Cluster synchronization in a network of nonlinear systems with directed topology and competitive relationships

This article studies the cluster synchronization problem of coupled nonlinear systems with directed topology and competitive relationships. We assume that nodes within same have intrinsic dynamics, while dynamics belonging to different clusters are different. In cluster, there only exist cooperative relationships, may relationships among clusters. Under assumptions dynamic each node satisfies one-sided Lipschitz condition, digraph is strongly connected, between cluster-input-equivalence some sufficient conditions for in cases linear coupling obtained respectively. The presented as algebraic which easy solve. Finally, results validated by two numerical simulations.