"Traveling wave" solutions of FitzHugh model with cross-diffusion.
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.
Berezovskaya
Faina
F
Department of Mathematics, Howard University, Washington DC 20059, USA. fsberezo@hotmail.com
Camacho
Erika
E
Wirkus
Stephen
S
Karev
Georgy
G
D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D000818:Animals; D002462:Cell Membrane / Q000378:metabolism; D003198:Computer Simulation; D004058:Diffusion; D006801:Humans; D008954:Models, Biological; D008959:Models, Neurological; D008962:Models, Theoretical; D009474:Neurons / Q000378:metabolism*