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Global asymptotic stability for Hopfield-type neural networks with diffusion effects |
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| Authors: | Yan Xiang-ping Li Wan-tong |
| Affiliation: | 1. Department of Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,P.R.China 2. School of Mathematics and Statistics,Lanzhou University,Lanzhou 730000,P.R.China |
| Abstract: | 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. |
| Keywords: | diffusion Hopfield-type neural networks equilibrium global asymptoticstability |
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