Geodesic
Relaxation oscillations and diffusion chaos in the Belousov reaction
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1400-1418 
S. D. Glyzin; A. Yu. Kolesov; N. Kh. Rozov. Relaxation oscillations and diffusion chaos in the Belousov reaction. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 8, pp. 1400-1418. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_8_a4/
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     title = {Relaxation oscillations and diffusion chaos in the {Belousov} reaction},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Asymptotic and numerical analysis of relaxation self-oscillations in a three-dimensional system of Volterra ordinary differential equations that models the well-known Belousov reaction is carried out. A numerical study of the corresponding distributed model – the parabolic system obtained from the original system of ordinary differential equations with the diffusive terms taken into account subject to the zero Neumann boundary conditions at the endpoints of a finite interval is attempted. It is shown that, when the diffusion coefficients are proportionally decreased while the other parameters remain intact, the distributed model exhibits the diffusion chaos phenomenon; that is, chaotic attractors of arbitrarily high dimension emerge.

[1] Glyzin S. D., Kolesov A. Yu., Rozov N. Kh., “Konechnomernye modeli diffuzionnogo khaosa”, Zh. vychisl. matem. i matem. fiz., 50:5 (2010), 860–875 | MR | Zbl

[2] Belousov B. P., “Periodicheski deistvuyuschaya reaktsiya i ee mekhanizmy”, Avtovolnovye protsessy v sistemakh s diffuziei, In-t prikl. fiz. AN SSSR, Gorkii, 1981, 176–186

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

[4] Kolesov Yu. S., Problema adekvatnosti ekologicheskikh uravnenii, Dep. v VINITI, No 1901-85, Yaroslavsl, 1985

[5] Ruoff P., Noyes R. M., “An amplified oregonator model simulating alternative excitabilities, transitions in types of oscillations, and temporary bistability in a closed system”, J. Chem. Phys., 84:5 (1986), 1413–1423 | DOI

[6] Milnor J., “On the concept of attractor”, Communs Math. Phys., 99:2 (1985), 177–196 | DOI | MR

[7] Frederickson P., Kaplan J., Yorke J., “The Lyapunov dimension of strange attractors”, J. Different. Equat., 49:2 (1983), 185–207 | DOI | MR | Zbl

[8] Kolesov Yu. S., “Neklassicheskii relaksatsionnyi tsikl odnoi trekhmernoi sistemy differentsialnykh uravnenii Lotki–Volterra”, Matem. sb., 191:4 (2000), 91–106 | MR | Zbl