Synchronization and clustering in ensembles of coupled chaotic oscillators

When identical chaotic oscillators interact, a state of complete or partial synchronization may be attained, providing a special kind of dynamical patterns called clusters. The simplest, coherent clusters arise when all oscillators display the same temporal behavior. Others, more complicated clusters are developed when population of the oscillators splits into subgroups such that all oscillators within a given group move in synchrony. Considering a system of mean-field coupled logistic maps, we study in details the transition from coherence to clustering and demonstrate that there are four different mechanisms of the desynchronization: riddling and blowout bifurcations, appearance of symmetric and asymmetric clusters. We also investigate the cluster-splitting bifurcation when the underlying dynamics is periodic. For the system of three and four coupled Rossler oscillators, we prove the existence of clusters and describe related bifurcations and in-cluster dynamics.