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Mat. Sb., 2000, Volume 191, Number 4, Pages 91–106 (Mi msb472)  

This article is cited in 3 scientific papers (total in 3 papers)

Non-classical relaxation cycle of a three-dimensional system of Lotka–Volterra equations

Yu. S. Kolesov

P. G. Demidov Yaroslavl State University

Abstract: A mathematical model of the well-known Belousov's reaction is the object of study. It is reasonable to assume that one coefficient in the corresponding system of differential equations is large, while the other parameters are finite. Non-standard tools taking account of the peculiarities of the problem bring one to a theorem on the existence of a relaxation cycle, allowing at the same time to reveal its characteristic features.

DOI: https://doi.org/10.4213/sm472

Full text: PDF file (226 kB)
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English version:
Sbornik: Mathematics, 2000, 191:4, 567–581

Bibliographic databases:

UDC: 517.9+541.128.7
MSC: Primary 34C05, 92E20; Secondary 34D99
Received: 20.11.1998 and 29.06.1999

Citation: Yu. S. Kolesov, “Non-classical relaxation cycle of a three-dimensional system of Lotka–Volterra equations”, Mat. Sb., 191:4 (2000), 91–106; Sb. Math., 191:4 (2000), 567–581

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Shahruz, SM, “Limit cycle behavior in three- or higher-dimensional non-linear systems: The Lotka-Volterra example”, Journal of Sound and Vibration, 246:2 (2001), 379  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    2. Shahruz S.M., “Limit cycle behavior in three or higher dimensional nonlinear systems: The Lotka-Volterra example”, IEEE Conference on Decision and Control, 2001, 3414–3418  isi
    3. S. D. Glyzin, A. Yu. Kolesov, N. Kh. Rozov, “Relaxation oscillations and diffusion chaos in the Belousov reaction”, Comput. Math. Math. Phys., 51:8 (2011), 1307–1324  mathnet  crossref  mathscinet  isi
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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