Iterative Schemes for Bump Solutions in a Neural Field Model

TL;DR

This paper introduces two iterative methods for constructing localized bump solutions in a neural field model, with proven convergence using monotone operator theory, advancing analytical tools for neural dynamics modeling.

Contribution

The paper presents two novel iterative schemes for bump solutions in a Wilson-Cowan model, with convergence proofs based on monotone operator theory.

Findings

Both schemes successfully construct bump solutions.

Convergence of the schemes is rigorously justified.

The methods enhance analytical approaches to neural field models.

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.