Numerical simulation of unstable oregonator regimes

A system of partial differential equations is presented, which is a mathematical model of a chemically active system (oregonator) with a diffusive type of coupling between components. The relevance of the study of systems with diffusion is related to the problem of the origin and forming of spatial structures in chemical, biological, and ecological systems. Equations for the stationary state of the system are written. The transition from the original system of differential equations to the system of differential equations in perturbations is performed. Computational algorithms have been developed for calculating the parameters of the oregonator model. Numerical studies of the presented model are carried out in the MATLAB package. Stationary States of the oregonator are calculated for different values of the stoichiometric coefficient that correspond to the physical meaning of the process. The stoichiometric coefficient is a bifurcation parameter of the system, and each of its values corresponds to a single positive stationary solution. The dispersion equation is derived. The instability criterion is the positive values of both the growth rate and the frequency of disturbances in the oregonator. Numerical modeling of the stability of the stationary state with respect to perturbations is carried out. Two types of instability in the oregonator are identified: change of stability and oscillatory instability. The results of computational experiments have shown that the diffusion of components generates more unstable modes with wave numbers other than zero. This indicates additional diffusive instability, which is a mechanism for the formation of spatial structures.