'Traveling wave'' solutions of Fitzhugh model with cross-diffusion
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...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2008-02-01
|
| Series: | Mathematical Biosciences and Engineering |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.239 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832590229668626432 |
|---|---|
| author | F. Berezovskaya Erika Camacho Stephen Wirkus Georgy Karev |
| author_facet | F. Berezovskaya Erika Camacho Stephen Wirkus Georgy Karev |
| author_sort | F. Berezovskaya |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-f33558a844d74db78930798770572cf0 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2008-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f33558a844d74db78930798770572cf02025-01-24T01:58:10ZengAIMS PressMathematical Biosciences and Engineering1551-00182008-02-015223926010.3934/mbe.2008.5.239'Traveling wave'' solutions of Fitzhugh model with cross-diffusionF. Berezovskaya0Erika Camacho1Stephen Wirkus2Georgy Karev3Department of Mathematics, Howard University, Washington D.C., 20059Department of Mathematics, Howard University, Washington D.C., 20059Department of Mathematics, Howard University, Washington D.C., 20059Department of Mathematics, Howard University, Washington D.C., 20059The 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.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.239fitzhughcross-diffusion.traveling wave solutions |
| spellingShingle | F. Berezovskaya Erika Camacho Stephen Wirkus Georgy Karev 'Traveling wave'' solutions of Fitzhugh model with cross-diffusion Mathematical Biosciences and Engineering fitzhugh cross-diffusion. traveling wave solutions |
| title | 'Traveling wave'' solutions of Fitzhugh model with cross-diffusion |
| title_full | 'Traveling wave'' solutions of Fitzhugh model with cross-diffusion |
| title_fullStr | 'Traveling wave'' solutions of Fitzhugh model with cross-diffusion |
| title_full_unstemmed | 'Traveling wave'' solutions of Fitzhugh model with cross-diffusion |
| title_short | 'Traveling wave'' solutions of Fitzhugh model with cross-diffusion |
| title_sort | traveling wave solutions of fitzhugh model with cross diffusion |
| topic | fitzhugh cross-diffusion. traveling wave solutions |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.239 |
| work_keys_str_mv | AT fberezovskaya travelingwavesolutionsoffitzhughmodelwithcrossdiffusion AT erikacamacho travelingwavesolutionsoffitzhughmodelwithcrossdiffusion AT stephenwirkus travelingwavesolutionsoffitzhughmodelwithcrossdiffusion AT georgykarev travelingwavesolutionsoffitzhughmodelwithcrossdiffusion |