Route to high-dimensional chaos

Mary Ann Harrison, Ying Cheng Lai

Research output: Contribution to journalArticle

55 Scopus citations

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 (US)
Pages (from-to)R3799-R3802
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume59
Issue number4
DOIs
StatePublished - Jan 1 1999
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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