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Ural Mathematical Journal, 2020, Volume 6, Issue 1, Pages 3–15
DOI: https://doi.org/10.15826/umj.2020.1.001 (Mi umj107) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Four-dimensional brusselator model with periodical solution

Odiljon S. Akhmedova, Abdulla A. Azamova, Gafurjan I. Ibragimovb

a Uzbekistan Academy of Sciences V. I. Romanovskiy Institute of Mathematics
b Department of Mathematics & Institute for Mathematical Research, University Putra Malaysia
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DOI: https://doi.org/10.15826/umj.2020.1.001
Abstract: In the paper, a four-dimensional model of cyclic reactions of the type Prigogine's Brusselator is considered. It is shown that the corresponding dynamical system does not have a closed trajectory in the positive orthant that will make it inadequate with the main property of chemical reactions of Brusselator type. Therefore, a new modified Brusselator model is proposed in the form of a four-dimensional dynamic system. Also, the existence of a closed trajectory is proved by the DN-tracking method for a certain value of the parameter which expresses the rate of addition one of the reagents to the reaction from an external source.
Keywords: chemical reaction, closed trajectory, dN-tracking method, discrete trajectory, numerical trajectory.
Funding agency Grant number
Ministry of Innovative Development of the Republic of Uzbekistan OT-Φ4-84
This work was supported by the grant of the Ministry of Innovative Development of the Republic of Uzbekistan (Project No. OT-Φ4-84).
Bibliographic databases:
Document Type: Article
Language: English
Citation: Odiljon S. Akhmedov, Abdulla A. Azamov, Gafurjan I. Ibragimov, “Four-dimensional brusselator model with periodical solution”, Ural Math. J., 6:1 (2020), 3–15
Citation in format AMSBIB
\Bibitem{AkhAzaIbr20}
\by Odiljon S. Akhmedov, Abdulla A. Azamov, Gafurjan I. Ibragimov
\paper Four-dimensional brusselator model with periodical solution
\jour Ural Math. J.
\yr 2020
\vol 6
\issue 1
\pages 3--15
\mathnet{http://mi.mathnet.ru/umj107}
\crossref{https://doi.org/10.15826/umj.2020.1.001}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4128756}
\zmath{https://zbmath.org/?q=an:07255684}
\elib{https://elibrary.ru/item.asp?id=43793620}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85089114580}
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    • This publication is cited in the following 2 articles:
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