Destruction of Chaotic Attractors in Coupled Chaotic Systems

with respect to the strength of a coupling parameter. By varying the coupling parameter, we investigate the sudden break-up of HCAs in symmetrically coupled one- dimensional (1D) maps. It is found that, when the cou- pling parameter passes through a threshold value, a HCA breaks up suddenly when a periodic saddle embedded in the HCA becomes stabilized via a reverse subcriti- cal pitchfork or period-doubling bifurcation. Then the asymptotic state of the system changes from a hyperchaotic state to a periodic state. Note also that the sudden destruction of the HCA occurs without any collision with its basin boundary. Hence the old basin becomes occupied by the new periodic attractor. This is in con- trast to the case of the boundary crisis [4], where the sudden destruction of both a chaotic attractor and its basin occurs when the chaotic attractor collides with its basin boundary. In order to examine robustness of the destruction of the HCAs, we also introduce a small perturbation of p