Almost Sure Synchronization of Multilayer Networks via Intermittent Pinning Noises: A White-Noise-Based Time-Varying Coupling

Abstract

This paper is concerned with the almost sure exponential synchronization of a multilayer network which is set up on a non-strongly connected digraph that can be classified into several layers by Tarjan's algorithm. Note that, in the multilayer network, white-noise-based time-varying coupling and drift term coupling are proposed to simulate two kinds of coexisting distinguishable interactions between vertices. We develop a normal analytical framework for studying synchronization of the multilayer network. Firstly, via aperiodically intermittent pinning noises, synchronization of vertices situated on the first layer is achieved in the layered network. Secondly, under the impact of the white-noise-based time-varying coupling in diffusion term, synchronization of the vertices located in other layer networks is developed with the support of synchronization for the pinned vertices. Employing Lyapunov method, graph theory and stochastic analysis technique, a criterion of almost sure global exponential synchronization is obtained. By adopting the concepts of average noise control rate and average noise control period proposed recently, we lessen the conservativeness of the conditions restricted on aperiodically intermittent noise control to optimize our results. Furthermore, an application to a class of Chua's circuits is exhibited in detail. In the end, we provide a numerical example to verify the validity of the theoretical results.