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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2015, Volume 55, Number 7, Pages 1136–1155
DOI: https://doi.org/10.7868/S0044466915070078 (Mi zvmmf10233) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Blue sky catastrophe as applied to modeling of cardiac rhythms

S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb

a Faculty of Mathematics, Yaroslavl State University, ul. Sovetskaya 14, Yaroslavl, 150000, Russia
b Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia
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DOI: https://doi.org/10.7868/S0044466915070078
Abstract: A new mathematical model for the electrical activity of the heart is proposed. The model represents a special singularly perturbed three-dimensional system of ordinary differential equations with one fast and two slow variables. A characteristic feature of the system is that its solution performs nonclassical relaxation oscillations and simultaneously undergoes a blue sky catastrophe bifurcation. Both these factors make it possible to achieve a phenomenological proximity between the time dependence of the fast component in the model and an ECG of the human heart.
Key words: singularly perturbed system, relaxation cycle, asymptotic behavior, stability, blue sky catastrophe, modeling of cardiac rhythms.
Received: 03.12.2014
English version:
Computational Mathematics and Mathematical Physics, 2015, Volume 55, Issue 7, Pages 1120–1137
DOI: https://doi.org/10.1134/S0965542515070076
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
Citation: S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Blue sky catastrophe as applied to modeling of cardiac rhythms”, Zh. Vychisl. Mat. Mat. Fiz., 55:7 (2015), 1136–1155; Comput. Math. Math. Phys., 55:7 (2015), 1120–1137
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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