Localized stationary solutions of a 2-population homogenized neural field model
Karina Kolodina, Anna Oleynik, John Andreas Wyller · AIP conference proceedings · 2018
We investigate the existence and stability of localized stationary solutions (referred to as single bumps) in a homogenized 2-population nonlocal neural field model of the Amari type with a Heaviside firing rate function. Solutions are constructed by using a pinning function technique in the case of independence of the local variable. The linear stability for the bumps is investigated by means of the spectral properties of a Fredholm integral operator, block diagonalization of this operator and the Fourier decomposition method.