### Abstract

Recent work has considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. The existence of invariant subspace often relies on certain symmetry of the system, which is, however, a nongeneric property as system defects and small random noise can destroy the symmetry. This paper addresses the influence of noise on riddling. We show that riddling can actually be induced by arbitrarily small noise even in parameter regimes where one expects no riddling in the absence of noise. Specifically, we argue that when there are attractors located off the invariant subspace, the basins of these attractors can be temporally riddled even when the chaotic attractor in the invariant subspace is transversely unstable. We investigate universal scaling laws for noise-induced temporal riddling. Our results imply that the phenomenon of riddling is robust, and it can be more prevalent than expected before, as noise is practically inevitable in physical systems.

Original language | English (US) |
---|---|

Pages (from-to) | 3897-3908 |

Number of pages | 12 |

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

Volume | 56 |

Issue number | 4 |

State | Published - 1997 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

**Scaling laws for noise-induced temporal riddling in chaotic systems.** / Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 56, no. 4, pp. 3897-3908.

}

TY - JOUR

T1 - Scaling laws for noise-induced temporal riddling in chaotic systems

AU - Lai, Ying-Cheng

PY - 1997

Y1 - 1997

N2 - Recent work has considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. The existence of invariant subspace often relies on certain symmetry of the system, which is, however, a nongeneric property as system defects and small random noise can destroy the symmetry. This paper addresses the influence of noise on riddling. We show that riddling can actually be induced by arbitrarily small noise even in parameter regimes where one expects no riddling in the absence of noise. Specifically, we argue that when there are attractors located off the invariant subspace, the basins of these attractors can be temporally riddled even when the chaotic attractor in the invariant subspace is transversely unstable. We investigate universal scaling laws for noise-induced temporal riddling. Our results imply that the phenomenon of riddling is robust, and it can be more prevalent than expected before, as noise is practically inevitable in physical systems.

AB - Recent work has considered the situation of riddling where, when a chaotic attractor lying in an invariant subspace is transversely stable, the basin of the attractor can be riddled with holes that belong to the basin of another attractor. The existence of invariant subspace often relies on certain symmetry of the system, which is, however, a nongeneric property as system defects and small random noise can destroy the symmetry. This paper addresses the influence of noise on riddling. We show that riddling can actually be induced by arbitrarily small noise even in parameter regimes where one expects no riddling in the absence of noise. Specifically, we argue that when there are attractors located off the invariant subspace, the basins of these attractors can be temporally riddled even when the chaotic attractor in the invariant subspace is transversely unstable. We investigate universal scaling laws for noise-induced temporal riddling. Our results imply that the phenomenon of riddling is robust, and it can be more prevalent than expected before, as noise is practically inevitable in physical systems.

UR - http://www.scopus.com/inward/record.url?scp=0031245212&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0031245212&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0031245212

VL - 56

SP - 3897

EP - 3908

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 4

ER -