Asymptotical Stability and Exponential Stability in Mean Square of Impulsive Stochastic Time-Varying Neural Network

Abstract

The effect of impulse on stability of neural network is evident not only in performance, that is, impulsive control and impulsive interference. The amount of impulse has a certain impact on stability of neural network. Unlike traditional average impulsive interval, a new strategy is applied in this paper, namely, impulsive density. Based on this strategy, by constructing Lyapunov function, we establish sufficient conditions for mean square asymptotical stability of impulsive stochastic time-varying neural network without time delay. As well as, under this strategy and uniformly asymptotically stable function, by combining trajectory based approach and improved Razumikhin method, mean square exponential stability criterion of impulsive stochastic time-varying neural network with time delay is established. Finally, to demonstrate the viability of our theoretical findings, some instances are provided.