Homogenization of Nonlocal Electrostatic Problems by Means of the Two-Scale Fourier Transform

Homogenization of a Wilson–Cowan model for neural fields

“…The above result was first proved by Visintin [29] in the periodic setting by using the two-scale transform or unfolding method. Theorem 2 allows us to pass to the limit in the convolution terms without using neither the Fourier transform, nor the Laplace transform, and hence without restricting ourselves to the Hilbertian setting as it is the case in [30]. Taking into account the fact that the brain is not necessarily a periodic medium (even if it can exhibit some kinds of periodicity), we can therefore emphasize that our work is a true advance in the neural field community.…”