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Iterative Schemes for Bump Solutions in a Neural Field Model

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.

preprint2013arXivOpen access
Anna OleynikArcady PonosovJohn Wyller
math.FA
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Anna OleynikArcady PonosovJohn Wyller

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