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Zh. Vychisl. Mat. Mat. Fiz., 2011, Volume 51, Number 8, Pages 1400–1418 (Mi zvmmf9522)  

This article is cited in 8 scientific papers (total in 8 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.

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English version:
Computational Mathematics and Mathematical Physics, 2011, 51:8, 1307–1324

Bibliographic databases:

UDC: 519.624.2
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

Citation in format AMSBIB
\by S.~D.~Glyzin, A.~Yu.~Kolesov, N.~Kh.~Rozov
\paper Relaxation oscillations and diffusion chaos in the Belousov reaction
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2011
\vol 51
\issue 8
\pages 1400--1418
\jour Comput. Math. Math. Phys.
\yr 2011
\vol 51
\issue 8
\pages 1307--1324

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    This publication is cited in the following articles:
    1. D. S. Glyzin, S. A. Kaschenko, “Dinamika kompleksnogo prostranstvenno-raspredelennogo uravneniya Khatchinsona”, Model. i analiz inform. sistem, 19:5 (2012), 35–39  mathnet
    2. S. D. Glyzin, “Razmernostnye kharakteristiki diffuzionnogo khaosa”, Model. i analiz inform. sistem, 20:1 (2013), 30–51  mathnet
    3. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “The theory of nonclassical relaxation oscillations in singularly perturbed delay systems”, Sb. Math., 205:6 (2014), 781–842  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. M. N. Nazarov, “Primenenie teoretiko-veroyatnostnogo podkhoda pri modelirovanii sistem khimicheskoi kinetiki”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 25:4 (2015), 492–500  mathnet  elib
    5. Glyzin S.D., Kolesov A.Yu., Rozov N.Kh., “Traveling-Wave Solutions in Continuous Chains of Unidirectionally Coupled Oscillators”, Vi International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 937, IOP Publishing Ltd, 2017, UNSP 012015  crossref  mathscinet  isi  scopus
    6. V. E. Goryunov, “Bifurkatsiya Andronova–Khopfa v odnoi biofizicheskoi modeli reaktsii Belousova”, Model. i analiz inform. sistem, 25:1 (2018), 63–70  mathnet  crossref  elib
    7. Glyzin S.D., Goryunov V.E., Kolesov A.Yu., Computer Simulations in Physics and Beyond (Csp2017), Journal of Physics Conference Series, 955, IOP Publishing Ltd, 2018  crossref  isi  scopus
    8. Goryunov V.E., “The Andronov-Hopf Bifurcation in a Biophysical Model of the Belousov Reaction”, Autom. Control Comp. Sci., 52:7 (2018), 694–699  crossref  mathscinet  isi  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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