49 citations · 253 across the 59 of their papers we have counts for
26 papers · 1 filter
Oscillations in a scalar differential equation coupled to a diffusive field
Merlin Pelz, Arnd Scheel
We study the emergence of periodic oscillations through a Hopf bifurcation in a scalar diffusion equation on the half line coupled to a dynamic boundary condition. Our results quan…
Diffusive synchronization of phase waves in the FitzHugh-Nagumo system
Montie Avery, Paul Carter, Björn de Rijk +1
We analyze synchronization of relaxation oscillations in multiple-timescale reaction-diffusion systems. Interpreting synchronization as convergence to frequency-synchronized wave-t…
Selection mechanisms in front invasion
Montie Avery, Matt Holzer, Arnd Scheel
We review progress on questions related to front propagation into unstable states and point out open problems in the area. We strive to highlight different theoretical perspectives…
Pulled fronts are not (just) pulled
Montie Avery, Matt Holzer, Arnd Scheel
Front propagation into unstable states is often determined by the linearization, that is, propagation speeds agree with predictions from the linearized equation at the unstable sta…
Pinning and dipole asymptotics of locally deformed striped phases
Arnd Scheel, Qiliang Wu
We investigate the effect of spatial inhomogeneity on perfectly periodic, self-organized striped patterns in spatially extended systems. We demonstrate that inhomogeneities select…
Stability of coherent pattern formation through invasion in the FitzHugh-Nagumo system
Montie Avery, Paul Carter, Björn de Rijk +1
We establish sharp nonlinear stability results for fronts that describe the creation of a periodic pattern through the invasion of an unstable state. The fronts we consider are cri…