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Vestn. YuUrGU. Ser. Vych. Matem. Inform., 2018, Volume 7, Issue 1, Pages 5–15 (Mi vyurv181)  

Computational Mathematics

Mathematical modelling of stationary state and oscillatory regimes in oregonator

L. A. Prokudina, S. U. Turlakova

South Ural State University (pr. Lenina 76, Chelyabinsk, 454080 Russia)

Abstract: Oscillatory systems are widely used in various areas of research (chemical, biological, environmental oscillators). The article presents the five-stage Field–Noyes–Köros model of the Belousov–Zhabotinsky reaction and the corresponding mathematical model of the oregonator. A system of equations for the stationary states of oregonator is derived. Stationary states of oregonator are calculated depending on the speed of direct reactions for various values of stoichiometric coefficient. Simulation of homogeneous stationary state of the system was conducted according to the experimental data of the authors of the model. The stationary solutions corresponded to the physical meaning of the model. In framework of the system of ordinary differential equations of the kinetics reactive systems oscillatory regimes are calculated. The time for oscillatory regime is determined. The amplitudes of the oscillations are corresponded to the experimental data of the authors of the model. The instability of the stationary state of the oregonator to perturbations is investigated.

Keywords: Belousov–Zhabotinsky’s reaction, oregonator, steady states, oscillatory regimes.

DOI: https://doi.org/10.14529/cmse180101

Full text: PDF file (682 kB)
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UDC: 519.87, 577.3, 544.1
Received: 18.07.2017

Citation: L. A. Prokudina, S. U. Turlakova, “Mathematical modelling of stationary state and oscillatory regimes in oregonator”, Vestn. YuUrGU. Ser. Vych. Matem. Inform., 7:1 (2018), 5–15

Citation in format AMSBIB
\Bibitem{ProTur18}
\by L.~A.~Prokudina, S.~U.~Turlakova
\paper Mathematical modelling of stationary state and oscillatory regimes in oregonator
\jour Vestn. YuUrGU. Ser. Vych. Matem. Inform.
\yr 2018
\vol 7
\issue 1
\pages 5--15
\mathnet{http://mi.mathnet.ru/vyurv181}
\crossref{https://doi.org/10.14529/cmse180101}
\elib{http://elibrary.ru/item.asp?id=32611426}


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  • Vestnik Yuzhno-Ural'skogo Gosudarstvennogo Universiteta. Seriya "Vychislitelnaya Matematika i Informatika"
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