Traveling pulse solutions in a three-component Fitzhugh-Nagumo model

Takashi Teramoto, Peter Van Heijster

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We use geometric singular perturbation techniques combined with an action functional approach to study traveling pulse solutions in a three-component FitzHugh-Nagumo model. First, we derive the profile of traveling 1-pulse solutions with undetermined width and propagating speed. Next, we compute the associated action functional for this profile from which we derive the conditions for existence and a saddle-node bifurcation as the zeros of the action functional and its derivatives. We obtain the same conditions by using a different analytical approach that exploits the singular limit of the problem. We also apply this methodology of the action functional to the problem for traveling 2-pulse solutions and derive the explicit conditions for existence and a saddle-node bifurcation. From these we deduce a necessary condition for the existence of traveling 2-pulse solutions. We end this article with a discussion related to Hopf bifurcations near the saddle-node bifurcation.
Original languageEnglish
Pages (from-to)371-402
Number of pages32
JournalSIAM Journal on Applied Dynamical Systems
Volume20
Issue number1
DOIs
Publication statusE-pub ahead of print - 4 Mar 2021

Keywords

  • Action functional
  • Existence
  • Reaction-diffusion systems
  • Saddle-node bifurcation
  • Singular limit

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