On the properties of nonlinear nonlocal operators arising in neural field models

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:398

Article

Oleynik, Anna ; Ponosov, Arcady ; Wyller, John

关键词: Neural field;    Nonlinear integral equations;    Continuous dependence;    Sobolev spaces;    Degree theory;   

DOI  :  10.1016/j.jmaa.2012.08.063

来源: Elsevier

【 摘 要 】

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. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free