| In recent years, complex networks have been widely studied such as synchronization and topology identification problems because natural or man-made network widely exist in the world. In this paper, based on the stochastic Lyapunov stability theory, matrix theory and so on, we consider a more general delayed complex network with stochastic perturbation and investigate its synchronization and topology identification problems. The main contains and innovations include:(1) The local adaptive Hoo consistency is intensively investigated for delayed complex dynamical networks with noise. The network under consideration contains unknown but bounded nonlinear coupling functions and time-varying delays which appear in the coupling term and the node system simultaneously. Based on the adaptive control, several local adaptive Hoo consistency schemes are established which guarantee robust asymptotically consistency for each node of noise-perturbed network as well as achieving a prescribed robust Hoo performance level.(2) Topology identification of general weighted complex network with time-varying delay and stochastic perturbation, which is a zero-mean real scalar Wiener process, is investigated. Based on the adaptive-feedback control method, the stochastic Lyapunov stability theory and the ito formula, some synchronous criteria are established which guarantee the asymptotical mean square synchronization of the drive network and the response network with stochastic disturbances as well as identify the topological structure of the uncertain general drive complex network.(3) Finite-time synchronization of delayed weighted complex network with stochastic perturbation is investigated. Under an appropriate controller, two complex networks with the same structure can achieve synchronization in a finite time, which can be accurately calculated.(4) Finally, detailed and satisfactory numerical simulations have validated the feasibility and the correctness of the proposed techniques. |
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