Synchronization of Stochastic Multiplex Networks With Impulsive Effects

This paper investigates synchronization of the stochastic multiplex networks with impulsive effects. Firstly, compared with the single-layer networks, multiplex networks can express more information. Meanwhile, stochastic perturbations and impulses are ubiquitous and both can affect synchronization. Therefore, a multiplex network with stochastic perturbations and impulses is proposed. Secondly, in order to solve the effect of impulses, the average impulsive interval method is applied. Based on the Lyapunov function method, Itô's formula and exponential martingale inequality, the sufficient conditions for the multiplex networks to achieve almost sure exponential synchronization are obtained. Finally, a numerical example of a two-layer multiplex network is given to illustrate the effectiveness of the theoretical results.