Mathematics of the USSR-Sbornik
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mathematics of the USSR-Sbornik, 1990, Volume 65, Issue 1, Pages 1–17
DOI: https://doi.org/10.1070/SM1990v065n01ABEH001928
(Mi sm1763)
 

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

Asymptotics of relaxation oscilations

A. Yu. Kolesov, E. F. Mishchenko
References:
Abstract: A complete asymptotics of relaxation oscillations in Rn 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.
Received: 21.03.1988
Bibliographic databases:
Document Type: Article
UDC: 517.926
MSC: Primary 34C45, 34E15; Secondary 34C25, 34C30
Language: English
Original paper language: Russian
Citation: A. Yu. Kolesov, E. F. Mishchenko, “Asymptotics of relaxation oscilations”, 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 Math. USSR-Sb.
\yr 1990
\vol 65
\issue 1
\pages 1--17
\mathnet{http://mi.mathnet.ru/eng/sm1763}
\crossref{https://doi.org/10.1070/SM1990v065n01ABEH001928}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=965877}
\zmath{https://zbmath.org/?q=an:0703.34046}
Linking options:
  • https://www.mathnet.ru/eng/sm1763
  • https://doi.org/10.1070/SM1990v065n01ABEH001928
  • https://www.mathnet.ru/eng/sm/v179/i1/p3
  • This publication is cited in the following 8 articles:
    1. 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
    2. 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
    3. 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
    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, 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
    7. 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
    8. 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
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:428
    Russian version PDF:116
    English version PDF:24
    References:63
    First page:2
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025