Cluster synchronisation in non-linearly coupled impulsive networks with non-identical nodes and time-varying delays

摘要

This study investigates cluster synchronisation of non-linearly coupled impulsive networks with time-varying delay. Without loss of generality, it is assumed that the nodes in the networks to be non-identical and the coupling matrix to be asymmetric. Two kinds of topological structures are concerned, which correspond to positive weighted network, as well as cooperative and competitive network, respectively. Pinning controllers are designed in order to achieve cluster synchronisation. According to the Lyapunov stability theory, impulsive delay differential inequalities and linear matrix inequalities, some criteria for cluster synchronisation of non-linear impulsive dynamical systems are obtained. Two numerical examples are given to demonstrate the effectiveness of the authors' new results.