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On the Existence of Unstable Bumps in Neural Networks
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics.
2013 (English)In: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 75, no 4, 445-458 p.Article in journal (Refereed) Published
Abstract [en]

We study the neuronal field equation, a nonlinear integro-differential equation of Hammerstein type. By means of the Amann three fixed point theorem we prove the existence of bump solutions to this equation. Using the Krein-Rutman theorem we show their Lyapunov instability.

Place, publisher, year, edition, pages
2013. Vol. 75, no 4, 445-458 p.
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Mathematics
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URN: urn:nbn:se:uu:diva-196851DOI: 10.1007/s00020-013-2045-5ISI: 000316366300001OAI: oai:DiVA.org:uu-196851DiVA: diva2:610971
Available from: 2013-03-13 Created: 2013-03-13 Last updated: 2017-12-06Bibliographically approved

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Oleynik, Anna

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