Attractors of Hopfield-type lattice models with increasing neuronal input

Abstract

Two Hopfield-type neural lattice models are considered, one with local n-neighborhood nonlinear interconnections among neurons and the other with global nonlinear interconnections among neurons. It is shown that both systems possess global attractors on a weighted space of bi-infinite sequences. Moreover, the attractors are shown to depend upper semi-continuously on the interconnection parameters as n → ∞.