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Existence and Upper Semicontinuity of Global Attractors for Neural Network in a Bounded Domain

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Abstract

In this work we prove the existence of a compact global attractor for the flow of the equation

$$\frac{\partial m(r,t)}{\partial t}=-m(r,t)+ J*(f\circ m)(r,t)+ h, \,\,\, h, > 0,$$

in L 2(S 1). We also give uniform estimates on the size of the attractor and show that the family of attractors \({\{{\mathcal A}_{J}\}}\) is upper semicontinuous at J 0.

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Authors and Affiliations

  1. Unidade Acadêmica de Matemática e Estatística UAME/CCT/UFCG, Bairro Universitário, CEP 58429-970, Rua Aprígio Veloso, 882, Campina Grande, PB, Brasil

    Severino Horácio da Silva

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  1. Severino Horácio da Silva
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Correspondence to Severino Horácio da Silva.

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da Silva, S.H. Existence and Upper Semicontinuity of Global Attractors for Neural Network in a Bounded Domain. Differ Equ Dyn Syst 19, 87–96 (2011). https://doi.org/10.1007/s12591-010-0072-0

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