'Traveling wave'' solutions of Fitzhugh model with cross-diffusion - F. Berezovskaya; Erika Camacho; Stephen Wirkus; Georgy Karev (Mathematical Biosciences and Engineering)
The FitzHugh-Nagumo equations have been used as a caricatureof the Hodgkin-Huxley equations of neuron FIring and to capture, qualitatively,the general properties of an excitable membrane. In this paper, we utilizea modified version of the FitzHugh-Nagumo equations to model the spatialpropagation of neuron firing; we assume that this propagation is (at least,partially) caused by the cross-diffusion connection between the potential andrecovery variables. We show that the cross-diffusion version of the model, be-sides giving rise to the typical fast traveling wave solution exhibited in theoriginal ''diffusion'' FitzHugh-Nagumo equations, additionally gives rise to aslow traveling wave solution. We analyze all possible traveling wave solutionsof 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.