Exponential synchronization for stochastic multi-links networks with time-varying delays

Abstract

This paper investigates the problem of exponential synchronization in stochastic multi-links networks with time-varying delays (SMNTDs). By employing graph theory and Lyapunov method, sufficient conditions for achieving $p$th moment exponential synchronization (PMES) and almost surely exponential synchronization (ASES) are simultaneously derived, which are associated with network’s topology, time-varying delays and coupled weights. Moreover, the role of negative feedback control mechanisms is emphasized in maintaining network synchronization. Specifically, any control gain satisfying the sufficient conditions in our theorems guarantees synchronization, and increasing gain generally improves convergence speed and robustness. Numerical simulations based on a Chua’s circuit network illustrate the theoretical results, and further demonstrate how increasing control strength improves convergence speed and synchronization precision.