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Trudy Inst. Mat. i Mekh. UrO RAN, 2013, Volume 19, Number 3, Pages 274–283 (Mi timm986)  

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

Stability of autoresonance models under perturbations that are bounded in the mean

O. A. Sultanov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: The paper is devoted to investigating the stability of growing solutions of nonlinear equations related to the autoresonance phenomenon. The stability of these solutions under persistent perturbations is analyzed. A class of perturbations is introduced, and its properties that provide the stability of autoresonance are described. The argument is based on the existence on the Lyapunov function of the unperturbed systems.

Keywords: autoresonance, stability, asymptotics, perturbations.

Full text: PDF file (183 kB)
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Bibliographic databases:

Document Type: Article
UDC: 517.925
Received: 23.04.2012

Citation: O. A. Sultanov, “Stability of autoresonance models under perturbations that are bounded in the mean”, Trudy Inst. Mat. i Mekh. UrO RAN, 19, no. 3, 2013, 274–283

Citation in format AMSBIB
\Bibitem{Sul13}
\by O.~A.~Sultanov
\paper Stability of autoresonance models under perturbations that are bounded in the mean
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2013
\vol 19
\issue 3
\pages 274--283
\mathnet{http://mi.mathnet.ru/timm986}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3363321}
\elib{http://elibrary.ru/item.asp?id=20234995}


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  • http://mi.mathnet.ru/eng/timm/v19/i3/p274

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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. L. A. Kalyakin, “Synchronization in a nonisochronous nonautonomous system”, Theoret. and Math. Phys., 181:2 (2014), 1339–1348  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    2. O. A. Sultanov, “Stability of capture into parametric autoresonance”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 156–167  mathnet  crossref  mathscinet  elib
    3. O. A. Sultanov, “Stability of autoresonance in dissipative systems”, Ufa Math. J., 7:1 (2015), 58–69  mathnet  crossref  isi  elib
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