### 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 |
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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 |

Publication status | Published - Oct 1997 |

### Keywords

- ON-OFF INTERMITTENCY
- SYMMETRY-BREAKING BIFURCATION
- FRACTAL BASIN BOUNDARIES
- DYNAMICAL-SYSTEMS
- INTERMINGLED BASINS
- SYNCHRONIZED CHAOS
- ATTRACTORS
- OSCILLATORS
- TRANSIENTS
- INSTABILITY

### Cite this

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

*56*(4), 3897-3908.