Distinct small-distance scaling behavior of on-off intermittency in chaotic dynamical systems

Y C Lai, Ying-Cheng Lai

Research output: Contribution to journalArticle

41 Citations (Scopus)

Abstract

On-off intermittency in chaotic dynamical systems refers to the situation where some dynamical variables exhibit two distinct states in their course of time evolution. One is the ''off'' state, where the variables remain approximately a constant, and the other is the ''on'' state, when the variables temporarily burst out of the off state. Previous work demonstrates that there appears to be a universal scaling behavior for on-off intermittency. In particular, the length of off time intervals, or the length of the laminar phase, obeys the algebraic scaling law. We present evidence that there are in fact distinct classes of on-off intermittency. Although the statistics of their laminar phase obeys the algebraic scaling, quantities such as the average transient time for trajectories to fall in a small neighborhood of the asymptotic off state exhibit qualitatively different scaling behaviors. The dynamical origin for producing these distinct classes of on-off intermittency is elucidated.

Original languageEnglish
Pages (from-to)321-327
Number of pages7
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume54
Issue number1
Publication statusPublished - Jul 1996

Keywords

  • RIDDLED BASINS
  • ATTRACTORS
  • TRANSITION

Cite this

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title = "Distinct small-distance scaling behavior of on-off intermittency in chaotic dynamical systems",
abstract = "On-off intermittency in chaotic dynamical systems refers to the situation where some dynamical variables exhibit two distinct states in their course of time evolution. One is the ''off'' state, where the variables remain approximately a constant, and the other is the ''on'' state, when the variables temporarily burst out of the off state. Previous work demonstrates that there appears to be a universal scaling behavior for on-off intermittency. In particular, the length of off time intervals, or the length of the laminar phase, obeys the algebraic scaling law. We present evidence that there are in fact distinct classes of on-off intermittency. Although the statistics of their laminar phase obeys the algebraic scaling, quantities such as the average transient time for trajectories to fall in a small neighborhood of the asymptotic off state exhibit qualitatively different scaling behaviors. The dynamical origin for producing these distinct classes of on-off intermittency is elucidated.",
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T1 - Distinct small-distance scaling behavior of on-off intermittency in chaotic dynamical systems

AU - Lai, Y C

AU - Lai, Ying-Cheng

PY - 1996/7

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N2 - On-off intermittency in chaotic dynamical systems refers to the situation where some dynamical variables exhibit two distinct states in their course of time evolution. One is the ''off'' state, where the variables remain approximately a constant, and the other is the ''on'' state, when the variables temporarily burst out of the off state. Previous work demonstrates that there appears to be a universal scaling behavior for on-off intermittency. In particular, the length of off time intervals, or the length of the laminar phase, obeys the algebraic scaling law. We present evidence that there are in fact distinct classes of on-off intermittency. Although the statistics of their laminar phase obeys the algebraic scaling, quantities such as the average transient time for trajectories to fall in a small neighborhood of the asymptotic off state exhibit qualitatively different scaling behaviors. The dynamical origin for producing these distinct classes of on-off intermittency is elucidated.

AB - On-off intermittency in chaotic dynamical systems refers to the situation where some dynamical variables exhibit two distinct states in their course of time evolution. One is the ''off'' state, where the variables remain approximately a constant, and the other is the ''on'' state, when the variables temporarily burst out of the off state. Previous work demonstrates that there appears to be a universal scaling behavior for on-off intermittency. In particular, the length of off time intervals, or the length of the laminar phase, obeys the algebraic scaling law. We present evidence that there are in fact distinct classes of on-off intermittency. Although the statistics of their laminar phase obeys the algebraic scaling, quantities such as the average transient time for trajectories to fall in a small neighborhood of the asymptotic off state exhibit qualitatively different scaling behaviors. The dynamical origin for producing these distinct classes of on-off intermittency is elucidated.

KW - RIDDLED BASINS

KW - ATTRACTORS

KW - TRANSITION

M3 - Article

VL - 54

SP - 321

EP - 327

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

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

SN - 1063-651X

IS - 1

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