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Iterative Schemes for Bump Solutions in a Neural Field Model
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics. Norwegian Univ Life Sci, Dept Math Sci & Technol, N-1432 As, Norway.;Norwegian Univ Life Sci, Ctr Integrat Genet, N-1432 As, Norway..
Norwegian Univ Life Sci, Dept Math Sci & Technol, N-1432 As, Norway.;Norwegian Univ Life Sci, Ctr Integrat Genet, N-1432 As, Norway..
Norwegian Univ Life Sci, Dept Math Sci & Technol, N-1432 As, Norway.;Norwegian Univ Life Sci, Ctr Integrat Genet, N-1432 As, Norway..
2015 (English)In: Differential Equations and Dynamical Systems, ISSN 0971-3514, E-ISSN 0974-6870, Vol. 23, no 1, 79-98 p.Article in journal (Refereed) Published
Abstract [en]

We develop two iteration schemes for construction of localized stationary solutions (bumps) of a one-population Wilson-Cowan model with a smooth 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.

Place, publisher, year, edition, pages
2015. Vol. 23, no 1, 79-98 p.
Keyword [en]
Neural field models, Iteration schemes for bumps, Monotone operators in ordered Banach spaces
National Category
Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-303599DOI: 10.1007/s12591-013-0191-5ISI: 000355632000007OAI: oai:DiVA.org:uu-303599DiVA: diva2:972412
Available from: 2016-09-20 Created: 2016-09-20 Last updated: 2017-11-21Bibliographically approved

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Oleynik, Anna

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