Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions

Journal article (2019)

Authors

W.M. Schouten-Straatman Universiteit Leiden
Hermen Jan Hupkes Universiteit Leiden
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Published Date

2019

Language

English

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Abstract

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 limit. For the verification of the spectral properties, we need to study a functional differential equation of mixed type (MFDE) with unbounded shifts. We avoid the use of exponential dichotomies and phase spaces, by building on a technique developed by Bates, Chen and Chmaj for the discrete Nagumo equation. This allows us to transfer several crucial Fredholm properties from the PDE setting to our discrete setting.