Analysis of Exponential Stability for Neutral Stochastic Cohen-Grossberg Neural Networks with Mixed Delays

Abstract

This paper is concerned with the mean-square exponential input-to-state stability problem for a class of stochastic Cohen-Grossberg neural networks. Different from prior works, neutral terms and mixed delays are discussed in our system. By employing the Lyapunov-Krasovskii functional method, Itô formula, Dynkin formula, and stochastic analysis theory, we obtain some novel sufficient conditions to ensure that the addressed system is mean-square exponentially input-to-state stable. Moreover, two numerical examples and their simulations are given to illustrate the correctness of the theoretical results.

Mean‐square exponential input‐to‐state stability of stochastic delayed recurrent neural networks with local Lipschitz condition

“…Obviously, Assumption 1, local Lipschitz condition, is weaker than uniform Lipschitz one given in [4–29]. Hence, our results have improved and generalized some existed ones of [4–29]. Moreover, we shall show that the main result of [19] is a particular case of this paper.…”

“…To our knowledge, rare researchers have considered stochastic delayed recurrent neural networks without uniform Lipschitz condition. Obviously, Assumption 1, local Lipschitz condition, is weaker than uniform Lipschitz one given in [4–29]. Hence, our results have improved and generalized some existed ones of [4–29].…”

“…Up until now, many researchers have deeply studied the stability of stochastic delayed recurrent neural networks (1.1), and the mainstream results can fall into two categories. One is the traditional stability, such as asymptotic stability [4][5][6], exponential stability [7][8][9][10][11][12][13][14][15][16], and almost sure exponential stability [17,18], and the other is the untraditional stability: input-to-state stability [19][20][21][22][23][24][25][26][27][28][29], where the states of stochastic neural networks do not converge to the equilibrium point as time goes to infinity. Unfortunately, both stability results of stochastic delayed recurrent neural networks (1.1) depend on the conditions that the activation functions satisfy uniform Lipschitz condition, which is somewhat restrictive.…”