W 1,2(Ω)- and X 1,2(Ω)-stability of reaction-diffusion cellular neural networks with delay

Abstract

With Poincare’s inequality and auxiliary function applied in a class of retarded cellular neural networks with reaction-diffusion, the conditions of the systems’ W1,2(Ω)-exponential and X1,2(Ω)-asmptotic stability are obtained. The stability conditions containing diffusion term are different from those obtained in the previous papers in their exponential stability conditions. One example is given to illustrate the feasibility of this method in the end.