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

Ying-Cheng Lai; Erik M. Bollt; Zonghua Liu

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

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

Ying-Cheng Lai, Erik M. Bollt, Zonghua Liu

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

9 Scopus citations

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.

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

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematics(all)
Physics and Astronomy(all)
Applied Mathematics

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10.1016/S0960-0779(02)00094-2

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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.",

author = "Ying-Cheng Lai and Bollt, {Erik M.} and Zonghua Liu",

note = "Funding Information: We thank L. Sauter for discussions during the initial phase of the project. YCL and ZL are supported by AFOSR under grant no. F49620-98-1-0400 and by NSF under grant no. PHY-9996454. EMB is supported by NSF under grant no. DMS-0071314.",

year = "2003",

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doi = "10.1016/S0960-0779(02)00094-2",

language = "English (US)",

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TY - JOUR

T1 - Low-dimensional chaos in high-dimensional phase space

T2 - How does it occur?

AU - Lai, Ying-Cheng

AU - Bollt, Erik M.

AU - Liu, Zonghua

N1 - Funding Information: We thank L. Sauter for discussions during the initial phase of the project. YCL and ZL are supported by AFOSR under grant no. F49620-98-1-0400 and by NSF under grant no. PHY-9996454. EMB is supported by NSF under grant no. DMS-0071314.

PY - 2003/1

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.

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.

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

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SP - 219

EP - 232

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

IS - 2

ER -

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

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