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U. G. Magomedbekov, U. G. Gasangadzhieva, Kh. M. Gasanova

Mathematical model of chemical oscillations arising in the homogeneous system of cysteine–oxigenated complexes of iron (II)

Abstract

The analysis of the mathematical model of the kinetics of homogeneous oxidation of cysteine in the presence of oxygenated complexes of iron (II) with dimethylglyoxime and cytosine represented as a system of three nonlinear differential equations was carried out. Simplification of the model on the basis of stoichiometric analysis of the offered kinetic scheme was conducted. On the basis of qualitative analysis of the system of differential equations it was determined that one stationary state with a singular point of the “spatial saddle–focus” type from which the bifurcation of Andronov–Hopf type is realized. Numerically solving the system of differential equations for different initial conditions it was found that the mathematical model has a solution in the form of a limit cycle and the process runs in an oscillatory mode at initial concentrations of cysteine and catalyst comparable with its amounts at which chemical oscillations can be experimentally observed. It was made a conclusion that the mathematical model satisfactorily describes processes running in the observed system.
Key words: oscillatory processes, mathematical modeling, kinetic analysis, stoichiometric analysis, cysteine, oxidation.
Moscow University Chemistry Bulletin.
2013, Vol. 54, No. 6, P. 330
   

Copyright (C) Chemistry Dept., Moscow State University, 2002
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