Adaptive cluster synchronization for a complex dynamical network with delays and stochastic perturbation

In this paper, the cluster mean square synchronization for a complex dynamical network with interval time-varying delays and stochastic perturbation, which is a zero-mean real scalar Wiener process, is investigated. The weight configuration matrix in the network under consideration is time-varying, which does not need to satisfy the diffusive coupling conditions or be symmetric. According to the stochastic Lyapunov stability theory, Itô’s differential rule, Kronecker product and adaptive control method, an adaptive strategy is established which guarantees the asymptotical cluster mean square synchronization for each node in the network. Furthermore, several numerical simulations illustrate the effectiveness and feasibility of the proposed method. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013