RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find






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


Zh. Vychisl. Mat. Mat. Fiz., 2014, Volume 54, Number 1, Pages 65–79 (Mi zvmmf9973)  

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

Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations

O. A. Sultanov

Institute of Mathematics and Computing Center, Ufa Scientific Center, Russian Academy of Sciences, ul. Chernyshevskogo 112, Ufa, 450008, Bashkortostan, Russia

Abstract: Systems of differential equations arising in the theory of nonlinear oscillations in resonance-related problems are considered. Of special interest are solutions whose amplitude increases without bound with time. Specifically, such solutions correspond to autoresonance. The stability of autoresonance solutions with respect to random perturbations is analyzed. The classes of admissible perturbations are described. The results rely on information on Lyapunov functions for the unperturbed equations.

Key words: systems of nonlinear oscillation equations, autoresonance, random perturbations, stability of solutions, Lyapunov function method.

DOI: https://doi.org/10.7868/S004446691401013X

Full text: PDF file (318 kB)
References: PDF file   HTML file

English version:
Computational Mathematics and Mathematical Physics, 2014, 54:1, 59–73

Bibliographic databases:

Document Type: Article
UDC: 519.624.2
Received: 19.04.2013
Revised: 25.07.2013

Citation: O. A. Sultanov, “Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations”, Zh. Vychisl. Mat. Mat. Fiz., 54:1 (2014), 65–79; Comput. Math. Math. Phys., 54:1 (2014), 59–73

Citation in format AMSBIB
\Bibitem{Sul14}
\by O.~A.~Sultanov
\paper Stability of autoresonance models subject to random perturbations for systems of nonlinear oscillation equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2014
\vol 54
\issue 1
\pages 65--79
\mathnet{http://mi.mathnet.ru/zvmmf9973}
\crossref{https://doi.org/10.7868/S004446691401013X}
\elib{http://elibrary.ru/item.asp?id=20991863}
\transl
\jour Comput. Math. Math. Phys.
\yr 2014
\vol 54
\issue 1
\pages 59--73
\crossref{https://doi.org/10.1134/S0965542514010126}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000332109500005}
\elib{http://elibrary.ru/item.asp?id=21866547}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84894607070}


Linking options:
  • http://mi.mathnet.ru/eng/zvmmf9973
  • http://mi.mathnet.ru/eng/zvmmf/v54/i1/p65

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    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. O. A. Sultanov, “Stability of capture into parametric autoresonance”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 156–167  mathnet  crossref  mathscinet  elib
    2. O. A. Sultanov, “Stability of autoresonance in dissipative systems”, Ufa Math. J., 7:1 (2015), 58–69  mathnet  crossref  isi  elib
    3. O. Sultanov, “Random perturbations of parametric autoresonance”, Nonlinear Dyn., 89:4 (2017), 2785–2793  crossref  mathscinet  zmath  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Number of views:
    This page:137
    Full text:26
    References:24
    First page:9

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019