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Izv. IMI UdGU, 2019, Volume 53, Pages 27–35 (Mi iimi368)  

Analysis of multimodal stochastic oscillations in a biochemical reaction model

I. A. Bashkirtseva, S. S. Zaitseva

Institute of Natural Science and Mathematics, Ural Federal University, ul. Lenina, 51, Yekaterinburg, 620083, Russia

Abstract: This paper studies the dynamics of the two-dimensional biochemical Goldbeter model under the influence of random disturbances. The model describes an enzymatic reaction with nonlinear recirculation of a product into a substrate. We investigate parametric zones where the system exhibits the phenomenon of bistability: the coexistence of two stable periodic regimes or the coexistence of a stable equilibrium and a stable limit cycle. The noise-induced transitions of stochastic trajectories between deterministic attractors resulting in multimodal oscillations are demonstrated via the direct numerical simulation. It is shown how the effect of noise on the system changes the frequency and amplitude characteristics of stochastic self-oscillations.

Keywords: Goldbeter model, bistability, stochastic dynamics, random disturbances.

Funding Agency Grant Number
Russian Science Foundation 16-11-10098
This work was supported by the Russian Science Foundation (project no. 16-11-10098).


DOI: https://doi.org/10.20537/2226-3594-2019-53-03

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UDC: 517.977
MSC: 93E03
Received: 05.04.2019

Citation: I. A. Bashkirtseva, S. S. Zaitseva, “Analysis of multimodal stochastic oscillations in a biochemical reaction model”, Izv. IMI UdGU, 53 (2019), 27–35

Citation in format AMSBIB
\Bibitem{BasZai19}
\by I.~A.~Bashkirtseva, S.~S.~Zaitseva
\paper Analysis of multimodal stochastic oscillations in a biochemical reaction model
\jour Izv. IMI UdGU
\yr 2019
\vol 53
\pages 27--35
\mathnet{http://mi.mathnet.ru/iimi368}
\crossref{https://doi.org/10.20537/2226-3594-2019-53-03}
\elib{http://elibrary.ru/item.asp?id=38503196}


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