On the Existence of Unstable Bumps in Neural Networks |
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| Authors: | Vadim Kostrykin Anna Oleynik |
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| Institution: | 1. FB 08, Institut für Mathematik, Johannes Gutenberg-Universit?t Mainz, Staudinger Weg 9, 55099, Mainz, Germany
2. Department of Mathematics, University of Uppsala, Box 480, 75106, Uppsala, Sweden
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| Abstract: | 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. |
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