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.
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Communicated by LI Ji-bin
Project supported by the National Natural Science Foundation of China (No.10571078) and the Natural Science Foundation of Gansu Province of China (No.3ZX062-B25-012)
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Yan, Xp., Li, Wt. Global asymptotic stability for Hopfield-type neural networks with diffusion effects. Appl Math Mech 28, 361–368 (2007). https://doi.org/10.1007/s10483-007-0309-x
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DOI: https://doi.org/10.1007/s10483-007-0309-x