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Mathematics > Dynamical Systems

arXiv:1807.11736 (math)
[Submitted on 31 Jul 2018 (v1), last revised 8 May 2019 (this version, v2)]

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

Authors:W.M. Schouten, H.J. Hupkes
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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.
Subjects: Dynamical Systems (math.DS)
MSC classes: 34A33, 34D35, 34K08, 34K26, 34K31
Cite as: arXiv:1807.11736 [math.DS]
  (or arXiv:1807.11736v2 [math.DS] for this version)
  https://doi.org/10.48550/arXiv.1807.11736
Related DOI: https://doi.org/10.3934/dcds.2019205

Submission history

From: Willem Schouten-Straatman [view email]
[v1] Tue, 31 Jul 2018 10:06:28 UTC (146 KB)
[v2] Wed, 8 May 2019 15:06:19 UTC (122 KB)
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