Characterization of blowout bifurcation by unstable periodic orbits

Yoshihiko Nagai, 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 (US)
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume55
Issue number2
StatePublished - 1997
Externally publishedYes

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Periodic Orbits
Bifurcation
Unstable
orbits
Chaotic Attractor
Transverse
Chaotic Dynamical Systems
dynamical systems
eigenvalues
Invariant Subspace
Eigenvalue
Distinct

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

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AU - Lai, Ying-Cheng

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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.

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