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Near-Pulse Solutions of the FitzHugh-Nagumo Equations on Cylindrical Surfaces | | Afroditi Talidou
; Almut Burchard
; Israel Michael Sigal
; | | Date: |
15 Apr 2020 | | Abstract: | We consider the FitzHugh-Nagumo (FHN) system on the surface of a long, thin
cylinder that represents the outer membrane of a nerve axon. It is known that
the FHN system admits fast pulse solutions. In this paper, it is shown that a
solution of the FHN system on the standard cylinder of constant radius, with
initial condition close to the fast pulse, decays exponentially to a translated
pulse in time. Moreover, on the surface of a warped cylinder -- a cylinder
whose radius varies slowly along its length -- pulse-like solutions persist if
the radius of that cylinder is close to a constant. | | Source: | arXiv, 2004.6878 | | Services: | Forum | Review | PDF | Favorites | |
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