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.