62 citations · 117 across the 28 of their papers we have counts for
4 papers · 1 filter
Threshold of front propagation in neural fields: An interface dynamics approach
Gregory Faye, Zachary P Kilpatrick
Neural field equations model population dynamics of large-scale networks of neurons. Wave propagation in neural fields is often studied by constructing traveling wave solutions in…
Bifurcation to locked fronts in two component reaction-diffusion systems
Gregory Faye, Matt Holzer
We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the ex…
Linear spreading speeds from nonlinear resonant interaction
Gregory Faye, Matt Holzer, Arnd Scheel
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such r…
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…