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

Cite this

Route to high-dimensional chaos. / Harrison, M A ; Lai, Y C ; Lai, Ying-Cheng.

In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 59, No. 4, 04.1999, p. R3799-R3802.

Research output: Contribution to journalArticle

Harrison, M A ; Lai, Y C ; Lai, Ying-Cheng. / Route to high-dimensional chaos. In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 1999 ; Vol. 59, No. 4. pp. R3799-R3802.
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KW - DYNAMIC-SYSTEMS

KW - TRANSITION

KW - ATTRACTORS

KW - TURBULENCE

KW - HYPERCHAOS

KW - EQUATIONS

KW - CRISES

KW - MAPS

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JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

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SN - 1063-651X

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ER -