3 papers
math.DS2020
Travelling wave solutions for fully discrete FitzHugh-Nagumo type equations with infinite-range interactions
Willem M. Schouten-Straatman, Hermen Jan Hupkes
We investigate the impact of spatial-temporal discretisation schemes on the dynamics of a class of reaction-diffusion equations that includes the FitzHugh-Nagumo system. For the te…
math.DS2020
Exponential Dichotomies for Nonlocal Differential Operators with Infinite Range Interactions
Willem M. Schouten-Straatman, Hermen Jan Hupkes
We show that MFDEs with infinite range discrete and/or continuous interactions admit exponential dichotomies, building on the Fredholm theory developed by Faye and Scheel for such…
math.DS2018
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…