Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations

. 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 dierence,g(c) = a1,a2 between the detuning parameters ai that is required to make both waves move at the same speed c. Of particular interest is the eect,of a coupling parameter,and an \alignment" parameter A on the function g. Numerical investigation indicates that for xed A, there exists a time delay value that results in g = 0; and for large enough wave speeds, multiple such values exist. Also, numerical results indicate that the perturbation of,away from zero will yield additional solutions with positive wave speed when A = , 2 . We employ both analytical and numerical results to demonstrate our claims.