Destruction of Chaotic Attractors in Coupled Chaotic Systems

We investigate the sudden destruction of hyperchaotic attractors in symmetrically coupled onedimensional maps. An asynchronous hyperchaotic attractor may appear through a blow-out bifurcation, where the synchronous chaotic attractor on the invariant synchronization line becomes unstable with respect to perturbations transverse to the synchronization line. It is found that such a hyperchaotic attractor may be broken up suddenly through stabilization of a periodic saddle embedded in the hyperchaotic attractor via a reverse subcritical pitchfork or period-doubling bifurcation. After break up of the hyperchaotic attractor, the asymptotic state transforms from the hyperchaotic state to a periodic state. Note that this sudden destruction of the hyperchaotic attractor occurs without any collision with its basin boundary, in constrast to the boundary crisis and is robust under a small perturbation of parameter mismatching.