Journal of Mathematical Biology

, Volume 38, Issue 1, pp 1-20

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

  • Xinfu ChenAffiliated withDepartment of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA
  • , Stuart P. HastingsAffiliated withDepartment of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

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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 v j and w j 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