Cluster synchronization in networked nonidentical chaotic oscillators.

In exploring oscillator synchronization, a general observation is that as the oscillators become nonidentical, e.g., introducing parameter mismatch among the oscillators, the propensity for synchronization will be deteriorated. Yet in realistic systems, parameter mismatch is unavoidable and even worse in some circumstances, the oscillators might follow different types of dynamics. Considering the significance of synchronization to the functioning of many realistic systems, it is natural to ask the following question: Can synchronization be achieved in networked oscillators of clearly different parameters or dynamics? Here, by the model of networked chaotic oscillators, we are able to demonstrate and argue that, despite the presence of parameter mismatch (or different dynamics), stable synchronization can still be achieved on symmetric complex networks. Specifically, we find that when the oscillators are configured on the network in such a way that the symmetric nodes have similar parameters (or follow the same type of dynamics), cluster synchronization can be generated. The stabilities of the cluster synchronization states are analyzed by the method of symmetry-based stability analysis, with the theoretical predictions in good agreement with the numerical results. Our study sheds light on the interplay between symmetry and cluster synchronization in complex networks and give insights into the functionalities of realistic systems where nonidentical nonlinear oscillators are presented and cluster synchronization is crucial.