Synchronization of stochastic complex networks with discrete-time and distributed coupling delayed via hybrid nonlinear and impulsive control

In this paper, the problem of pinning and impulsive synchronization for a class of general hybrid coupling delayed stochastic complex networks is investigated. The involving hybrid coupling delays terms are not only included current-state coupling, but also contained discrete-time and distributed coupling delays. Moreover, in order to achieve synchronization, a hybrid controller, which contains a nonlinear controller and a pinning impulsive controller is introduced simultaneously. By taking the advantage of Lyapunov method in synchronization analysis, some sufficient conditions are obtained through two different algorithms, which guarantee global synchronization of stochastic complex networks with large delay. Meanwhile, the relationship between the number of pinned nodes and impulsive gain are quantitatively analyzed. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.