Transition from strange nonchaotic to strange chaotic attractors

Y C Lai, Ying-Cheng Lai

Research output: Contribution to journalArticle

67 Citations (Scopus)

Abstract

We investigate the transition from strange nonchaotic to strange chaotic attractors in quasiperiodically driven dynamical systems. It is found that whether,the asymptotic attractor of the system is strange nonchaotic or strange chaotic is determined by the relative weight of the contraction and expansion for infinitesimal vectors along a typical trajectory on the attractor. When the average contraction dominates the average expansion, the attractor is strange nonchaotic. Strange chaotic attractors arise-when the average expansion dominates the average contraction. The transition from strange nonchaotic to strange chaotic attractors occurs when the average contraction and expansion are balanced. A characteristic signature of this route to chaos is that the Lyapunov exponent passes through zero linearly. We provide numerical confirmation using both a quasiperiodically driven map and a quasiperiodic flow.

Original languageEnglish
Pages (from-to)57-65
Number of pages9
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume53
Issue number1
Publication statusPublished - Jan 1996

Keywords

  • DYNAMICAL-SYSTEMS
  • TURBULENCE
  • CRISES
  • FLUID

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