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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2014, Volume 54, Number 1, Pages 65–79
DOI: https://doi.org/10.7868/S004446691401013X (Mi zvmmf9973) 		 
This article is cited in 5 scientific papers (total in 5 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
Full-text PDF (318 kB) Citations (5)
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DOI: https://doi.org/10.7868/S004446691401013X
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.
Received: 19.04.2013
Revised: 25.07.2013
English version:
Computational Mathematics and Mathematical Physics, 2014, Volume 54, Issue 1, Pages 59–73
DOI: https://doi.org/10.1134/S0965542514010126
Bibliographic databases:
Document Type: Article
UDC: 519.624.2
Language: Russian
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
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  • https://www.mathnet.ru/eng/zvmmf/v54/i1/p65
    • This publication is cited in the following 5 articles:
    1. O. M. Kiselev, “Conditions for Phase Locking and Dephasing of Autoresonant Pumping”, Rus. J. Nonlin. Dyn., 15:3 (2019), 381–394  mathnet  crossref  mathscinet
    2. O. Sultanov, “Random perturbations of parametric autoresonance”, Nonlinear Dyn., 89:4 (2017), 2785–2793  crossref  mathscinet  zmath  isi
    3. O. A. Sultanov, “Random Perturbations of Autoresonance in Oscillating Systems with Small Dissipation”, J Math Sci, 219:2 (2016), 267  crossref
    4. O. A. Sultanov, “Stability of capture into parametric autoresonance”, Proc. Steklov Inst. Math. (Suppl.), 295, suppl. 1 (2016), 156–167  mathnet  crossref  mathscinet  isi  elib
    5. O. A. Sultanov, “Stability of autoresonance in dissipative systems”, Ufa Math. J., 7:1 (2015), 58–69  mathnet  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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    References:57
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