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