Pinning Control Strategy of Multicommunity Structure Networks

Abstract

In order to investigate the effects of community structure on synchronization, a pinning control strategy is researched in a class of complex networks with community structure in this paper. A feedback control law is designed based on the network community structure information. The stability condition is given and proved by using Lyapunov stability theory. Our research shows that as to community structure networks, there being a threshold hT≈5, when coupling strength bellows this threshold, the stronger coupling strength corresponds to higher synchronizability; vice versa, the stronger coupling strength brings lower synchronizability. In addition the synchronizability of overlapping and nonoverlapping community structure networks was simulated and analyzed; while the nodes were controlled randomly and intensively, the results show that intensive control strategy is better than the random one. The network will reach synchronization easily when the node with largest betweenness was controlled. Furthermore, four difference networks’ synchronizability, such as Barabási-Albert network, Watts-Strogatz network, Erdös-Rényi network, and community structure network, are simulated; the research shows that the community structure network is more easily synchronized under the same control strength.