Geodesic
Four-dimensional brusselator model with periodical solution
Ural mathematical journal, Tome 6 (2020) no. 1, pp. 3-15

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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. 
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     title = {Four-dimensional brusselator model with periodical solution},
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Odiljon S. Akhmedov; Abdulla A. Azamov; Gafurjan I. Ibragimov. Four-dimensional brusselator model with periodical solution. Ural mathematical journal, Tome 6 (2020) no. 1, pp. 3-15. http://geodesic.mathdoc.fr/item/UMJ_2020_6_1_a0/