Symmetry-breaking bifurcation with on-off intermittency in chaotic dynamical systems

Ying-Cheng Lai

Research output: Contribution to journalArticle

58 Citations (Scopus)

Abstract

When a dynamical system possesses certain symmetry, there can be an invariant subspace in the phase space. In the invariant subspace there can be a chaotic attractor. As a parameter changes through a critical value, the chaotic attractor can lose stability with respect to perturbations transverse to the invariant subspace. We show that the loss of the transverse stability can lead to a symmetry-breaking bifurcation characterized by lack of the system symmetry in the asymptotic attractor. An accompanying physical phenomenon is an extreme type of temporally intermittent bursting behavior. The mechanism for this type of symmetry-breaking bifurcation is elucidated.

Original languageEnglish
Pages (from-to)R4267-R4270
Number of pages4
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume53
Issue number5
DOIs
Publication statusPublished - May 1996

Keywords

  • attractors
  • oscillators

Cite this

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abstract = "When a dynamical system possesses certain symmetry, there can be an invariant subspace in the phase space. In the invariant subspace there can be a chaotic attractor. As a parameter changes through a critical value, the chaotic attractor can lose stability with respect to perturbations transverse to the invariant subspace. We show that the loss of the transverse stability can lead to a symmetry-breaking bifurcation characterized by lack of the system symmetry in the asymptotic attractor. An accompanying physical phenomenon is an extreme type of temporally intermittent bursting behavior. The mechanism for this type of symmetry-breaking bifurcation is elucidated.",
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N2 - When a dynamical system possesses certain symmetry, there can be an invariant subspace in the phase space. In the invariant subspace there can be a chaotic attractor. As a parameter changes through a critical value, the chaotic attractor can lose stability with respect to perturbations transverse to the invariant subspace. We show that the loss of the transverse stability can lead to a symmetry-breaking bifurcation characterized by lack of the system symmetry in the asymptotic attractor. An accompanying physical phenomenon is an extreme type of temporally intermittent bursting behavior. The mechanism for this type of symmetry-breaking bifurcation is elucidated.

AB - When a dynamical system possesses certain symmetry, there can be an invariant subspace in the phase space. In the invariant subspace there can be a chaotic attractor. As a parameter changes through a critical value, the chaotic attractor can lose stability with respect to perturbations transverse to the invariant subspace. We show that the loss of the transverse stability can lead to a symmetry-breaking bifurcation characterized by lack of the system symmetry in the asymptotic attractor. An accompanying physical phenomenon is an extreme type of temporally intermittent bursting behavior. The mechanism for this type of symmetry-breaking bifurcation is elucidated.

KW - attractors

KW - oscillators

U2 - 10.1103/PhysRevE.53.R4267

DO - 10.1103/PhysRevE.53.R4267

M3 - Article

VL - 53

SP - R4267-R4270

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

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ER -