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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2018, Volume 28, Issue 1, Pages 3–14
DOI: https://doi.org/10.20537/vm180101
(Mi vuu615)
 

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

The phenomenon of stochastic excitability in the enzymatic reaction model

I. A. Bashkirtseva, S. S. Zaitseva

Institute of Natural Science and Mathematics, Ural Federal University, ul. Lenina, 51, Yekaterinburg, 620083, Russia
References:
Abstract: We study the influence of noise on the Goldbeter model of the enzymatic reaction, which describes the mechanism of oscillatory synthesis of cyclic adenosine monophosphate in a cell. It is shown that the model is highly sensitive to variations of parameters and initial conditions. The phenomenon of stochastic excitability in a stable equilibrium zone is demonstrated and studied. We show that the noise results in a sharp transition from low-amplitude stochastic oscillations to large-amplitude spike oscillations. For the parametric analysis of this phenomenon, the technique of stochastic sensitivity functions and the method of confidence ellipses are used. We study how the critical value of the noise intensity corresponding to the generation of large-amplitude oscillations depends on the proximity of a control parameter to a bifurcation point. For a detailed analysis of the frequency properties of stochastic oscillations, a statistical analysis of interspike intervals is carried out, and a phenomenon of coherent resonance is found.
Keywords: random disturbances, excitability, stochastic sensitivity, confidence ellipses.
Funding agency Grant number
Russian Science Foundation 16-11-10098
Received: 25.12.2017
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 93E03
Language: Russian
Citation: I. A. Bashkirtseva, S. S. Zaitseva, “The phenomenon of stochastic excitability in the enzymatic reaction model”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 28:1 (2018), 3–14
Citation in format AMSBIB
\Bibitem{BasZai18}
\by I.~A.~Bashkirtseva, S.~S.~Zaitseva
\paper The phenomenon of stochastic excitability in the enzymatic reaction model
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2018
\vol 28
\issue 1
\pages 3--14
\mathnet{http://mi.mathnet.ru/vuu615}
\crossref{https://doi.org/10.20537/vm180101}
\elib{https://elibrary.ru/item.asp?id=32697211}
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  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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