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Mat. Sb. (N.S.), 1988, Volume 137(179), Number 1(9), Pages 3–18 (Mi msb1763)  

This article is cited in 7 scientific papers (total in 8 papers)

Asymptotics of relaxation oscilations

A. Yu. Kolesov, E. F. Mishchenko


Abstract: A complete asymptotics of relaxation oscillations in $R^n$ is constructed. The process is divided into two steps: the construction of the asymptotics of the integral manifold of the system under consideration and the asymptotic integration of the equation in this manifold, with regular dependence on the small parameter. Together with the previously solved stability problem this completes the study of all the main questions connected with the asymptotics of a multidimensional relaxation cycle.
Bibliography: 8 titles.

Full text: PDF file (748 kB)
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English version:
Mathematics of the USSR-Sbornik, 1990, 65:1, 1–17

Bibliographic databases:

UDC: 517.926
MSC: Primary 34C45, 34E15; Secondary 34C25, 34C30
Received: 21.03.1988

Citation: A. Yu. Kolesov, E. F. Mishchenko, “Asymptotics of relaxation oscilations”, Mat. Sb. (N.S.), 137(179):1(9) (1988), 3–18; Math. USSR-Sb., 65:1 (1990), 1–17

Citation in format AMSBIB
\Bibitem{KolMis88}
\by A.~Yu.~Kolesov, E.~F.~Mishchenko
\paper Asymptotics of relaxation oscilations
\jour Mat. Sb. (N.S.)
\yr 1988
\vol 137(179)
\issue 1(9)
\pages 3--18
\mathnet{http://mi.mathnet.ru/msb1763}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=965877}
\zmath{https://zbmath.org/?q=an:0703.34046}
\transl
\jour Math. USSR-Sb.
\yr 1990
\vol 65
\issue 1
\pages 1--17
\crossref{https://doi.org/10.1070/SM1990v065n01ABEH001928}


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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, “Duck trajectories of relaxation systems connected with violation of the normal switching conditions”, Math. USSR-Sb., 68:1 (1991), 291–301  mathnet  crossref  mathscinet  zmath  isi
    2. A. Yu. Kolesov, “On the instability of duck-cycles arising during the passage of an equilibrium of a multidimensional relaxation system through the disruption manifold”, Russian Math. Surveys, 44:5 (1989), 203–205  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. A. Yu. Kolesov, E. F. Mishchenko, “The Pontryagin delay phenomenon and stable ducktrajectories for multidimensional relaxation systems with one slow variable”, Math. USSR-Sb., 70:1 (1991), 1–10  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. A. Yu. Kolesov, Yu. S. Kolesov, “Relaxation cycles in systems with delay”, Russian Acad. Sci. Sb. Math., 76:2 (1993), 507–522  mathnet  crossref  mathscinet  zmath  isi
    5. A. Yu. Kolesov, Yu. S. Kolesov, “Relaxation cycles of differential-difference equations”, Russian Acad. Sci. Izv. Math., 41:1 (1993), 75–94  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. A. Yu. Kolesov, “Application of techniques of relaxation oscillations to a system of differential-difference equations from ecology”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 77–86  mathnet  crossref  mathscinet  zmath  isi
    7. A. Yu. Kolesov, Yu. S. Kolesov, N. Kh. Rozov, “Chaos of 'split torus' type in three-dimensional relaxation systems”, Sb. Math., 188:11 (1997), 1571–1586  mathnet  crossref  crossref  mathscinet  zmath  isi
    8. D. V. Anosov, S. M. Aseev, R. V. Gamkrelidze, S. P. Konovalov, M. S. Nikol'skii, N. Kh. Rozov, “Evgenii Frolovich Mishchenko (on the 90th anniversary of his birth)”, Russian Math. Surveys, 67:2 (2012), 385–402  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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