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The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium (if it exists) is globally asymptotically stable and this implies that the equilibrium of the system is unique. 相似文献
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Qiu Weigen Liu YongqingGuangdong University of Technology Guangzhou . Automation Department of South China University of Technology Guangzhou 《高校应用数学学报(英文版)》2000,(2)
§ 1 IntroductionAs compared with the ODEs system,the generalized system is of many distinctiveproperties[1 ] ,forexam ple,the level structural problem of system state solutions,the uncon-sistent initial value problem,the uniqueness of initial value problem and so on.The asymp-totic stability problem of zero solution of generalized system involves the tractability andunimpulsivity.These properties are of great importance in engineering applications.Theconclusion on the ODEs system can not … 相似文献
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PERTURBINGFAMILIESOFGENERALIZEDLYAPUNOV FUNCTIONSANDRELATIVESTABILITYINTERMSOFTWO MEASURESShangLijun(商立军)(TheFourthMilitaryMe... 相似文献
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