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.
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
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\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
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\crossref{https://doi.org/10.15826/umj.2020.1.001}
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This publication is cited in the following 2 articles:
A.K.M. Nazimuddin, M. Humayun Kabir, M. Osman Gani, “Spiral patterns and numerical bifurcation analysis in a three-component Brusselator model for chemical reactions”, Mathematics and Computers in Simulation, 203 (2023), 577
Ekaterina E. Kopets, Artur I. Karimov, Aliya M. Khafizova, Evgenii A. Katser, Tatiana G. Shchetinina, 2022 Conference of Russian Young Researchers in Electrical and Electronic Engineering (ElConRus), 2022, 704