Synchronization of multiplex networks with stochastic perturbations via pinning adaptive control

摘要

This paper investigates the synchronization problems for the multiplex networks with both interlayer and intra-layer couplings subject to the stochastic perturbations. In particular, the topologies of all layers are not the same, so the model can represent a class of multiplex networks. To synchronize the multiplex networks onto the trajectory of a virtual leader, a pinning adaptive protocol is proposed and some pinning criteria are derived for guaranteeing complete synchronization. Furthermore, when the results are extended to the systems with time delays, the pinning adaptive strategy is still proved to be effective. Finally, a two-layer network and a three-layer network are selected for numerical simulations to illustrate the theoretical results. ? 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.