Four-dimensional brusselator model with periodical solution

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 o...

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Main Authors: Akhmedov, Odiljon S., Azamov, Abdulla A., Ibragimov, Gafurjan I.
Format: Article
Language:English
Published: Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences 2020
Online Access:http://psasir.upm.edu.my/id/eprint/89062/
http://psasir.upm.edu.my/id/eprint/89062/1/FOUR.pdf
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author Akhmedov, Odiljon S.
Azamov, Abdulla A.
Ibragimov, Gafurjan I.
author_facet Akhmedov, Odiljon S.
Azamov, Abdulla A.
Ibragimov, Gafurjan I.
author_sort Akhmedov, Odiljon S.
building UPM Institutional Repository
collection Online Access
description 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.
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spelling upm-890622021-09-21T23:13:13Z http://psasir.upm.edu.my/id/eprint/89062/ Four-dimensional brusselator model with periodical solution Akhmedov, Odiljon S. Azamov, Abdulla A. Ibragimov, Gafurjan I. 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. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of Russian Academy of Sciences 2020 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/89062/1/FOUR.pdf Akhmedov, Odiljon S. and Azamov, Abdulla A. and Ibragimov, Gafurjan I. (2020) Four-dimensional brusselator model with periodical solution. Ural Mathematical Journal, 6 (1). pp. 3-15. ISSN 2414-3952 https://umjuran.ru/index.php/umj/article/view/220 10.15826/umj.2020.1.001
spellingShingle Akhmedov, Odiljon S.
Azamov, Abdulla A.
Ibragimov, Gafurjan I.
Four-dimensional brusselator model with periodical solution
title Four-dimensional brusselator model with periodical solution
title_full Four-dimensional brusselator model with periodical solution
title_fullStr Four-dimensional brusselator model with periodical solution
title_full_unstemmed Four-dimensional brusselator model with periodical solution
title_short Four-dimensional brusselator model with periodical solution
title_sort four-dimensional brusselator model with periodical solution
url http://psasir.upm.edu.my/id/eprint/89062/
http://psasir.upm.edu.my/id/eprint/89062/
http://psasir.upm.edu.my/id/eprint/89062/
http://psasir.upm.edu.my/id/eprint/89062/1/FOUR.pdf