Loss of coherence in a system of globally coupled maps - art. no. 026205

We study the formation of symmetric (i.e., equally sized) or nearly symmetr ic clusters in an ensemble of the coherent state and globally coupled, iden tical chaotic maps. It is shown that the loss of synchronization for the em ergence of subgroups of oscillators with synchronized behavior are two dist inct processes, and that the type of behavior that arises after the loss of total synchronization depends sensitively on the dynamics of the individua l map. For our system of globally coupled logistic maps, symmetric two-clus ter formation is found to proceed through a periodic state associated with the stabilization either of an asynchronous period-2 cycle or of an asynchr onous period-4 cycle. With further reduction of the coupling strength, each of the principal clustering states undergoes additional bifurcations leadi ng to cycles of higher periodicity or to quasiperiodic and chaotic dynamics . If desynchronization of the coherent chaotic state occurs before the form ation of stable clusters becomes possible, high-dimensional chaotic motion is observed in the intermediate parameter interval.