Global mean square exponential stability of stochastic neural networks with retarded and advanced argument

This paper focuses on the global mean square exponential stability of stochastic neural networks with retarded and advanced argument. By employing the theory of differential equations with piecewise constant argument of generalized type, several sufficient conditions in form of algebraic inequalities are proposed to ensure the existence and uniqueness of solution. Considering that the piecewise alternately retarded and advanced argument exists, we estimate dynamic effect of system status in the current time and in the deviating function. Theoretical analysis of global mean square exponential stability is carried out by the stability theory of stochastic differential equations. Finally, numerical examples are exploited to illustrate the effectiveness of the results established.