"Traveling wave" solutions of Fitzhugh model with cross-diffusion

Faina Berezovskaya, Erika Camacho, Stephen Wirkus, Georgy Karev

Research output: Contribution to journalArticle

9 Scopus citations

Abstract

The PitzHugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing and to capture, qualitatively, the general properties of an excitable membrane. In this paper, we utilize a modified version of the FitzHugh-Nagumo equations to model the spatial propagation of neuron firing; we assume that this propagation is (at least, partially) caused by the cross-diffusion connection between the potential and recovery variables. We show that the cross-diffusion version of the model, besides giving rise to the typical fast traveling wave solution exhibited in the original "diffusion" FitzHugh-Nagumo equations, additionally gives rise to a slow traveling wave solution. We analyze all possible traveling wave solutions of the model and show that there exists a threshold of the cross-diffusion coefficient (for a given speed of propagation), which bounds the area where "normal" impulse propagation is possible.

Original languageEnglish (US)
Pages (from-to)239-260
Number of pages22
JournalMathematical Biosciences and Engineering
Volume5
Issue number2
DOIs
StatePublished - Apr 2008

Keywords

  • Cross-diffusion
  • Fitzhugh
  • Traveling wave solutions

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences(all)
  • Computational Mathematics
  • Applied Mathematics

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