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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Main Author: Robert Artebrant
Format: Article
Language:English
Published: Wiley 2009-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2009/292183
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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.
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institution Kabale University
issn 1110-757X
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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