Nonlinear stochastic synchronization of complex dynamical networks with delays

This paper investigates the problem of synchronization for complex networks with time delays and stochastic uncertainties. Based on Lyapunov-Krasovskii functional theory, some sufficient conditions are derived. To deal with random uncertainties in networks, some suitable nonlinear adaptive controllers are designed, and some updating laws are used to deal with the feedback factor. The designed nonlinear adaptive controller can be used not only for synchronization of networks with delayed nodes, but also for the synchronization of networks with delayed random noises and delayed nodes. Finally, numerical examples illustrating the effectiveness of the proposed theoretical results are provided.