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On the Existence and Stability of Fast Traveling Waves in a Doubly Diffusive FitzHugh--Nagumo System

On the Existence and Stability of Fast Traveling Waves in a Doubly Diffusive FitzHugh--Nagumo System

The FitzHugh-Nagumo equation, which was derived as a simplification of the Hodgkin-Huxley model for nerve impulse propagation, has been extensively studied as a paradigmatic activator-inhibitor system. We consider the version of this system in which two agents diffuse at an equal rate. Using geometric singular perturbation theory, we prove the …