Scaling laws for symmetry breaking by blowout bifurcation in chaotic systems

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17 Citations (Scopus)

Abstract

Recent works have demonstrated that a blowout bifurcation can lead to symmetry breaking in chaotic systems with a simple kind of symmetry. That is, as a system parameter changes, when a chaotic attractor lying in some invariant subspace becomes unstable with respect to perturbations transverse to the invariant subspace, a symmetry-broken attractor can be born. As the parameter varies further, a symmetry-increasing bifurcation can occur, after which the attractor possesses the system symmetry. The purpose of this paper is to present numerical experiments and heuristic arguments for the scaling laws associated with this type of symmetry-breaking and symmetry-increasing bifurcations. Specifically, we investigate (1) the scaling of the average transient time preceding the blowout bifurcation and (2) the scaling of the average switching time after the symmetry-increasing bifurcation. We also study the effect of noise. It is found that small-amplitude noise can restore the symmetry in the attractor after the blowout bifurcation and that the average time for trajectories to switch between the symmetry-broken components of the attractor scales algebraically with the noise amplitude.

Original languageEnglish (US)
Pages (from-to)1407-1413
Number of pages7
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume56
Issue number2
StatePublished - Aug 1997
Externally publishedYes

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Scaling Laws
Symmetry Breaking
scaling laws
Chaotic System
broken symmetry
Bifurcation
Symmetry
symmetry
Attractor
Invariant Subspace
scaling
Scaling
Chaotic Attractor
Time-average
switches
trajectories
perturbation
Switch
Transverse
Unstable

ASJC Scopus subject areas

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

Cite this

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abstract = "Recent works have demonstrated that a blowout bifurcation can lead to symmetry breaking in chaotic systems with a simple kind of symmetry. That is, as a system parameter changes, when a chaotic attractor lying in some invariant subspace becomes unstable with respect to perturbations transverse to the invariant subspace, a symmetry-broken attractor can be born. As the parameter varies further, a symmetry-increasing bifurcation can occur, after which the attractor possesses the system symmetry. The purpose of this paper is to present numerical experiments and heuristic arguments for the scaling laws associated with this type of symmetry-breaking and symmetry-increasing bifurcations. Specifically, we investigate (1) the scaling of the average transient time preceding the blowout bifurcation and (2) the scaling of the average switching time after the symmetry-increasing bifurcation. We also study the effect of noise. It is found that small-amplitude noise can restore the symmetry in the attractor after the blowout bifurcation and that the average time for trajectories to switch between the symmetry-broken components of the attractor scales algebraically with the noise amplitude.",
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