8 papers
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…
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…
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…
Instability of anchored spirals in geometric flows
Anthony Cortez, Nan Li, Nathan Mihm +3
We investigate existence, stability, and instability of anchored rotating spiral waves in a model for geometric curve evolution. We find existence in a parameter regime limiting on…
Vacuum bubble and fissure formation in collective motion with competing attractive and repulsive forces
Olivia Clifton, Angel Chavez, Antonio Madrigal +3
We study the continuum limit of the motion of agents in the plane driven by competing short-range repulsion and long-range attractive forces. At a critical parameter value, we find…
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…