Effects of external influences on the development of~disturbances in~the~oregonator with~diffusion

L. A. Prokudina

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 2, pp. 50-55

Résumé

The article presents the Field–Noyes–Kërös model of the Belousov–Zhabotinsky reaction, called an oregonator, on account of the component diffusion and external influences. Of great scientific importance are the works of such scientists as A. M. Zhabotinsky and V. A. Vavilin devoted to the deformation of the region of oscillation existence and the production of complex oscillation modes. The effect of external influences on the initial state of a chemically reacting system enables to produce new reagents, unusual for the original set, its stationary states, as well as to control oscillations modes. Stationary solutions of the system have been found corresponding to its physical meaning for different values of the stoichiometric ratio both in case of absence of external influences and under external influence. The dispersion equation is derived which enables to calculate the rate of the perturbation growth in the system and the oscillation frequency. The results of computational experiments made on the system instability on account of components diffusion and external influences are presented. Rates of perturbation growth for different values of the stoichiometric ratio have been calculated. Two unstable modes have been distinguished, such as the stability change and the oscillatory instability. It is shown that the time of the system transition to the vibrational mode decreases with the increase of the values of the stoichiometric ratio and under external influences.

Détail

Keywords: oregonator; instability; perturbation; diffusion; vibrational modes; the external influence.