Synchronization of stochastic multi-weighted complex networks with Lévy noise based on graph theory

Abstract

This paper addresses the synchronization problem of stochastic multi-weighted complex networks with Lévy noise. Based on the drive-response concept and graph theory, global Lyapunov function of the error network between drive-response networks is obtained by the weighted summation of Lyapunov functions of vertex systems. According to the stochastic analysis and state feedback control technique, the rigorous synchronization analysis of drive-response networks in the pth moment and probability sense is presented. The obtained synchronization criteria are closely related with multi-weights and the intensity of Lévy noise. Finally, some numerical simulations are provided to illustrate the effectiveness of the theoretical results.