Delay-Dependent Exponential Stability for Nonlinear Reaction-Diffusion Uncertain Cohen-Grossberg Neural Networks with Partially Known Transition Rates via Hardy-Poincaré Inequality  

作　　者：Ruofeng RAO 

机构地区：[1]Department of Mathematics, Yibin University [2]Institution of Mathematics, Yibin University

出　　处：《Chinese Annals of Mathematics,Series B》2014年第4期575-598,共24页数学年刊（B辑英文版）

基　　金：supported by the National Basic Research Program of China(No.2010CB732501);the Scientific Research Fund of Science Technology Department of Sichuan Province(Nos.2010JY0057,2012JYZ010);the Sichuan Educational Committee Science Foundation(Nos.08ZB002,12ZB349);the Scientific Research Fund of Sichuan Provincial Education Department(Nos.14ZA0274,08ZB002,12ZB349)

摘　　要：In this paper, stochastic global exponential stability criteria for delayed im- pulsive Markovian jumping reaction-diffusion Cohen-Grossberg neural networks （CCNNs for short） are obtained by using a novel Lyapunov-Krasovskii functional approach, lin- ear matrix inequalities （LMIs for short） technique, Ito formula, Poincare inequality and Hardy-Poincare inequality, where the CGNNs involve uncertain parameters, partially un known Markovian transition rates, and even nonlinear p-Laplace diffusion （p 〉 1）. It is worth mentioning that ellipsoid domains in Rm （m 〉 3） can be considered in numerical simulations for the first time owing to the synthetic applications of Poincare inequality and Hardy-Poincare inequality. Moreover, the simulation numerical results show that even the corollaries of the obtained results are more feasible and effective than the main results of some recent related literatures in view of significant improvement in the Mlowable upper bounds of delays.

关 键 词：Hardy-Poincare inequality Laplace diffusion Linear matrix inequality 

分 类 号：O211.62[理学—概率论与数理统计]