Stochastic asymptotic stability for stochastic inertial Cohen-Grossberg neural networks with time-varying delay

Abstract

This paper studies stochastic asymptotic stability for stochastic inertial Cohen-Grossberg neural networks with time-varying delay. Firstly, the second-order differential equation is converted into the first-order differential equation by appropriate variable substitution. Secondly, the existence of the equilibrium point is derived by using homeomorphic mapping, finite increment formula of Lagrange mean value theorem and linear matrix inequality. The sufficient conditions for the stochastic asymptotic stability of the equilibrium point of the system are derived by defining the appropriate operator, and constructing the appropriate positive Lyapunov function and positive-definite matrix. Thirdly, a numerical example illustrates the correctness of these theorems.