Global asymptotic stability for Hopfield-type neural networks with diffusion effects  

作　　者：颜向平 李万同 

机构地区：[1]Department of Mathematics,Lanzhou Jiaotong University [2]School of Mathematics and Statistics,Lanzhou University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2007年第3期361-368,共8页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China (No.10571078);the Natural Science Foundation of Gansu Province of China (No.3ZX062-B25-012)

摘　　要：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.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.

关 键 词：DIFFUSION Hopfield-type neural networks EQUILIBRIUM global asymptotic stability 

分 类 号：O175[理学—数学]