Transition among synchronized states mediated by attractor-repeller collision crisis

We studied the transition from a single-value generalized synchronization state to a double-value one in a unidirectionally coupled two-dimensional map system. It is found that this discontinuous transition is mediated by the attractor-repeller collision crisis and is different from the blowout bifurcation in many respects. By using the unstable periodic orbits decomposition method, it is shown that the attractor is generally nondifferential in the parameter regime about the transition. Based on the nondifferential character of the attractor, we propose a mechanism for the attractor-repeller collision crisis.