Intermingled basins and two-state on-off intermittency

Ying-Cheng Lai, Celso Grebogi

Research output: Contribution to journalArticle

138 Citations (Scopus)

Abstract

We consider dynamical systems which possess two low-dimensional symmetric invariant subspaces. In each subspace, there is a chaotic attractor, and there are no other attractors in the phase space. As a parameter of the system changes, the largest Lyapunov exponents transverse to the invariant subspaces can change from negative to positive: the former corresponds to the situation where the basins of the attractors are intermingled, while the latter corresponds to the case where the system exhibits a two-state on-off intermittency. The phenomenon is investigated using a physical example where particles move in a two-dimensional potential, subjected to friction and periodic forcing.

Original languageEnglish
Pages (from-to)R3313-R3316
Number of pages4
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume52
Issue number4
Publication statusPublished - Oct 1995

Keywords

  • dynamic-systems
  • oscillator
  • chaos
  • attractors
  • motion

Cite this

Intermingled basins and two-state on-off intermittency. / Lai, Ying-Cheng; Grebogi, Celso.

In: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 52, No. 4, 10.1995, p. R3313-R3316.

Research output: Contribution to journalArticle

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N2 - We consider dynamical systems which possess two low-dimensional symmetric invariant subspaces. In each subspace, there is a chaotic attractor, and there are no other attractors in the phase space. As a parameter of the system changes, the largest Lyapunov exponents transverse to the invariant subspaces can change from negative to positive: the former corresponds to the situation where the basins of the attractors are intermingled, while the latter corresponds to the case where the system exhibits a two-state on-off intermittency. The phenomenon is investigated using a physical example where particles move in a two-dimensional potential, subjected to friction and periodic forcing.

AB - We consider dynamical systems which possess two low-dimensional symmetric invariant subspaces. In each subspace, there is a chaotic attractor, and there are no other attractors in the phase space. As a parameter of the system changes, the largest Lyapunov exponents transverse to the invariant subspaces can change from negative to positive: the former corresponds to the situation where the basins of the attractors are intermingled, while the latter corresponds to the case where the system exhibits a two-state on-off intermittency. The phenomenon is investigated using a physical example where particles move in a two-dimensional potential, subjected to friction and periodic forcing.

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