Almost sure exponential synchronization of network systems under a new intermittent noise-diffusion layer

Abstract In this paper, a novel intermittent noise-diffusion layer is proposed to synchronize a network system. Different from most of the traditional noise-induced synchronization or noise stabilization (noise exists in nodes of the network), we give an intermittent noise-diffusion layer (the noise exists in the edges of the network) to study the almost sure exponential synchronization. The theoretical results show that the general network system can be synchronized in the almost sure sense as long as the topological structure of the network in the intermittent noise-diffusion layer is an undirected connected graph. Two examples are proposed to illustrate the theory obtained.