title: Cluster synchronization induced by one-node clusters in networks with asymmetric negative couplings.
abstract: This paper deals with the problem of cluster synchronization in networks with asymmetric negative couplings. By decomposing the coupling matrix into three matrices, and employing Lyapunov function method, sufficient conditions are derived for cluster synchronization. The conditions show that the couplings of multi-node clusters from one-node clusters have beneficial effects on cluster synchronization. Based on the effects of the one-node clusters, an effective and universal control scheme is put forward for the first time. The obtained results may help us better understand the relation between cluster synchronization and cluster structures of the networks. The validity of the control scheme is confirmed through two numerical simulations, in a network with no cluster structure and in a scale-free network.
authors.affiliation: School of Science, Hangzhou Dianzi University, Hangzhou 310018, China.
authors.forename: Jianbao
authors.initials: J
authors.lastname: Zhang
authors.affiliation: School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China.
authors.forename: Zhongjun
authors.initials: Z
authors.lastname: Ma
authors.affiliation: College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China.
authors.forename: Gang
authors.initials: G
authors.lastname: Zhang
mesh_terms: D001683:Biological Clocks; D008962:Models, Theoretical