Cardiac Alternans Arising from an Unfolded Border-Collision Bifurcation

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dc.creatorZhao, Xiaopeng
dc.creatorSchaeffer, David G.
dc.creatorBerger, Carolyn M.
dc.creatorKrassowska, Wanda
dc.creatorGauthier, Daniel J.
dc.date2007-12-20
dc.date.accessioned2026-07-07T08:50:32Z
dc.date.available2026-07-07T08:50:32Z
dc.descriptionFollowing an electrical stimulus, the transmembrane voltage of cardiac tissue rises rapidly and remains at a constant value before returning to the resting value, a phenomenon known as an action potential. When the pacing rate of a periodic train of stimuli is increased above a critical value, the action potential undergoes a period-doubling bifurcation, where the resulting alternation of the action potential duration is known as alternans in the medical literature. Existing cardiac models treat alternans either as a smooth or as a border-collision bifurcation. However, recent experiments in paced cardiac tissue reveal that the bifurcation to alternans exhibits hybrid smooth/nonsmooth behaviors, which can be qualitatively described by a model of so-called unfolded border-collision bifurcation. In this paper, we obtain analytical solutions of the unfolded border-collision model and use it to explore the crossover between smooth and nonsmooth behaviors. Our analysis shows that the hybrid smooth/nonsmooth behavior is due to large variations in the system's properties over a small interval of the bifurcation parameter, providing guidance for the development of future models.
dc.description18 pages, 6 figures
dc.identifierhttps://arxiv.org/abs/0712.3336
dc.identifierhttp://arxiv.org/abs/0712.3336
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144632
dc.subjectBiological Physics
dc.titleCardiac Alternans Arising from an Unfolded Border-Collision Bifurcation
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