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' W 1,2 (Ω )-exponential and X 1,2 (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. cellular neural networks, reaction-diffusion, W

Sufficient and necessary conditions for Lyapunov stability of Lorenz system and their application

“…This is just a brief sufficient condition. It is generally recognized that it is not easy to obtain less conservative sufficient conditions for stability of nonlinear systems [16][17][18][19][20][21][22]. Therefore, we often take no account of the sufficient and necessary conditions for stability of Lorenz system.…”