Interplay of degree correlations and cluster synchronization.

We study the evolution of coupled chaotic dynamics on networks and investigate the role of degree-degree correlation in the networks' cluster synchronizability. We find that an increase in the disassortativity can lead to an increase or a decrease in the cluster synchronizability depending on the degree distribution and average connectivity of the network. Networks with heterogeneous degree distribution exhibit significant changes in cluster synchronizability as well as in the phenomena behind cluster synchronization as compared to those of homogeneous networks. Interestingly, cluster synchronizability of a network may be very different from global synchronizability due to the presence of the driven phenomenon behind the cluster formation. Furthermore, we show how degeneracy at the zero eigenvalues provides an understanding of the occurrence of the driven phenomenon behind the synchronization in disassortative networks. The results demonstrate the importance of degree-degree correlations in determining cluster synchronization behavior of complex networks and hence have potential applications in understanding and predicting dynamical behavior of complex systems ranging from brain to social systems.