Existence of a complex closed trajectory in a three-dimensional dynamical system

Азамов, Абдулла; Akhmedov, Odiljon S.

doi:10.1134/s0965542511080033

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Cited by 3 publications

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“…One may conclude that the only way to prove the existence of a closed trajectory is to apply the method of Poincaré map. To construct the Poincaré map, we use the DN-tracking method [3,5]. To this end, first, it is necessary to choose the starting point as close to the proposed closed trajectory as possible.…”

Section: Resultsmentioning

confidence: 99%

Four–dimensional Brusselator Model With Periodical Solution

Akhmedov

Азамов

Ibragimov

2020

UMJ

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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.

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Section: Resultsmentioning

confidence: 99%