RESUMEN

We consider a coupled system of discrete Nagumo equations and derive traveling wave solutions to this system using McKean's caricature of the cubic. A certain form of this system is used to model ephaptic coupling between pairs of nerve axons. We study the difference $g(c)=a_1-a_2$ between the detuning parameters $a_i$ that is required to make both waves move at the same speed $c$. Of particular interest is the effect of a coupling parameter $\alpha$ and an "alignment" parameter $A$ on the function $g$. Numerical investigation indicates that for fixed $A$, there exists a time delay value $\beta$ that results in $g=0$, and for large enough wave speeds, multiple such $\beta$ values exist. Also, numerical results indicate that the perturbation of $\alpha$ away from zero will yield additional solutions with positive wave speed when $A={1\over 2}$. We employ both analytical and numerical results to demonstrate our claims.