Homogenization of a Wilson–Cowan model for neural fields

Homogenization of Wilson–Cowan type of nonlocal neural field models is investigated. Motivated by the presence of a convolution term in this type of models, we first prove some general convergence results related to convolution sequences. We then apply these 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.