The bifurcation of homoclinic orbits from two heteroclinic orbits-a topological approach

Abstract

Conditions are found for a homoclinic orbit to bifurcate from a heteroclinic loop for autonomous ordinary differential equations. The results axe applied to prove the existence of traveling wave solutions of the FitzHugh-Nagumo equations and a system of reaction diffusion equations which arise as a model for a two step combustion process.

Keywords:

• Bifurcation
• homoclinic orbits
• heteroclinic orbits