Scalable synchronization cluster in networked chaotic oscillators

Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the other oscillators remain desynchronized. Interestingly, with the increase of the coupling strength, the cluster is expanding gradually by recruiting the desynchronized oscillators one by one. This new synchronization phenomenon, which is named ``scalable synchronization cluster", is explored theoretically by the method of eigenvector-based analysis, and it is revealed that the scalability of the cluster is attributed to the unique feature of the eigenvectors of the network coupling matrix. The transient dynamics of the cluster in response to random perturbations are also studied, and it is shown that in restoring to the synchronization state, oscillators inside the cluster are stabilized in sequence, illustrating again the hierarchy of the oscillators. The findings shed new light on the collective behaviors of networked chaotic oscillators, and are helpful for the design of real-world networks where scalable synchronization clusters are concerned.