FOUR–DIMENSIONAL BRUSSELATOR MODEL WITH PERIODICAL SOLUTION

Odiljon S. Akhmedov     (Uzbekistan Academy of Sciences V. I. Romanovskiy Institute of Mathematics, Tashkent, 100041, Uzbekistan)
Abdulla A. Azamov     (Uzbekistan Academy of Sciences V. I. Romanovskiy Institute of Mathematics, Tashkent, 100041, Uzbekistan)
Gafurjan I. Ibragimov     (Department of Mathematics & Institute for Mathematical Research, University Putra Malaysia, 43400 Serdang Selangor, Malaysia)

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.

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DOI: http://dx.doi.org/10.15826/umj.2020.1.001

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