Low-dimensional chaos in high-dimensional phase space: how does it occur?

Ying-Cheng Lai; E M  Bollt; Z H  Liu

doi:10.1016/S0960-0779(02)00094-2

Low-dimensional chaos in high-dimensional phase space: how does it occur?

Ying-Cheng Lai
, E M Bollt
, Z H Liu

Physics

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

Abstract

A fundamental observation in nonlinear dynamics is that the asymptotic chaotic invariant sets in many high-dimensional systems are low-dimensional. We argue that such a behavior is typically associated with chaos synchronism. Numerical support using coupled chaotic systems including a class derived from a nonlinear partial differential equation is provided. (C) 2002 Elsevier Science Ltd. All rights reserved.

Original language	English
Pages (from-to)	219-232
Number of pages	14
Journal	Chaos, Solitons & Fractals
Volume	15
Issue number	2
DOIs	https://doi.org/10.1016/S0960-0779(02)00094-2
Publication status	Published - Jan 2003

Keywords

coupled-oscillator-systems
dynamical-systems
generalized synchronization
hyperchaos transition
lag synchronization
bifurcation
equation
scheme
orbits
motion

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10.1016/S0960-0779(02)00094-2

Cite this

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title = "Low-dimensional chaos in high-dimensional phase space: how does it occur?",

abstract = "A fundamental observation in nonlinear dynamics is that the asymptotic chaotic invariant sets in many high-dimensional systems are low-dimensional. We argue that such a behavior is typically associated with chaos synchronism. Numerical support using coupled chaotic systems including a class derived from a nonlinear partial differential equation is provided. (C) 2002 Elsevier Science Ltd. All rights reserved.",

keywords = "coupled-oscillator-systems, dynamical-systems, generalized synchronization, hyperchaos transition, lag synchronization, bifurcation, equation, scheme, orbits, motion",

author = "Ying-Cheng Lai and Bollt, \{E M\} and Liu, \{Z H\}",

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AU - Bollt, E M

AU - Liu, Z H

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Y1 - 2003/1

N2 - A fundamental observation in nonlinear dynamics is that the asymptotic chaotic invariant sets in many high-dimensional systems are low-dimensional. We argue that such a behavior is typically associated with chaos synchronism. Numerical support using coupled chaotic systems including a class derived from a nonlinear partial differential equation is provided. (C) 2002 Elsevier Science Ltd. All rights reserved.

AB - A fundamental observation in nonlinear dynamics is that the asymptotic chaotic invariant sets in many high-dimensional systems are low-dimensional. We argue that such a behavior is typically associated with chaos synchronism. Numerical support using coupled chaotic systems including a class derived from a nonlinear partial differential equation is provided. (C) 2002 Elsevier Science Ltd. All rights reserved.

KW - coupled-oscillator-systems

KW - dynamical-systems

KW - generalized synchronization

KW - hyperchaos transition

KW - lag synchronization

KW - bifurcation

KW - equation

KW - scheme

KW - orbits

KW - motion

U2 - 10.1016/S0960-0779(02)00094-2

DO - 10.1016/S0960-0779(02)00094-2

M3 - Article

SN - 0960-0779

VL - 15

SP - 219

EP - 232

JO - Chaos, Solitons & Fractals

JF - Chaos, Solitons & Fractals

IS - 2

ER -

Low-dimensional chaos in high-dimensional phase space: how does it occur?

Abstract

Keywords

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