Bipartite synchronization of stochastic complex networks with time-varying delays and multi-links

Abstract

This article introduces a novel model to achieve bipartite leader-following synchronization of stochastic complex networks characterized by time-varying delays and multi-links, through the use of negative feedback control. Utilizing graph theory and the Lyapunov method, we develop global Lyapunov functions for the error system and derive new sufficient conditions for both mean-square exponential bipartite synchronization and almost sure exponential bipartite synchronization between the leader node and the follower nodes. These conditions are closely related to the topological properties of the complex networks, offering new insights and methodologies for synchronization control and stability analysis in stochastic complex networks. Finally, we validate the theoretical results by applying them to coupled Chua’s circuits and confirming their effectiveness and practicality through numerical simulations.