Singular perturbation of N-front traveling waves in the Fitzhugh-Nagumo equations. Nonlinear Anal

Abstract. In this paper we consider travelling wave solutions of the FitzHugh-Nagumo equations vt = vxx + f(v) − w, wt = (v − γw), which are singularly perturbed by the parameter 0 < ¿ 1. The equations possess n-front travelling waves that correspond to n-front heteroclinic orbits in a travelling coordinate frame. These solutions bifurcate from a double twisted heteroclinic loop at = 0. Previous works showed that the n-front bifurcation branches in the γc-parameter space, where c is the propagation speed of the travelling waves, shrink to the bifurcation loop point as → 0+. A proof is sketched to show that these n-front bifurcation branches can be uniformly continued in a γc-parameter region independent of → 0+