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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 3, Pages 67–84 (Mi izv336)  

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

The buffer phenomenon in a mathematical model of the van der Pol self-oscillator with distributed parameters

A. Yu. Kolesova, N. Kh. Rozovb

a P. G. Demidov Yaroslavl State University
b M. V. Lomonosov Moscow State University

Abstract: We establish that a mathematical model of the distributed van der Pol self-oscillator, which is a non-linear boundary-value problem of hyperbolic type, exhibits the buffer phenomenon, which means that the system can have any given number of stable cycles if its parameters are properly chosen.

DOI: https://doi.org/10.4213/im336

Full text: PDF file (1476 kB)
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English version:
Izvestiya: Mathematics, 2001, 65:3, 485–501

Bibliographic databases:

MSC: 35K50, 35B25, 35B10, 35C20
Received: 26.04.2000

Citation: A. Yu. Kolesov, N. Kh. Rozov, “The buffer phenomenon in a mathematical model of the van der Pol self-oscillator with distributed parameters”, Izv. RAN. Ser. Mat., 65:3 (2001), 67–84; Izv. Math., 65:3 (2001), 485–501

Citation in format AMSBIB
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\by A.~Yu.~Kolesov, N.~Kh.~Rozov
\paper The buffer phenomenon in a~mathematical model of the van der Pol self-oscillator with distributed parameters
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 3
\pages 67--84
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\crossref{https://doi.org/10.4213/im336}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1853366}
\zmath{https://zbmath.org/?q=an:0994.35015}
\elib{http://elibrary.ru/item.asp?id=13859250}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 3
\pages 485--501
\crossref{https://doi.org/10.1070/IM2001v065n03ABEH000336}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746830897}


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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. A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Buffer Phenomenon in Nonlinear Physics”, Proc. Steklov Inst. Math., 250 (2005), 102–168  mathnet  mathscinet  zmath
    2. Liangliang Li, Yu Huang, Mingqing Xiao, “Observer Design for Wave Equations with van der Pol Type Boundary Conditions”, SIAM J. Control Optim, 50:3 (2012), 1200  crossref  mathscinet  zmath  isi  scopus
    3. Jun Liu, Yu Huang, Haiwei Sun, Mingqing Xiao, “Numerical methods for weak solution of wave equation with van der Pol type nonlinear boundary conditions”, Numer. Methods Partial Differential Eq, 2015, n/a  crossref  mathscinet  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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