Adaptive synchronization of nonlinearly stochastically coupled networks with two types of time-varying delays

In this paper, a general model of nonlinearly stochastically coupled network with two types of time-varying delays is proposed. The network model is subject to stochastic disturbance described by Wiener process in the nonlinear coupling term. The two types of time-varying delays are the system delay in the nodes dynamics and the coupling delay between nodes. By employing the stochastic It differential formula and the LaSalle´s invariant principle of the stochastic differential equation, several sufficient criteria are deduced to ensure the synchronization in mean square for the whole nonlinearly stochastically coupled network. The presented adaptive controller for the network synchronization is rather simple in form which is useful for future practical engineering design. A numerical simulation is given to show the effectiveness of the theoretical result.