Geodesic
Effects of external influences on the development of disturbances in the oregonator with diffusion
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 2, pp. 50-55 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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.
Keywords: oregonator; instability; perturbation; diffusion; vibrational modes; the external influence. 
@article{VYURM_2015_7_2_a5,
     author = {L. A. Prokudina},
     title = {Effects of external influences on the development of~disturbances in~the~oregonator with~diffusion},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {50--55},
     year = {2015},
     volume = {7},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2015_7_2_a5/}
}
TY  - JOUR
AU  - L. A. Prokudina
TI  - Effects of external influences on the development of disturbances in the oregonator with diffusion
JO  - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
PY  - 2015
SP  - 50
EP  - 55
VL  - 7
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/VYURM_2015_7_2_a5/
LA  - ru
ID  - VYURM_2015_7_2_a5
ER  - 
%0 Journal Article
%A L. A. Prokudina
%T Effects of external influences on the development of disturbances in the oregonator with diffusion
%J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika
%D 2015
%P 50-55
%V 7
%N 2
%U http://geodesic.mathdoc.fr/item/VYURM_2015_7_2_a5/
%G ru
%F VYURM_2015_7_2_a5
L. A. Prokudina. Effects of external influences on the development of disturbances in the oregonator with diffusion. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 7 (2015) no. 2, pp. 50-55. http://geodesic.mathdoc.fr/item/VYURM_2015_7_2_a5/

[1] Zhabotinskiy A. M., Concentration autooscillations, Nauka Publ., M., 1974, 178 pp. (in Russ.)

[2] V. Volpert, S. Petrovskii, “Reaction-diffusion waves in biology”, Physics of Life Reviews, 6 (2009), 267–310 | DOI

[3] R. Lev Bar-Or, R. Maya, L. Segel et al., “Generation of oscillations by the p53-MDm2 feedback loop: A theoretical and experimental study”, PNAS, 97:21 (2000), 11250–11255 | DOI

[4] Voropaeva O. F., Senchukova S. R., Brodt K. V., Garbuzov K. E., Melnitchenko A. V., Starikova A. A., “Numerical Simulation of Ultradian Oscillations in p53-Mdm2-Network under Stress Conditions”, Matematicheskoe Modelirovanie, 26:11 (2014), 105–122 (in Russ.)

[5] Abramenko I. V., Zavgorodnyaya A. V., Balan V. I., Krechok I. A., Chumak A. A., Onkologiya, 10:2 (2008), 225–229

[6] Prokudina L. A., Kholpanov L. P., Teoreticheskie osnovy khimicheskoy tekhnologii, 38:6 (2004), 675–682 (in Russ.)

[7] D. Edelson, R. J. Field, R. M. Noyes, “Mechanistic details of the Belousov–Zhabotinskii oscillations”, International Journal of Chemical Kinetics, 7:3 (1975), 417–432 | DOI

[8] Prokudina L. A., Nonlinear World, 12:1 (2014), 042–047 (in Russ.)

[9] Zhabotinskiy A. M., DAN SSSR, 157 (1964), 392–395 (in Russ.)

[10] Vavilin V. A., Zhabotinskiy A. M., Zaikin A. N., Zhurnal fizicheskoy khimii, 42 (1968), 3091

[11] H. G. Busse, “A spatial periodic homogeneous chemical reaction”, J. Phys. Chem., 73:3 (1969), 750–750 | DOI

[12] M. Herschkowitz-Kaufman, “Structures dissipatives dans une reaction chimique onhomogene”, Comp. Rend. Acad. Sci., C270:12 (1970), 1049–1052

[13] M. T. Beck, Z. B. Varadi, “One, two and three-dimensional spatially periodic chemical reactions”, Nature Phys. Sci., 235 (1972), 15–16 | DOI