Characterization of blowout bifurcation by unstable periodic orbits

Y Nagai, Y C Lai, Ying-Cheng Lai

Research output: Contribution to journalArticle

34 Citations (Scopus)

Abstract

Blowout bifurcation in chaotic dynamical systems occurs when a chaotic attractor, lying in some invariant subspace, becomes transversely unstable. We establish quantitative characterization of the blowout bifurcation by unstable periodic orbits embedded in the chaotic attractor. We argue that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits. There are two distinct groups of periodic orbits: one transversely stable and another transversely unstable. The bifurcation occurs when some properly weighted transverse eigenvalues of these two groups are balanced.

Original languageEnglish
Pages (from-to)R1251-R1254
Number of pages4
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume55
Issue number2
Publication statusPublished - Feb 1997

Keywords

  • ON-OFF INTERMITTENCY
  • CHAOTIC ATTRACTORS
  • STRANGE ATTRACTORS
  • RIDDLED BASINS
  • SYSTEMS
  • METAMORPHOSES
  • DIMENSIONS
  • BOUNDARIES
  • MOTION

Cite this

Characterization of blowout bifurcation by unstable periodic orbits. / Nagai, Y ; Lai, Y C ; Lai, Ying-Cheng.

In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 55, No. 2, 02.1997, p. R1251-R1254.

Research output: Contribution to journalArticle

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AU - Lai, Ying-Cheng

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N2 - Blowout bifurcation in chaotic dynamical systems occurs when a chaotic attractor, lying in some invariant subspace, becomes transversely unstable. We establish quantitative characterization of the blowout bifurcation by unstable periodic orbits embedded in the chaotic attractor. We argue that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits. There are two distinct groups of periodic orbits: one transversely stable and another transversely unstable. The bifurcation occurs when some properly weighted transverse eigenvalues of these two groups are balanced.

AB - Blowout bifurcation in chaotic dynamical systems occurs when a chaotic attractor, lying in some invariant subspace, becomes transversely unstable. We establish quantitative characterization of the blowout bifurcation by unstable periodic orbits embedded in the chaotic attractor. We argue that the bifurcation is mediated by changes in the transverse stability of an infinite number of unstable periodic orbits. There are two distinct groups of periodic orbits: one transversely stable and another transversely unstable. The bifurcation occurs when some properly weighted transverse eigenvalues of these two groups are balanced.

KW - ON-OFF INTERMITTENCY

KW - CHAOTIC ATTRACTORS

KW - STRANGE ATTRACTORS

KW - RIDDLED BASINS

KW - SYSTEMS

KW - METAMORPHOSES

KW - DIMENSIONS

KW - BOUNDARIES

KW - MOTION

M3 - Article

VL - 55

SP - R1251-R1254

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

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

SN - 1063-651X

IS - 2

ER -