On the Existence of Unstable Bumps in Neural Networks
Dynamical Systems
2013-02-07 v2 Functional Analysis
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.
Keywords
Cite
@article{arxiv.1112.2941,
title = {On the Existence of Unstable Bumps in Neural Networks},
author = {Vadim Kostrykin and Anna Oleynik},
journal= {arXiv preprint arXiv:1112.2941},
year = {2013}
}