Self-oscillations in homogeneous chemical reactions proceeding in a linear stepwise manner

Oscillating chemical and biochemical reactions are of particular interest for understanding complex mechanisms underlying the evolution and self-organization of wildlife. Sustained oscillations (self-oscillations) are observed in a number of chemical and biological reactions: reactions of Belousov – Zhabotinsky (“bromate oscillators”), Briggs – Rauscher (“iodine clock”), Bray – Liebhafsky, liquid-phase oxidation of benzaldehyde, etc. In the ideal kinetics of the law of mass action, self-oscillations are described only by nonlinear mechanisms that can yield an unstable reaction. The present study aims to explore the possibility of describing self-oscillations in homogeneous chemical reactions proceeding according to linear mechanisms with nonideal kinetics. In the course of work, the qualitative theory of ordinary differential equations and numerical methods for their solution were used. The study considers homogeneous chemical reactions proceeding according to linear stepwise schemes with three or more reactants with nonideal Marcelin – de Donder kinetics in an open isothermal gradientless reactor. These reactions are shown to involve the self-oscillations of reactant concentrations and reaction rate, with varying periodicity and frequency. For these reactions, mathematical models were constructed to describe self-oscillations associated with deviations from the ideal kinetics of the law of mass action, taking the possible mutual influence of reactants into account. Examples are given of linear stepwise schemes based on the Brusselator, a classical model for chemical oscillations, and the butene isomerization reaction. An alternative explanation is proposed for the possible causes of self-oscillations: stable modes of homogeneous reactions are disrupted due to the nonideal kinetics, which enables the description of self-oscillations in such reactions by linear stepwise schemes.