Iterative Schemes for Bump Solutions in a Neural Field Model
Functional Analysis
2013-02-22 v1
Abstract
We develop two iteration schemes for construction of localized stationary solutions (bumps) of a one-population Wilson-Cowan model with a smoothed Heaviside firing rate function. The first scheme is based on the fixed point formulation of the stationary Wilson-Cowan model. The second one is formulated in terms of the excitation width of a bump. Using the theory of monotone operators in ordered Banach spaces we justify convergence of both iteration schemes.
Cite
@article{arxiv.1302.5322,
title = {Iterative Schemes for Bump Solutions in a Neural Field Model},
author = {Anna Oleynik and Arcady Ponosov and John Wyller},
journal= {arXiv preprint arXiv:1302.5322},
year = {2013}
}
Comments
10 figures