The FitzHugh-Nagumo equations have been used as a caricature
of the Hodgkin-Huxley equations of neuron FIring and to capture, qualitatively,
the general properties of an excitable membrane. In this paper, we utilize
a modified version of the FitzHugh-Nagumo equations to model the spatial
propagation of neuron firing; we assume that this propagation is (at least,
partially) caused by the cross-diffusion connection between the potential and
recovery variables. We show that the cross-diffusion version of the model, be-
sides giving rise to the typical fast traveling wave solution exhibited in the
original ''diffusion'' FitzHugh-Nagumo equations, additionally gives rise to a
slow traveling wave solution. We analyze all possible traveling wave solutions
of the model and show that there exists a threshold of the cross-diffusion coefficient (for a given speed of propagation), which bounds the area where ''normal''
impulse propagation is possible.
Mathematics Subject Classification: Primary: 34C20, 34C23; Secondary: 92C99.