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Upper semi-continuous convergence of attractors for a Hopfield-type lattice model. (English) Zbl 1444.34029

Summary: To investigate the dynamical behavior of a Hopfield neural network model when its dimension becomes increasingly large, a Hopfield-type lattice system is developed as the infinite dimensional extension of the classical Hopfield model. The existence of global attractors is established for both the lattice system and its finite dimensional approximations. Moreover, the global attractors for the finite dimensional approximations are shown to converge to the attractor for the infinite dimensional lattice system upper semi-continuously.

MSC:

34A33 Ordinary lattice differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34D45 Attractors of solutions to ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
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