Exponential and almost sure exponential stability of stochastic fuzzy delayed Cohen–Grossberg neural networks

In this paper, we study a class of stochastic fuzzy delayed Cohen–Grossberg neural networks. Two kinds of stability are discussed in our investigation. One is exponential stability in the mean square and the other is almost sure exponential stability. First, some sufficient conditions are derived to guarantee the exponential stability in the mean square for the considered system based on the Lyapunov–Krasovskii functional, stochastic analysis theory and the Itô's formula as well as the Dynkin formula. Then, we further investigate the almost sure exponential stability by employing the nonnegative semi-martingale convergence theorem. Moreover, we prove that the addressed system is both almost sure exponentially stable and exponentially stable in the mean square under suitable conditions. Finally, three numerical examples are also given to show the effectiveness of the theoretical results. In particular, the simulation figures establish that fuzzy systems do have more advantages than non-fuzzy systems.