### 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

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

*62*(4), R4505-R4508.

**Catastrophe of riddling.** / Lai, Y C ; Lai, Ying-Cheng.

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 62, no. 4, pp. R4505-R4508.

}

TY - JOUR

T1 - Catastrophe of riddling

AU - Lai, Y C

AU - Lai, Ying-Cheng

PY - 2000/10

Y1 - 2000/10

N2 - 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.

AB - 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.

KW - FRACTAL BASIN BOUNDARIES

KW - CHAOTIC ATTRACTORS

KW - DYNAMICAL-SYSTEMS

KW - BIFURCATION

KW - TRANSIENTS

M3 - Article

VL - 62

SP - R4505-R4508

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 -