Brusselator: an abstract chemical reaction?
A.I. Lavrova a
E.B. Postnikov b
Yu.M. Romanovsky c
a Humboldt-Universität zu Berlin, Institut für Physik, Newtonstraße 15, Berlin, 12489, Germany
b Physics and Mathematics Faculty, Kursk State University, ul. Radishcheva 33, Kursk, 305000, Russian Federation
c Lomonosov Moscow State University, Department 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.