Topic
Chaotic
About: Chaotic is a research topic. Over the lifetime, 28560 publications have been published within this topic receiving 483285 citations.
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Book•
29 Nov 1995
TL;DR: Regular Dynamics: Newton to Poincare KAM Theorem, and the Chaos Toolkit: Making 'Physics' out of Chaos.
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
2,083 citations
Book•
01 Sep 1989TL;DR: The goal of this book is to present an elementary introduction on chaotic systems for the non-specialist, and to present and extensive package of computer algorithms for simulating and characterizing chaotic phenomena.
Abstract: The goal of this book qre to present an elementary introduction on chaotic systems for the non-specialist, and to present and extensive package of computer algorithms ( in the form of pseudocode) for simulating and characterizing chaotic phenomena. These numerical algorithms have been implemented in a software package called INSITE (Interactive Nonlinear System Investigative Toolkit for Everyone) which is being distributed separately.
1,859 citations
TL;DR: An error estimate is presented for this forecasting technique for chaotic data, and its effectiveness is demonstrated by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow.
Abstract: We present a forecasting technique for chaotic data. After embedding a time series in a state space using delay coordinates, we ``learn'' the induced nonlinear mapping using local approximation. This allows us to make short-term predictions of the future behavior of a time series, using information based only on past values. We present an error estimate for this technique, and demonstrate its effectiveness by applying it to several examples, including data from the Mackey-Glass delay differential equation, Rayleigh-Benard convection, and Taylor-Couette flow.
1,836 citations
Book•
15 Feb 2002
TL;DR: In this paper, the authors present a broad overview of nonlinear phenomena point attractors in autonomous systems, including limit cycles in autonomous system, and chaotic behaviour of one-and two-dimensional maps.
Abstract: Preface. Preface to the First Edition. Acknowledgements from the First Edition. Introduction PART I: BASIC CONCEPTS OF NONLINEAR DYNAMICS An overview of nonlinear phenomena Point attractors in autonomous systems Limit cycles in autonomous systems Periodic attractors in driven oscillators Chaotic attractors in forced oscillators Stability and bifurcations of equilibria and cycles PART II ITERATED MAPS AS DYNAMICAL SYSTEMS Stability and bifurcation of maps Chaotic behaviour of one--and two--dimensional maps PART III FLOWS, OUTSTRUCTURES AND CHAOS The Geometry of Recurrence The Lorenz system Rosslers band Geometry of bifurcations PART IV APPLICATIONS IN THE PHYSICAL SCIENCES Subharmonic resonances of an offshore structure Chaotic motions of an impacting system Escape from a potential well Appendix. Illustrated Glossary. Bibliography. Online Resource. Index.
1,731 citations
TL;DR: In this paper, it is shown that the deciding factor for integrable or chaotic particle motion is the nature of the motion of the agitator, which is a very simple model which provides an idealization of a stirred tank.
Abstract: In the Lagrangian representation, the problem of advection of a passive marker particle by a prescribed flow defines a dynamical system. For two-dimensional incompressible flow this system is Hamiltonian and has just one degree of freedom. For unsteady flow the system is non-autonomous and one must in general expect to observe chaotic particle motion. These ideas are developed and subsequently corroborated through the study of a very simple model which provides an idealization of a stirred tank. In the model the fluid is assumed incompressible and inviscid and its motion wholly two-dimensional. The agitator is modelled as a point vortex, which, together with its image(s) in the bounding contour, provides a source of unsteady potential flow. The motion of a particle in this model device is computed numerically. It is shown that the deciding factor for integrable or chaotic particle motion is the nature of the motion of the agitator. With the agitator held at a fixed position, integrable marker motion ensues, and the model device does not stir very efficiently. If, on the other hand, the agitator is moved in such a way that the potential flow is unsteady, chaotic marker motion can be produced. This leads to efficient stirring. A certain case of the general model, for which the differential equations can be integrated for a finite time to produce an explicitly given, invertible, area-preserving mapping, is used for the calculations. The paper contains discussion of several issues that put this regime of chaotic advection in perspective relative to both the subject of turbulent advection and to recent work on critical points in the advection patterns of steady laminar flows. Extensions of the model, and the notion of chaotic advection, to more realistic flow situations are commented upon.
1,730 citations