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

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.