Mathematical model and cluster synchronization for a complex dynamical network with two types of chaotic oscillators

We propose a mathematical model of a complex dynamical network consisting of two types of chaotic oscillators and investigate the schemes and corresponding criteria for cluster synchronization. the global asymptotically stable criteria for the linearly or adaptively coupled network are derived to ensure that each group of oscillators is synchronized to the same behavior. the cluster synchronization can be guaranteed by increasing the inner coupling strength in each cluster or enhancing the external excitation. theoretical analysis and numerical simulation results show that the external excitation is more conducive to the cluster synchronization. all of the results are proved rigorously. finally,a network with a scale-free subnetwork and a small-world subnetwork is illustrated,and the corresponding numerical simulations verify the theoretical analysis. copyright © 2012 zhen jia and guangming deng.