Consistency Of A Complex Delayed Dynamical Network With Stochastic Disturbance

Synchronization behavior is a very common phenomenon in the actual systems. With thesynchronization phenomenon founded for the first time, the research of the synchronization hasnot been stopped. At present, there are a lot of literatures which are about the synchronization forthe complex networks, and the nodes of the complex networks under consideration were mainlydynamical. Furthermore, a few of them have taken uncertain factors into account. In fact, thepractical complex networks in the real world are not exist isolated, stochastic disturbance andtime delays are everywhere, which will make a great influence on the behavior of the actualcomplex networks. Therefore, it has important theoretical meaning and realistic meaning for usto take the uncertain factors into account on the analysis of the complex networks behavior.This paper focuses on the consistency problem of a complex delayed dynamical networkwith stochastic disturbance. The complex network under consideration includes not onlystochastic disturbance but also the varying time-delay which appear in the coupling term and thenode system simultaneously. Therefore, such a network is more general. Firstly, based on thestochastic Lyapunov stability theory, linear feedback control and linear matrix inequality, somenew asymptotic consistency sufficient conditions are established which guarantee theconsistency for the nodes of this network and an isolated system in the delay-independent anddelay-dependent levels. And some illustrative simulations are provided to verify the correctnessand effectiveness of the proposed schemes. Secondly, with pinning control method and feedbackcontrol, a novel strategy is established which guarantees the asymptotical mean squaresynchronization for each node and the isolated system with several controllers.