62 citations · 117 across the 28 of their papers we have counts for
4 papers · 1 filter
Pinning and Unpinning in Nonlocal Systems
Taylor Anderson, Gregory Faye, Arnd Scheel +1
We investigate pinning regions and unpinning asymptotics in nonlocal equations. We show that phenomena are related to but different from pinning in discrete and inhomogeneous media…
Modulated traveling fronts for a nonlocal Fisher-KPP equation: a dynamical systems approach
Gregory Faye, Matt Holzer
We consider a nonlocal generalization of the Fisher-KPP equation in one spatial dimension. As a parameter is varied the system undergoes a Turing bifurcation. We study the dynamics…
Pulsatile localized dynamics in delayed neural-field equations in arbitrary dimension
Grégory Faye, Jonathan Touboul
Neural field equations are integro-differential systems describing the macroscopic activity of spatially extended pieces of cortex. In such cortical assemblies, the propagation of…
Pulse bifurcations in stochastic neural fields
Zachary P Kilpatrick, Gregory Faye
We study the effects of additive noise on traveling pulse solutions in spatially extended neural fields with linear adaptation. Neural fields are evolution equations with an integr…