Crises and riddling behavior of 2-dimensional symmetric chaotic systems

Crises and riddling behavior describe the occurrence of sudden qualitative changes of chaotic attractors, that are important topics in the recent research of nonlinear dynamical systems. In this paper, phenomena of crises and riddled basins in a certain D-m-symmetric chaotic system are investigated by using stable and unstable manifolds of periodic saddles. It can be found from the analyses that the symmetry axes, serving as one-dimensional invariant subspaces, play a key role. In order to study the quantitative measurement for riddled basins the concept of riddling ratio is introduced in this paper.