Abstract
In this paper, the distributed synchronization of stochastic coupled neural networks with time-varying delay is concerned via randomly occurring control. We use two Bernoulli stochastic variables to describe the occurrence of distributed adaptive control and updating law according to certain probabilities. The distributed adaptive control and updating law for each vertex in the network depend on the state information on each vertex’s neighborhood. Based on Lyapunov stability theory, Itô differential equations, etc., by constructing the appropriate Lyapunov functional, we study and obtain sufficient conditions for the distributed synchronization of such networks in mean square.
Highlights
With the rapid development of the information age, complex networks have received extensive attention as a frontier of interdisciplinary and challenging research fields
Based on Lyapunov stability theory, Itô differential equations, etc., by constructing the appropriate Lyapunov functional, we study and obtain sufficient conditions for the distributed synchronization of such networks in mean square
In reference [29], considering that the controlled system is interfered by random mutations, a method of randomly occurring control is proposed, and the synchronization behavior of complex networks is studied, but it does not take into account the impact of time-delay factors, so its model is somewhat conservative
Summary
With the rapid development of the information age, complex networks have received extensive attention as a frontier of interdisciplinary and challenging research fields. In reference [29], considering that the controlled system is interfered by random mutations, a method of randomly occurring control is proposed, and the synchronization behavior of complex networks is studied, but it does not take into account the impact of time-delay factors, so its model is somewhat conservative. Based on the above viewpoints, a more general coupled time-varying delay complex dynamical network model under randomly occurring control is proposed in this paper. This model has the following characteristics: both controller activation and updating law of control gain occur in a probabilistic way, and the synchronization of stochastic complex networks is studied by considering randomly occurring control and updating law. Based on the Lyapunov stability theory, by constructing appropriate Lyapunov functional, the sufficient conditions for the distributed synchronization of such networks in mean square are obtained
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