Mathematical model of chemical oscillations arising in a homogeneous system of cysteine and oxygenated complexes of iron(II)

A mathematical model of the homogeneous oxidation kinetics of cysteine in the presence of oxygenated complexes of iron(II) with dimethylglyoxime and cytosine expressed in the form of a system of three nonlinear differential equations is analyzed. The model is simplified by stoichiometric analysis of the suggested kinetic scheme. As determined on the basis of qualitative analysis of the system of differential equations, a single stationary state with the singular point assigned to the focus—spatial saddle type, from which a bifurcation of the Andronov-Hopf type can occur, is implemented. Upon solving numerically the system of differential equations for different initial conditions, it is found that the mathematical model has a solution in the form of a limit cycle, and the process runs in an oscillatory mode at such initial concentrations of the catalyst and cysteine that are comparable to their contents at which chemical oscillations are observed in experiments.