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math.AP2018★ 7 cited
A gradient flow formulation for the stochastic Amari neural field model
Christian Kuehn, Jonas M. Tölle
We study stochastic Amari-type neural field equations, which are mean-field models for neural activity in the cortex. We prove that under certain assumptions on the coupling kernel…
math.AP2018
Pattern formation in the doubly-nonlocal Fisher-KPP equation
Christian Kuehn, Pasha Tkachov
We study the existence, bifurcations, and stability of stationary solutions for the doubly-nonlocal Fisher-KPP equation. We prove using Lyapunov-Schmidt reduction that under suitab…