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International Journal of Applied Mathematics and Computer Science

Journal of University of Zielona Gora and Lubuskie Scientific Society

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Volume 24, Issue 4


A modified van der Pol equation with delay in a description of the heart action

Beata Zduniak
  • Faculty of Applied Informatics and Mathematics Warsaw University of Life Sciences, Nowoursynowska 159, 02-776 Warsaw, Poland
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/ Marek Bodnar
  • Faculty of Mathematics, Informatics and Mechanics University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
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/ Urszula Foryś
  • Faculty of Mathematics, Informatics and Mechanics University of Warsaw, Banacha 2, 02-097 Warsaw, Poland
  • Other articles by this author:
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Published Online: 2014-12-20 | DOI: https://doi.org/10.2478/amcs-2014-0063


In this paper, a modified van der Pol equation is considered as a description of the heart action. This model has a number of interesting properties allowing reconstruction of phenomena observed in physiological experiments as well as in Holter electrocardiographic recordings. Our aim is to study periodic solutions of the modified van der Pol equation and take into consideration the influence of feedback and delay which occur in the normal heart action mode as well as in pathological modes. Usage of certain values for feedback and delay parameters allows simulating the heart action when an accessory conducting pathway is present (Wolff-Parkinson-White syndrome).

Keywords : system with feedback; stability; action potential


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About the article

Received: 2013-10-02

Revised: 2014-01-08

Published Online: 2014-12-20

Published in Print: 2014-12-01

Citation Information: International Journal of Applied Mathematics and Computer Science, Volume 24, Issue 4, Pages 853–863, ISSN (Online) 2083-8492, DOI: https://doi.org/10.2478/amcs-2014-0063.

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© by Beata Zduniak. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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