### Abstract

When a chaotic attractor lies in an invariant subspace, as in systems with symmetry, riddling can occur. Riddling refers to the situation where the basin of a chaotic attractor is riddled with holes that belong to the basin of another attractor. We establish properties of the riddling bifurcation that occurs when an unstable periodic orbit embedded in the chaotic attractor, usually of low period, becomes transversely unstable. An immediate physical consequence of the riddling bifurcation is that an extraordinarily low fraction of the trajectories in the invariant subspace diverge when there is a symmetry breaking.

Original language | English |
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Pages (from-to) | 55-58 |

Number of pages | 4 |

Journal | Physical Review Letters |

Volume | 77 |

Issue number | 1 |

Publication status | Published - 1 Jul 1996 |

### Keywords

- TRANSIENTS
- ATTRACTORS

### Cite this

*Physical Review Letters*,

*77*(1), 55-58.

**Riddling bifurcation in chaotic dynamical systems.** / Lai, Y C ; Grebogi, C ; Yorke, J A ; Venkataramani, S C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review Letters*, vol. 77, no. 1, pp. 55-58.

}

TY - JOUR

T1 - Riddling bifurcation in chaotic dynamical systems

AU - Lai, Y C

AU - Grebogi, C

AU - Yorke, J A

AU - Venkataramani, S C

AU - Lai, Ying-Cheng

PY - 1996/7/1

Y1 - 1996/7/1

N2 - When a chaotic attractor lies in an invariant subspace, as in systems with symmetry, riddling can occur. Riddling refers to the situation where the basin of a chaotic attractor is riddled with holes that belong to the basin of another attractor. We establish properties of the riddling bifurcation that occurs when an unstable periodic orbit embedded in the chaotic attractor, usually of low period, becomes transversely unstable. An immediate physical consequence of the riddling bifurcation is that an extraordinarily low fraction of the trajectories in the invariant subspace diverge when there is a symmetry breaking.

AB - When a chaotic attractor lies in an invariant subspace, as in systems with symmetry, riddling can occur. Riddling refers to the situation where the basin of a chaotic attractor is riddled with holes that belong to the basin of another attractor. We establish properties of the riddling bifurcation that occurs when an unstable periodic orbit embedded in the chaotic attractor, usually of low period, becomes transversely unstable. An immediate physical consequence of the riddling bifurcation is that an extraordinarily low fraction of the trajectories in the invariant subspace diverge when there is a symmetry breaking.

KW - TRANSIENTS

KW - ATTRACTORS

M3 - Article

VL - 77

SP - 55

EP - 58

JO - Physical Review Letters

JF - Physical Review Letters

SN - 0031-9007

IS - 1

ER -