Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6418955 | Journal of Mathematical Analysis and Applications | 2013 | 17 Pages |
Abstract
We study the existence and continuous dependence of stationary solutions of the one-population Wilson-Cowan model on the steepness of the firing rate functions. We investigate the properties of the nonlinear nonlocal operators which arise when formulating the stationary one-population Wilson-Cowan model as a fixed point problem. The theory is used to study the existence and continuous dependence of localized stationary solutions of this model on the steepness of the firing rate functions. The present work generalizes and complements previously obtained results as we relax on the assumptions that the firing rate functions are given by smoothed Heaviside functions.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Anna Oleynik, Arcady Ponosov, John Wyller,