RESUMEN

This paper studies traveling wave solutions for two coupled parallel excitable fibers with piecewise linear FitzHugh–Nagumo dynamics. Singular perturbation techniques are used to reduce the study of traveling waves to a Poincare map of a line segment to itself. The map is shown to have a very complicated structure, and there are correspondingly an infinite variety of (approximate) traveling wave solutions. The behavior of these traveling wave solutions depends strongly on the strength of coupling and the frequency of stimulus, leading to the conclusion that the fibers decouple under high frequency stimulus and weak coupling.