Elsevier

Physica D: Nonlinear Phenomena

Volume 76, Issue 4, 15 September 1994, Pages 384-410
Physica D: Nonlinear Phenomena

The transition to chaotic attractors with riddled basins

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Abstract

Recently it has been shown that there are chaotic attractors whose basins are such that any point in the basin has pieces of another attractor basin arbitrarily nearby (the basin is “riddled” with holes). Here we consider the dynamics near the transition to this situation as a parameter is varied. Using a simple analyzable model, we obtain the characteristic behaviors near this transition. Numerical tests on a more typical system are consistent with the conjecture that these results are universal for the class of systems considered.

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