-dimensional vortex structures - point vortices, contour kinematics and stirring-properties, V.V. Meleshko and G.J.F. van Heijst an analytical study of chaotic stirring in tidal areas, S.P. Beerens et al stretching and alignment in chaotic and turbulent flows, M. Tabor and I. Klapper comparisons of mixing in chaotic and turbulent flows, K.B. Southerland et al tracer microstructure in the large-eddy dominated regime, R.T. Pierrehumbert spectra of local and nonlocal two-dimensional turbulence, R.T. Pierrehumbert et al.

Detecting periodic unstable points in noisy chaotic and limit cycle attractors with applications to biology.

Abstract: Recently, biological preparations which are thought to be chaotic have been controlled using algorithms based on the detection and manipulation of periodic unstable points. The dynamics of these systems are, however, contaminated with noise; thus detection becomes a statistical process. Here we show that low dimensional chaos can be reliably detected with large noise contamination and distinguished from noisy limit cycles. We also examine a purely chaotic high dimensional system.

Information encoder/decoder using chaotic systems

Abstract: The present invention discloses a chaotic system-based information encoder and decoder that operates according to a relationship defining a chaotic system Encoder input signals modify the dynamics of the chaotic system comprising the encoder The modifications result in chaotic, encoder output signals that contain the encoder input signals encoded within them The encoder output signals are then capable of secure transmissions using conventional transmission techniques A decoder receives the encoder output signals (ie, decoder input signals) and inverts the dynamics of the encoding system to directly reconstruct the original encoder input signals

Retrieving dynamical invariants from chaotic data using narmax models

Abstract: This paper is concerned with the estimation of dynamical invariants from relatively short and possibly noisy sets of chaotic data In order to overcome the difficulties associated with the size and quality of the data records, a two-step procedure is investigated Firstly NARMAX models are fitted to the data Secondly, such models are used to generate longer and cleaner time sequences from which dynamical invariants such as Lyapunov exponents, correlation dimension, the geometry of the attractors, Poincare maps and bifurcation diagrams can be estimated with relative ease An additional advantage of this procedure is that because the models are global and have a simple structure, such models are amenable for analysis It is shown that the location and stability of the fixed points of the original systems can be analytically recovered from the identified models A number of examples are included which use the logistic and Henon maps, Duffing and modified van der Pol oscillators, the Mackey-Glass delay system, Chua’s circuit, the Lorenz and Rossler attractors The identified models of these systems are provided including discrete multivariable models for Chua’s double scroll, Lorenz and Rossler attractors which are used to reconstruct the trajectories in a three-dimensional state space

Methods for chaotic signal estimation

Abstract: A dynamic programming algorithm and a suboptimal but computationally efficient method for estimation of a chaotic signal in white Gaussian noise are proposed The nonlinear map is assumed known so that only the initial condition need be estimated Computer simulations confirm that both approaches produce efficient estimates at high signal-to-noise ratios >

Nonlinear analysis of sleep EEG data in schizophrenia: calculation of the principal Lyapunov exponent

Abstract: The generating mechanism of the electroencephalogram (EEG) points to the hypothesis that EEG signals derive from a nonlinear dynamic system. Hence, the unpredictability of the EEG might be considered as a phenomenon exhibiting its chaotic character. The essential property of chaotic dynamics is the so-called sensitive dependence on initial conditions. This property can be quantified by calculating the system's first positive Lyapunov exponent, L1. We calculated L1 for sleep EEG segments of 13 schizophrenic patients and 13 control subjects that corresponded to sleep stages I, II, III, IV and REM (rapid eye movement), as defined by Rechtschaffen and Kales, for the lead positions Cz and Pz. During REM sleep, for both electrode positions, the principal Lyapunov exponent L1 was significantly increased in schizophrenic patients compared with control subjects. This finding points to altered nonlinear brain dynamics during REM sleep in schizophrenia.

Chaotic memory dynamics in a recurrent neural network with cycle memories embedded by pseudo-inverse method

Abstract: It is shown that hierarchical bifurcation of chaotic intermittency among memories can be induced by reducing neural connectivity when sequences of similar patterns are stored in a recurrent neural network using the pseudo-inverse method. This chaos is potentially useful for memory search and synthesis.

Communicating with use of filtered, synchronized, chaotic signals

Abstract: The principles of synchronization of chaotic systems are extended to the case where the drive signal is filtered. A feedback loop in the response system with an identical filter is used to reconstruct the original drive signal, allowing synchronization. A simple parameter switching scheme is used to send information from a drive circuit to a receiver. It is also possible to add a chaotic signal with very similar frequency characteristics and still detect information encoded in the original chaotic carrier (but not the added chaotic signal), demonstrating the possibility of adding and separating multiple chaotic carriers with similar frequency characteristics. >

Fractal boundaries in open hydrodynamical flows: Signatures of chaotic saddles

Abstract: We introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken experiments carried out with passive tracer particles colored differently. It is shown that the signature for the presence of a chaotic saddle in the advection dynamics is a fractal boundary between regions of different colors. The fractal parts of the boundaries found in the two experiments contain either the stable or the unstable manifold of this chaotic set. We point out that these boundaries coincide with streak lines passing through appropriately chosen points. As an illustrative numerical experiment, we consider a model of the von K\'arm\'an vortex street, a time periodic two-dimensional flow of a viscous fluid around a cylinder.

The chaotic monopolist

Abstract: The search of a profit maximum by a monopolistic firm is studied, given a demand function with variable elasticity of demand. The system has multiple optimal solutions, so the search algorithm may result in chaotic behaviour.