Exponential synchronization of stochastic complex dynamical networks with time-varying delay and impulsive effects

This paper investigates globally exponential synchronization of stochastic nonlinear dynamical networks with time-varying delay and impulsive effects. Based on a time-dependent Lyapanov function, a sufficient condition is established under which the stochastic nonlinear dynamical networks with time-varying delay and impulsive effects are mean square exponentially synchronized to a desired state. Above all, we generalize the work of [2] into the stochastic systems. Specifically, 1) we consider the stochastic disturbance in the network model; 2) the comparison principle and Schur complement Lemma are abandoned in the process of proofing exponential synchronization; 3) we come up with a new method to deal with the time delayauxiliary monotone function method rather than proof by contradiction.