24 citations · 72 across the 28 of their papers we have counts for
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Travelling waves for spatially discrete systems of FitzHugh-Nagumo type with periodic coefficients
W. M. Schouten, H. J. Hupkes
We establish the existence and nonlinear stability of travelling wave solutions for a class of lattice differential equations (LDEs) that includes the discrete FitzHugh-Nagumo syst…
Stability of Traveling Waves for Systems of Reaction-Diffusion Equations with Multiplicative Noise
Christian Hamster, Hermen Jan Hupkes
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable traveling wave solutions to the determi…
Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions
W. M. Schouten, H. J. Hupkes
We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum l…
Bichromatic travelling waves for lattice Nagumo equations
Hermen Jan Hupkes, Leonardo Morelli, Petr Stehlík
We discuss bichromatic (two-color) front solutions to the bistable Nagumo lattice differential equation. Such fronts connect the stable spatially homogeneous equilibria with spatia…