Journal of Mathematical Biology

, Volume 38, Issue 1, pp 1–20 | Cite as

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

  • Xinfu Chen
  • Stuart P. Hastings

Abstract.

 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 medium Pulse wave Traveling wave 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations