Route to high-dimensional chaos

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

Research output: Contribution to journalArticle

55 Citations (Scopus)

Abstract

We present a route to high-dimensional chaos, that is, chaos with more than one positive Lyapunov exponent. In this route, as a system parameter changes, a subsystem becomes chaotic through, say, a cascade of period-doubling bifurcations, after which the complementary subsystem becomes chaotic, leading to an additional positive Lyapunov exponent for the whole system. A characteristic feature of this route, as suggested by numerical evidence, is that the second largest Lyapunov exponent passes through zero continuously. Three examples are presented: a discrete-time map, a continuous-time flow, and a population model for species dispersal in evolutionary ecology.

Original languageEnglish
Pages (from-to)R3799-R3802
Number of pages4
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume59
Issue number4
Publication statusPublished - Apr 1999

Keywords

  • PERIODIC-ORBITS
  • DYNAMIC-SYSTEMS
  • TRANSITION
  • ATTRACTORS
  • TURBULENCE
  • HYPERCHAOS
  • EQUATIONS
  • CRISES
  • MAPS

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