Homogenization of a Wilson-Cowan model for neural fields

TL;DR

This paper investigates the homogenization of Wilson-Cowan neural field models with convolution terms, establishing convergence results and applying them to derive effective models using algebraic and sigma-convergence techniques.

Contribution

It introduces a general framework for homogenizing Wilson-Cowan models with convolution, utilizing algebras with mean value and sigma-convergence methods.

Findings

Proved convergence results for convolution sequences

Applied homogenization techniques to neural field models

Provided a rigorous mathematical foundation for effective neural field equations

Abstract

Homogenization of Wilson-Cowan type of nonlocal neural field models is investigated. Motivated by the presence of a convolution terms in this type of models, we first prove some general convergence results related to convolution sequences. We then apply theses results to the homogenization problem of the Wilson-Cowan type model in a general deterministic setting. Key ingredients in this study are the notion of algebras with mean value and the related concept of sigma-convergence.