On the Existence of Unstable Bumps in Neural Networks
Vadim V. Kostrykin, Anna Oleynik · arXiv (Cornell University) · 2011
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.