Catastrophe of riddling

Y C Lai, Ying-Cheng Lai

Research output: Contribution to journalArticle

8 Citations (Scopus)

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 languageEnglish
Pages (from-to)R4505-R4508
Number of pages4
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume62
Issue number4
Publication statusPublished - Oct 2000

Keywords

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

Cite this