dorsal/arxiv
View SchemaTraveling wave solutions of Fitzhugh model with cross-diffusion
| Authors | F. Berezovskaya, E. Camacho, S. Wirkus, G. Karev |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0505031 |
| URL | https://arxiv.org/abs/q-bio/0505031 |
Abstract
The Fitzhugh-Nagumo equations have been used as a caricature of the Hodgkin-Huxley equations of neuron firing to better understand the essential dynamics of the interaction of the membrane potential and the restoring force and to capture, qualitatively, the general properties of an excitable membrane. Even though its simplicity allows very valuable insight to be gained, the accuracy of reproducing real experimental results is limited. 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, besides giving rise to the typical fast traveling wave solution exhibited in the original diffusion Fitzhugh-Nagumo equations, also gives rise to a slow traveling wave solution. We analyze all possible traveling wave solutions of the Fitzhugh-Nagumo equations with this cross-diffusion term and show that there exists a threshold of the cross-diffusion coefficient (the maximum value for a given speed of propagation), which bounds the area where normal impulse propagation is possible.
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"abstract": "The Fitzhugh-Nagumo equations have been used as a caricature of the\nHodgkin-Huxley equations of neuron firing to better understand the essential\ndynamics of the interaction of the membrane potential and the restoring force\nand to capture, qualitatively, the general properties of an excitable membrane.\nEven though its simplicity allows very valuable insight to be gained, the\naccuracy of reproducing real experimental results is limited. In this paper, we\nutilize a modified version of the Fitzhugh-Nagumo equations to model the\nspatial propagation of neuron firing; we assume that this propagation is (at\nleast, partially) caused by the cross-diffusion connection between the\npotential and recovery variables. We show that the cross-diffusion version of\nthe model, besides giving rise to the typical fast traveling wave solution\nexhibited in the original diffusion Fitzhugh-Nagumo equations, also gives rise\nto a slow traveling wave solution. We analyze all possible traveling wave\nsolutions of the Fitzhugh-Nagumo equations with this cross-diffusion term and\nshow that there exists a threshold of the cross-diffusion coefficient (the\nmaximum value for a given speed of propagation), which bounds the area where\nnormal impulse propagation is possible.",
"arxiv_id": "q-bio/0505031",
"authors": [
"F. Berezovskaya",
"E. Camacho",
"S. Wirkus",
"G. Karev"
],
"categories": [
"q-bio.NC"
],
"title": "Traveling wave solutions of Fitzhugh model with cross-diffusion",
"url": "https://arxiv.org/abs/q-bio/0505031"
},
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