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On the properties of nonlinear nonlocal operators arising in neural field models
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 398, no 1, 335-351 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2013. Vol. 398, no 1, 335-351 p.
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Mathematical Analysis
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URN: urn:nbn:se:uu:diva-182934DOI: 10.1016/j.jmaa.2012.08.063ISI: 000310659500028OAI: oai:DiVA.org:uu-182934DiVA: diva2:561447
Available from: 2012-10-18 Created: 2012-10-18 Last updated: 2017-12-07Bibliographically approved

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Oleynik, Anna

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