Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics
We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHugh-Nagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the (bound...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2009/292183 |
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| _version_ | 1832567852642598912 |
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| author | Robert Artebrant |
| author_facet | Robert Artebrant |
| author_sort | Robert Artebrant |
| collection | DOAJ |
| description | We study Hopf bifurcation solutions to the Monodomain model equipped with FitzHugh-Nagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the (bounded) spatial domain consists of two subdomains: a collection of automatic
cells surrounded by collections of normal cells. Thus, the cell model features a discontinuous coefficient. Analytical techniques are applied to approximate the time-periodic solution that arises at the Hopf bifurcation point. Accurate numerical experiments are employed to complement our findings. |
| format | Article |
| id | doaj-art-2f94fe5d2bce4180b8d37939e967b4cc |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-2f94fe5d2bce4180b8d37939e967b4cc2025-02-03T01:00:24ZengWileyJournal of Applied Mathematics1110-757X1687-00422009-01-01200910.1155/2009/292183292183Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo KineticsRobert Artebrant0Department of Scientific Computing, Simula Research Laboratory, P.O. Box 134, 1325 Lysaker, NorwayWe study Hopf bifurcation solutions to the Monodomain model equipped with FitzHugh-Nagumo cell dynamics. This reaction-diffusion system plays an important role in the field of electrocardiology as a tractable mathematical model of the electrical activity in the human heart. In our setting the (bounded) spatial domain consists of two subdomains: a collection of automatic cells surrounded by collections of normal cells. Thus, the cell model features a discontinuous coefficient. Analytical techniques are applied to approximate the time-periodic solution that arises at the Hopf bifurcation point. Accurate numerical experiments are employed to complement our findings.http://dx.doi.org/10.1155/2009/292183 |
| spellingShingle | Robert Artebrant Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics Journal of Applied Mathematics |
| title | Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics |
| title_full | Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics |
| title_fullStr | Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics |
| title_full_unstemmed | Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics |
| title_short | Bifurcating Solutions to the Monodomain Model Equipped with FitzHugh-Nagumo Kinetics |
| title_sort | bifurcating solutions to the monodomain model equipped with fitzhugh nagumo kinetics |
| url | http://dx.doi.org/10.1155/2009/292183 |
| work_keys_str_mv | AT robertartebrant bifurcatingsolutionstothemonodomainmodelequippedwithfitzhughnagumokinetics |