On the Existence of Unstable Bumps in Neural Networks

2011/12/13 by Vadim Kostrykin, Kostrykin, Vadim, Anna Oleynik +1
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Model Reduction and Neural Networks #Neural Networks Stability and Synchronization #Stability and Controllability of Differential Equations #math.DS #math.FA #msc:37C75 #msc:47H07 #msc:47H10 #msc:92B20

paper · pdf · doi:10.48550/arxiv.1112.2941

arxiv created 2013/02/05 · arxiv updated 2013/02/07

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.

Citations

• Fixed Point Equations and Nonlinear Eigenvalue Problems in Ordered Banach Spaces

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