### 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 language | English |
---|---|

Pages (from-to) | R3313-R3316 |

Number of pages | 4 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 52 |

Issue number | 4 |

Publication status | Published - Oct 1995 |

### Keywords

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

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*52*(4), R3313-R3316.

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

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 52, no. 4, pp. R3313-R3316.

}

TY - JOUR

T1 - Intermingled basins and two-state on-off intermittency

AU - Lai, Ying-Cheng

AU - Grebogi, Celso

PY - 1995/10

Y1 - 1995/10

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.

KW - dynamic-systems

KW - oscillator

KW - chaos

KW - attractors

KW - motion

M3 - Article

VL - 52

SP - R3313-R3316

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

IS - 4

ER -