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

查看全文 作　　者：Ruofeng [1,2]RAO 高影响力作者 机构地区：[1]Department of Mathematics, Yibin University;[2]Institution of Mathematics, Yibin University高影响力机构 出　　处：《Chinese Annals of Mathematics,Series B》索引2014年第35卷第4期,共24页高影响力期刊 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 impulsive Markovian jumping reaction-diffusion Cohen-Grossberg neural networks(CGNNs for short) are obtained by using a novel Lyapunov-Krasovskii functional approach, linear matrix inequalities(LMIs for short) technique, It formula, Poincar′e inequality and Hardy-Poincaré inequality, where the CGNNs involve uncertain parameters, partially unknown 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 Poincar′e inequality and Hardy-Poincar′e 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 allowable upper bounds of delays. 关 键 词：POINCARE不等式 全局指数稳定性 反应扩散 神经网络 非线性 时滞相关 科恩 跃迁
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