Bifurcation to high-dimensional chaos

Mary Ann Harrison, Ying-Cheng Lai

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

High-dimensional chaos has been an area of growing recent investigation. The questions of how dynamical systems become high-dimensionally chaotic with multiple positive Lyapunov exponents, and what the characteristic features associated with the transition are, remain less investigated. In this paper, we present one possible route to high-dimensional chaos. By this route, a subsystem becomes chaotic with one positive Lyapunov exponent via one of the known routes to low-dimensional chaos, after which the complementary subsystem becomes chaotic, leading to additional positive Lyapunov exponents for the whole system. A characteristic feature of this route is that the additional Lyapunov exponents pass through zero smoothly. As a consequence, the fractal dimension of the chaotic attractor changes continuously through the transition, in contrast to the transition to low-dimensional chaos at which the fractal dimension changes abruptly. We present a heuristic theory and numerical examples to illustrate this route to high-dimensional chaos.

Original languageEnglish (US)
Pages (from-to)1471-1483
Number of pages13
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Volume10
Issue number6
DOIs
StatePublished - Jun 2000

ASJC Scopus subject areas

  • Modeling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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