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 |
|---|---|
| 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