Brusselator: an abstract chemical reaction?

A.I. Lavrova^a, E.B. Postnikov^b, Yu.M. Romanovsky^c
^aHumboldt-Universität zu Berlin, Institut für Physik, Newtonstraße 15, Berlin, 12489, Germany
^bPhysics and Mathematics Faculty, Kursk State University, ul. Radishcheva 33, Kursk, 305000, Russian Federation
^cLomonosov Moscow State University, Faculty of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation

In this paper we consider the Brusselator and the Sel’kov model, which describes the irreversible reaction of glycolysis in the regime of self-sustained oscillations. We show that these two differently constructed models can be reduced to a single equation— a generalized Rayleigh equation. The physical basis for this generality is investigated. The advantages of this equation as a tool for qualitative and quantitative analyses, as well as the similarities and differences of the solutions realized for each of the two concrete models in the cases of almost harmonic and relaxation self-sustained oscillations, are discussed.

PACS: 02.30.Hq, 82.39.−k, 82.40.Bj (all)
DOI: 10.3367/UFNe.0179.200912h.1327
URL: https://ufn.ru/en/articles/2009/12/d/
Web of Science

000285142600003
Scopus

2-s2.0-78650930573
ADS NASA

2009PhyU...52.1239L
Citation: Lavrova A I, Postnikov E B, Romanovsky Yu M "Brusselator: an abstract chemical reaction?" Phys. Usp. 52 1239–1244 (2009)

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Оригинал: Лаврова А И, Постников Е Б, Романовский Ю М «Брюсселятор — абстрактная химическая реакция?» УФН 179 1327–1332 (2009); DOI: 10.3367/UFNr.0179.200912h.1327