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

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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 bifur-cation is elucidated.

Original languageEnglish (US)
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume53
Issue number5 SUPPL. A
StatePublished - 1996
Externally publishedYes

Fingerprint

Chaotic Dynamical Systems
Intermittency
intermittency
Invariant Subspace
Symmetry Breaking
dynamical systems
broken symmetry
Bifurcation
Chaotic Attractor
Transverse
Symmetry
Bursting
symmetry
Critical value
Attractor
Phase Space
Extremes
Dynamical system
Perturbation
cations

ASJC Scopus subject areas

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

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 bifur-cation is elucidated.",
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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 bifur-cation is elucidated.

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