Bifurcation to high-dimensional chaos

M A Harrison, Y C Lai, Ying-Cheng Lai

Research output: Contribution to journalArticle

14 Citations (Scopus)

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
Pages (from-to)1471-1483
Number of pages13
JournalInternational Journal of Bifurcation and Chaos
Volume10
Issue number6
Publication statusPublished - Jun 2000

Keywords

  • DYNAMICAL-SYSTEMS
  • PERIODIC-ORBITS
  • RING CAVITY
  • ATTRACTORS
  • TRANSITION
  • HYPERCHAOS
  • OSCILLATORS
  • SYNCHRONIZATION
  • INSTABILITY
  • COMPLEXITY

Cite this

Harrison, M. A., Lai, Y. C., & Lai, Y-C. (2000). Bifurcation to high-dimensional chaos. International Journal of Bifurcation and Chaos, 10(6), 1471-1483.