62 citations · 117 across the 28 of their papers we have counts for
4 papers · 1 filter
Existence of pulses in excitable media with nonlocal coupling
Gregory Faye, Arnd Scheel
We prove the existence of fast traveling pulse solutions in excitable media with non-local coupling. Existence results had been known, until now, in the case of local, diffusive co…
Fredholm properties of nonlocal differential operators via spectral flow
Gregory Faye, Arnd Scheel
We establish Fredholm properties for a class of nonlocal differential operators. Using mild convergence and localization conditions on the nonlocal terms, we also show how to compu…
Continuation of localised coherent structures in nonlocal neural field equations
James Rankin, Daniele Avitabile, Javier Baladron +2
We study localised activity patterns in neural field equations posed on the Euclidean plane; such models are commonly used to describe the coarse-grained activity of large ensemble…
Pattern formation for the Swift-Hohenberg equation on the hyperbolic plane
Pascal Chossat, Grégory Faye
We present an overview of pattern formation analysis for an analogue of the Swift-Hohenberg equation posed on the real hyperbolic space of dimension two, which we identify with the…