Synchronization Analysis for Stochastic Delayed Multilayer Network With Additive Couplings

This paper is concerned with the synchronization of stochastic delayed multilayer networks with additive couplings. Multilayer networks are a kind of complex networks with different layers, which consist of different kinds of interactions or multiple subnetworks. Additive couplings are designed to capture the different layered connections. Based on additive couplings, several sufficient conditions are obtained to guarantee the synchronization of chaotic stochastic delayed coupled multilayer network. More specifically, on one hand, we obtain some sufficient conditions to guarantee that the stochastic multilayer network can be synchronized almost surely without control input. On the other hand, we propose three synchronization schemes by designing controllers. Scheme I: It is assumed that only a part of the nodes are allowed to be controlled directly. Scheme II: Control all nodes of the complex system by using only one controller. Scheme III: Pinning adaptive controller. Finally, an example and its simulations are given to show the effectiveness of our control schemes.