### Abstract

Most existing works on riddling assume that the underlying dynamical system possesses an invariant subspace. We find that, under arbitrarily small, deterministic perturbations, a riddled basin is typically destroyed and replaced by fractal ones, a catastrophe of riddling. We elucidate, based on analyzing unstable periodic orbits, the dynamical mechanism of the catastrophe. Analysis of the critical behaviors leads to the finding of a transient chaotic behavior that is different from those reported previously.

Original language | English |
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Pages (from-to) | R4505-R4508 |

Number of pages | 4 |

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

Volume | 62 |

Issue number | 4 |

Publication status | Published - Oct 2000 |

### Keywords

- FRACTAL BASIN BOUNDARIES
- CHAOTIC ATTRACTORS
- DYNAMICAL-SYSTEMS
- BIFURCATION
- TRANSIENTS

## Cite this

Lai, Y. C., & Lai, Y-C. (2000). Catastrophe of riddling.

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,*62*(4), R4505-R4508.