Cluster Synchronization on Multiple Nonlinearly Coupled Dynamical Subnetworks of Complex Networks With Nonidentical Nodes.

Abstract

In this paper, cluster synchronization on multiple nonlinearly coupled dynamical subnetworks of complex networks with nonidentical nodes and stochastic perturbations is studied. Based on the general leader-follower's model, an improved network structure model that consists of multiple pairs of matching subnetworks, each of which includes a leaders' subnetwork and a followers' subnetwork, is proposed. Moreover, the dynamical behaviors of the nodes belonging to the same pair of matching subnetworks are identical, while the ones belonging to different pairs of unmatched subnetworks are nonidentical. In this new setting, the aim is to design some suitable adaptive pinning controllers on the chosen nodes of each followers' subnetwork, such that the nodes in each subnetwork can be exponentially synchronized onto their reference state. Then, some cluster synchronization criteria for multiple nonlinearly coupled dynamical subnetworks of complex networks are established, and a pinning control scheme that the nodes with very large or low degrees are good candidates for applying pinning controllers is presented. Suitable adaptive update laws are used to deal with the unknown feedback gains between the pinned nodes and their leaders. Finally, several numerical simulations are given to demonstrate the effectiveness and applicability of the proposed approach.