Near-Pulse Solutions of the FitzHugh-Nagumo Equations on Cylindrical Surfaces
Analysis of PDEs
2021-05-12 v2
Abstract
We introduce a geometrical extension of the FitzHugh-Nagumo equations describing propagation of electrical impulses in nerve axons. In this extension, the axon is modeled as a warped cylinder, rather than a straight line, as is usually done, while pulses propagate on its surface, as is the case with real axons. We prove the stability of electrical impulses for a standard cylinder and existence and stability of pulse-like solutions for warped cylinders whose radii are small and vary slowly along their lengths.
Keywords
Cite
@article{arxiv.2004.06878,
title = {Near-Pulse Solutions of the FitzHugh-Nagumo Equations on Cylindrical Surfaces},
author = {Afroditi Talidou and Almut Burchard and Israel Michael Sigal},
journal= {arXiv preprint arXiv:2004.06878},
year = {2021}
}