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math.AP2026
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…
math.AP2026
Stability and dynamics of planar fronts in reaction-diffusion systems under nonlocalized perturbations
Björn de Rijk, Joris van Winden
We analyze the stability and dynamics of bistable planar fronts in multicomponent reaction-diffusion systems on . Under standard spectral stability assumptions, we…
math.AP2026
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…