Exponential stability analysis of stochastic reaction-diffusion Cohen–Grossberg neural networks with mixed delays

Abstract

In this paper, we study a new class of stochastic Cohen–Grossberg neural networks with reaction-diffusion and mixed delays. Without the aid of nonnegative semimartingale convergence theorem, the method of variation parameter and linear matrix inequalities technique, a set of novel sufficient conditions on the exponential stability for the considered system is obtained by utilizing a new Lyapunov–Krasovskii functional, the Poincaré inequality and stochastic analysis theory. The obtained results show that the reaction-diffusion term does contribute to the exponentially stabilization of the considered system. Therefore, our results generalize and improve some earlier publications. Moreover, two numerical examples are given to show the effectiveness of the theoretical results and demonstrate that the stability criteria existed in the earlier literature fail.