Exponential Stability in Mean Square of Stochastic Neural Networks with Delays

Abstract

In this paper we shall dicuss the exponential stability in mean square for a stochastic neural network with delays of the form dx ( t ) = [— Bx ( t ) + Ag ( x (t))] dt + σ( x ( t ), g ( x (t))dω( t ). In the case when σ( х , у ) ≡ 0 the stochastic network becomes a deterministic network with deladys ů ( t ) = — Bx ( t ) + Ag ( x (t)). So as corollaries, we also obtain a number of useful criteria for this delay network to be exponentially stable, and these corollaries are new even to the content of exponential stability of ordinary differential delay equations. Several interesting examples are also given for illustration.