6 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…
Selection of pushed pattern-forming fronts in the FitzHugh-Nagumo system
Montie Avery, Paul Carter, Björn de Rijk
We establish nonlinear stability of fronts that describe the creation of a periodic pattern through the invasion of an unstable state. Our results concern pushed fronts, that is, f…
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…
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…
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…
Fronts and patterns with a dynamic parameter ramp
Montie Avery, Odalys Garcia-Lopez, Ryan Goh +2
We examine the effect of a slowly-varying time-dependent parameter on invasion fronts for which an unstable homogeneous equilibrium is invaded by either another homogeneous state o…