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arXiv · 1112.2941

On the Existence of Unstable Bumps in Neural Networks

Vadim Kostrykin·Anna Oleynik
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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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Vadim Kostrykin, Anna Oleynik. 2013-02-05. On the Existence of Unstable Bumps in Neural Networks. https://arxiv.org/abs/1112.2941

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