Stochastic Synchronization of Multiplex Networks With Continuous and Impulsive Couplings

This paper focuses on global almost sure exponential synchronization of a class of two-layer stochastic multiplex networks. In the two-layer stochastic multiplex networks, the first layer is equipped with continuous couplings, but the second layer is endowed with impulsive couplings, which is different from other multiplex networks. By utilizing the average impulsive interval method and Lyapunov stability theory, the sufficient criteria for synchronization are obtained. In addition, due to the instability of nodal connections and nodal dynamics, switchings are considered. Therefore, global almost sure exponential synchronization of switched multiplex network is also investigated. When the multiplex network has both switchings and impulses, these two behaviors are assumed to happen asynchronously. To reduce the conservativeness, the mode-dependent average dwell time method and the mode-dependent average impulsive interval method are applied to solve the influence of switchings and impulses, respectively. Then, a more practical relationship among the average dwell time, the average impulsive interval and the switching modes is established. Moreover, if the stochastic perturbations disappear, then the corollaries are given for this special situation. Finally, the validity of the theoretical results is verified by two numerical examples.