Adaptive and impulsive cluster synchronization of a general complex dynamical network

Recently, cluster synchronization has attracted an increasing interest in various disciplines, including mathematics, physics, and engineering sciences. This paper further investigates the cluster synchronization of a complex dynamical network by using adaptive and impulsive control techniques, respectively. Based on a complex dynamical network with two different clusters, several adaptive and impulsive cluster synchronization criteria are then proposed. It should be especially pointed out that the dynamics and its dimensions of the individual dynamical systems are different in the two different clusters. Also, some numerical simulations are given to verify the effectiveness of the above theoretical results.