Unstable dimension variability and complexity in chaotic systems

Y C  Lai; Ying-Cheng Lai

Unstable dimension variability and complexity in chaotic systems

Y C Lai, Ying-Cheng Lai

Physics

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

29 Citations (Scopus)

Abstract

We examine the interplay between complexity and unstable periodic orbits in high-dimensional chaotic systems. Argument and numerical evidence are presented suggesting that complexity can arise when the system is severely nonhyperbolic in the sense that periodic orbits with a distinct number of unstable directions coexist and are densely mixed. A quantitative measure is introduced to characterize this unstable dimension variability.

Original language	English
Pages (from-to)	R3807-R3810
Number of pages	4
Journal	Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume	59
Issue number	4
Publication status	Published - Apr 1999

Keywords

PERIODIC-ORBITS
DYNAMICAL-SYSTEMS
RING CAVITY
ATTRACTORS
BASINS

Cite this

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title = "Unstable dimension variability and complexity in chaotic systems",

abstract = "We examine the interplay between complexity and unstable periodic orbits in high-dimensional chaotic systems. Argument and numerical evidence are presented suggesting that complexity can arise when the system is severely nonhyperbolic in the sense that periodic orbits with a distinct number of unstable directions coexist and are densely mixed. A quantitative measure is introduced to characterize this unstable dimension variability.",

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author = "Lai, {Y C} and Ying-Cheng Lai",

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T1 - Unstable dimension variability and complexity in chaotic systems

AU - Lai, Y C

AU - Lai, Ying-Cheng

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N2 - We examine the interplay between complexity and unstable periodic orbits in high-dimensional chaotic systems. Argument and numerical evidence are presented suggesting that complexity can arise when the system is severely nonhyperbolic in the sense that periodic orbits with a distinct number of unstable directions coexist and are densely mixed. A quantitative measure is introduced to characterize this unstable dimension variability.

AB - We examine the interplay between complexity and unstable periodic orbits in high-dimensional chaotic systems. Argument and numerical evidence are presented suggesting that complexity can arise when the system is severely nonhyperbolic in the sense that periodic orbits with a distinct number of unstable directions coexist and are densely mixed. A quantitative measure is introduced to characterize this unstable dimension variability.

KW - PERIODIC-ORBITS

KW - DYNAMICAL-SYSTEMS

KW - RING CAVITY

KW - ATTRACTORS

KW - BASINS

M3 - Article

SN - 1063-651X

VL - 59

SP - R3807-R3810

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

IS - 4

ER -

Unstable dimension variability and complexity in chaotic systems

Abstract

Keywords

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