Chemical instabilities during oxidation of 1,4-naphthalenediol in a homogeneous medium: II. Thermodynamic analysis and mathematical modeling

A possible mechanism of 1,4-naphthalenediol oxidation in the oscillatory regime has been considered, and a mathematical model describing the kinetics has been developed. Based on a thermodynamic Lyapunov function, it has been shown that the source of chemical instabilities is in the existence of autocatalytic steps and dynamic feedbacks. Qualitative analysis and numerical solution of the set of differential equations that model the reaction kinetics have been performed. The character of the stationary state and the possibility of bifurcations have been determined. The mathematical model satisfactorily describes the processes occurring in the system.     

Nonlinear (Fluctuational) dynamics and mathematical modeling of homogenous oxidation of biological substrates

Nonlinear dynamics and mathematical modeling approaches were presented for studying chemical oscillations during homogeneous oxidation of biological substrates in the presence of oxygenated complexes of iron(II). It was shown that examination of fluctuational dynamics is only possible via consistent use of several algorithms for time series processing and that flicker-noise spectroscopic technique is best suited to deriving the most exhaustive information from the patterns of temporal variation of signals. The qualitative analysis was performed, and numerical solution was found for the system of differential equations modeling the reactions kinetics. The nature of the steady state was elucidated, and the possibility of Andronov-Hopf type bifurcation with realization of an oscillatory mode was demonstrated.     

The Dynamics of Homogeneous Oxidation of Cysteine in the Presence of Oxygenated Complexes of Cobalt(II) with o-Disalicylidene-Phenylenediamine and Cytosine in a Reactor with Mixing

Moscow University Chemistry Bulletin - The homogeneous process of cysteine oxidation in a stirred reactor is studied. We found that oscillatory mode can be realized in the cysteine–cobalt(II)...     

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.     

Formation of dissipative structures upon homogenous oxidation of biosubstrata: Evaluation of dynamic characteristics and parameterization of time series

The possibility of formation of dissipative structures in the system consisting of biosubstrate and oxygenated iron (II) complexes is shown by the example of liquid-phase oxidation of cysteine. The results of evaluation of dynamic characteristics of the investigated processes (type of dynamics, dimensions of phase space and attractor, Lyapunov indicators, and the Kolmogorov-Sinai entropy) are given. Parameterization of the resulting time series was carried out using the approaches of flicker-noise spectroscopy.     

Chemical instabilities in oxidation of 1,4-naphthalenediol in homogeneous medium: I. The deterministic character of 1,4-naphthodiol oxidation and its quantitative parameters

The chemical oscillatory processes that occur upon oxidation of 1,4-naphthalenediol in the presence of oxygenated cobalt(II) complexes in a homogeneous medium have been studied. The limits of the reagent and catalyst concentrations, pH, and temperature at which chemical oscillations are generated have been determined. The types of dynamics of the occurring processes and the dynamic parameters have been determined based on discrete Fourier transform, reconstruction of dynamics from time series of data, and calculations of the Lyapunov characteristic exponents and the Komogorov-Sinai entropy.