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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2011, Volume 51, Number 8, Pages 1400–1418
(Mi zvmmf9522)
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This article is cited in 13 scientific papers (total in 13 papers)
Relaxation oscillations and diffusion chaos in the Belousov reaction
S. D. Glyzina, A. Yu. Kolesova, N. Kh. Rozovb a Faculty of Mathematics, Yaroslavl State University, Sovetskaya ul. 14, Yaroslavl, 150000 Russia
b Faculty of Mathematics and Mechanics, Moscow State University, Moscow 119992 Russia
Abstract:
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.
Key words:
Belousov reaction, distributed model, diffusion chaos, relaxation cycle, attractor, Lyapunov dimension.
Received: 18.01.2011
Citation:
S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Relaxation oscillations and diffusion chaos in the Belousov reaction”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011), 1400–1418; Comput. Math. Math. Phys., 51:8 (2011), 1307–1324
Linking options:
https://www.mathnet.ru/eng/zvmmf9522 https://www.mathnet.ru/eng/zvmmf/v51/i8/p1400
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Abstract page: | 491 | Full-text PDF : | 132 | References: | 46 | First page: | 17 |
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