Journal of Mathematical Biology

, Volume 38, Issue 1, pp 1–20

Pulse waves for a semi-discrete Morris–Lecar type model

  • Xinfu Chen
  • Stuart P. Hastings

DOI: 10.1007/s002859970001

Cite this article as:
Chen, X. & Hastings, S. J Math Biol (1999) 38: 1. doi:10.1007/s002859970001


 We establish the existence of a pulse traveling wave for an infinite system of ODEs modeling a one dimensional string of nerve cells of identical Morris–Lecar type dynamics:

Here vj and wj represent, respectively, the electrical potential and the conductance of electrically active membrane of the jth nerve cell. We assume that D is a small positive constant, and F and G are certain nonlinear functions such that the ode system v′=F, w′=G has three equilibria: one is stable, another is a saddle, and the third is unstable.

Key words: Excitable mediumPulse waveTraveling wave

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Xinfu Chen
    • 1
  • Stuart P. Hastings
    • 1
  1. 1.Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USAUS