Lag stochastic synchronization of chaotic mixed time-delayed neural networks with uncertain parameters or perturbations

This paper investigates the problem of lag synchronization for a kind of chaotic neural networks with discrete and distributed delays (mixed delays). The driver system has uncertain parameters and uncertain nonlinear external perturbations, while the response system has channel noises. A simple but all-powerful robust adaptive controller is designed to circumvent the effects of uncertain external perturbations such that the response system synchronize with the driver system. Based on the invariance principle of stochastic differential equations and some suitable Lyapunov functions, several sufficient conditions are developed to solve this problem. Moreover, under certain conditions, parameters of the uncertain master system can be estimated. Numerical simulations are exploited to show the effectiveness of the theoretical results.