Riddling bifurcation in chaotic dynamical systems

Ying Cheng Lai, Celso Grebogi, James A. Yorke, Shankar C Venkataramani

Research output: Contribution to journalArticle

181 Citations (Scopus)

Abstract

When a chaotic attractor lies in an invariant subspace, as in systems with symmetry, riddling can occur. Riddling refers to the situation where the basin of a chaotic attractor is riddled with holes that belong to the basin of another attractor. We establish properties of the riddling bifurcation that occurs when an unstable periodic orbit embedded in the chaotic attractor, usually of low period, becomes transversely unstable. An immediate physical consequence of the riddling bifurcation is that an extraordinarily low fraction of the trajectories in the invariant subspace diverge when there is a symmetry breaking.

Original languageEnglish (US)
Pages (from-to)55-58
Number of pages4
JournalPhysical Review Letters
Volume77
Issue number1
StatePublished - 1996
Externally publishedYes

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dynamical systems
broken symmetry
trajectories
orbits
symmetry

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Lai, Y. C., Grebogi, C., Yorke, J. A., & Venkataramani, S. C. (1996). Riddling bifurcation in chaotic dynamical systems. Physical Review Letters, 77(1), 55-58.

Riddling bifurcation in chaotic dynamical systems. / Lai, Ying Cheng; Grebogi, Celso; Yorke, James A.; Venkataramani, Shankar C.

In: Physical Review Letters, Vol. 77, No. 1, 1996, p. 55-58.

Research output: Contribution to journalArticle

Lai, YC, Grebogi, C, Yorke, JA & Venkataramani, SC 1996, 'Riddling bifurcation in chaotic dynamical systems', Physical Review Letters, vol. 77, no. 1, pp. 55-58.
Lai, Ying Cheng ; Grebogi, Celso ; Yorke, James A. ; Venkataramani, Shankar C. / Riddling bifurcation in chaotic dynamical systems. In: Physical Review Letters. 1996 ; Vol. 77, No. 1. pp. 55-58.
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