Conditions are found for a unique homoclinic or periodic orbit to bifurcate from a heteroclinic loop for autonomous ordinary differential equations. This leads to a codimension 2 unfolding of a heteroclinic loop. This approach, based on an idea developed by Šil’nikov, reduces the problem to the study of bifurcation equations. The result is applied to various types of traveling wave solutions of the FitzHugh–Nagumo equations with a cubic nonlinear term.
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Chow et al. (1990) studied this question.