Mathematical modeling of oregonator with a diffusion type communication

L. A. Prokudina

Journal of computational and engineering mathematics, Tome 3 (2016) no. 2, pp. 48-56.

Résumé

We presented a mathematical model of the Belousov–Zhabotinsky reaction for Field–Noyes mechanism, which is called oregonator, taking into account the diffusion of components. A range of stoichiometric coefficient changes, which corresponds to a stationary state oregonator, is found. We study a diffusion instability and two types of unstable modes, as well as the points of oregonator bifurcation.

Détail

Keywords: Field–Noyes model, oregonator, diffusion instability, bifurcation point.

Bibliographie

[1] P. Glensdorf, I. Prigozhin, Termodinamicheskaya teoriya struktury, ustoichivosti i fluktuatsii, Mir, M., 1973 | MR

[2] P. Glensdorf, I. Prigozhin, Samoorganizatsiya v neravnovesnykh sistemakh, Mir, M., 1979

[3] G. Nikolis, I. Prigozhin, Poznanie slozhnogo, Mir, M., 1990

[4] I. Prigozhin, Ot suschestvuyuschego k voznikayuschemu, Nauka, M., 1985

[5] G. Khaken, Sinergetika, Mir, M., 1980 | MR

[6] G. Khaken, Sinergetika. Ierarkhiya neustoichivostei v samoorganizuyuschikhsya sistemakh i ustroistvakh, Mir, M., 1985 | MR

[7] V. Ebeling, Obrazovanie struktur pri neobratimykh protsessakh, Mir, M., 1979

[8] M. Herschkowitz–Kaufman, “Structures Dissipatives Dans Une Reaction Chimique Onhomogene”, Comp. Rend. Acad. Sci., 270:12 (1970), 1049–1052

[9] Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence, Springer, Berlin, Heidelberg, 1984 | DOI | MR | Zbl

[10] A. M. Zhabotinskii, Kontsentratsionnye avtokolebaniya, Nauka, M., 1974

[11] E. Këros, M. Orban, Kolebatelnye protsessy v biologicheskikh i khimicheskikh sistemakh, Nauka, M., 1978

[12] R. Fild, M. Burger, Kolebaniya i beguschie volny v khimicheskikh sistemakh, Mir, M., 1988 | MR

[13] H. G. Busse, “A Spatial Periodic Homogeneous Chemical Reaction”, J. Phys. Chem., 73:3 (1969), 750 | DOI

[14] M. T. Beck, Z. B. Varadi, “Two and Three-Dimensional Spatially Periodic Chemical Reactions”, Nature Phys. Sci., 235 (1972), 15–16 | DOI

[15] A. M. Turing, “The Chemical Basis of Morphogenesis”, Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 237:641 (1952), 37–72 | DOI | MR

[16] E. Schrodiner, What is Life, Cambridge Press, Cambridge, 1944

[17] A. M. Zhabotinskii, “Periodicheskie reaktsii okisleniya v zhidkoi faze”, DAN SSSR, 157 (1964), 392–395

[18] B. P. Belousov, “Periodicheski deistvuyuschaya reaktsiya i ee mekhanizmy”, Sb. referatov po radiatsionnoi meditsine, 1959, 145–148

[19] A.M. Zhabotinskii, “Periodicheskii protsess okisleniya malonovoi kisloty v rastvore (issledovanie kinetiki reaktsii Belousova)”, Biofizika, 1964, no. 9, 306–311

[20] R. J. Field, E. Köros, R. M. Noyes, “Oscillations in Chemical Systems. 2. Thorough Analysis of Temporal Oscillations in the Bromate- Cerium- Malonic Acid System”, J. Am. Chem. Soc., 94:25 (1972), 8649–8664 | DOI

[21] R. J. Field, R. M. Noyes, “Oscillations in Chemical Systems IV. Limit Cycle Behaviour in a Model of a Real Chemical Reaction”, J. Chem. Phys., 60:5 (1974), 1877–1884 | DOI

[22] A. J. Lotka, “Contribution to the Theory of Periodic Reactions”, Phys. Chem. Soc., 1910, no. 14, 271–274

[23] A. J. Lotka, “Undamped Oscillations Derived from the Law of Mass Action”, J. Am. Chem. Soc., 1920, no. 42, 1595–1599 | DOI

[24] A. J. Lotka, “Analytical Note on Certain Rhytmic Relations in Inorganic Systems”, Proc. Natl. Acad. Sci. USA, 1920, no. 6, 410–415 | DOI

[25] D. Edelson, R. J. Field, R. M. Noyes, “Mechanistic Details of the Belousov–Zhabotinskii Reaction”, Int. J. Chem. Kin., 7:3 (1975), 417–432 | DOI

[26] L. A. Prokudina, “Modelirovanie neustoichivosti oregonatora s diffuziei”, Nelineinyi mir, 12:1 (2014), 042–047