Partial Synchronization in a System of Coupled Logistic Maps

Clustering (or partial synchronization) in a system of globally coupled chaotic oscillators is studied by means of a model of three coupled logistic maps. For this model we determine the regions in parameter space where total and partial synchronization take place, examine the bifurcations through which total synchronization tone-cluster dynamics) breaks down to give way to two- and three-cluster dynamics, and follow the subsequent transformations of the various asynchronous periodic, quasiperiodic and chaotic states. Different forms of riddling of the basins of attraction for the fully synchronized state are observed, and we discuss the mechanisms through which they arise.