Numerical simulation of the diffusion instability of the oregonator

Abstract

Starting with the work of A.M. Turing in 1952, studies of chemical, physico-chemical, and biological systems indicate the influence of component diffusion on the instability of processes. Diffusive instability is associated with the formation and de- velopment of spatial structures in systems of different nature. Stationary structures were observed not only in experimental studies, but also in working reactors. Objective: numerical simulation of the characteristics of unstable modes of the oregonator, taking into account the diffusion of components. For the five-stage Field-Keros-Noyes model of the Belousov-Zhabotinskii reaction, called the Oregonator, kinetic equations are presented without taking into account the inverse reactions, with the inclusion of the diffusion of components. To study the steady state of the oregonator at different values of the stoichiometric coefficient, a computational algorithm is developed. The program for calculating the steady states of the oregonator is written in Matlab. In computational experiments to determine the steady states of the oregonator, the constants of the reaction rates obtained by the authors of the model are used. The transition to a system of partial differential equations for perturbations of component concentrations is carried out. The dispersion relation is derived. A computational algorithm and programs for calculating the characteristics of the orego- nator under diffusion instability are developed. The results of computational experiments of unstable modes for different values of the stoichiometric coefficient, which is a bifurcation parameter of the system, are presented. Two types of unstable modes of the oregonator under conditions of diffusive instability, namely, the mode of oscillatory instability and the change of stability, are identified. The increase rates of perturbations in the system are calculated. The dependence of the perturbation increase rate on the value of the stoichiometric coefficient is shown. The stability change mode is characterized by higher rates of perturbation increase in comparison with the oscillatory instability mode.