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Nelin. Dinam., 2019, Volume 15, Number 3, Pages 381–394 (Mi nd667)  

Mathematical problems of nonlinearity

Conditions for Phase Locking and Dephasing of Autoresonant Pumping

O. M. Kiselev

Institute of Mathematics with Computing Centre, ul. Chernyshevskogo 112, Ufa, 450008 Russia

Abstract: We study the asymptotic behavior of nonlinear oscillators under an external driver with slowly changing frequency and amplitude. As a result, we obtain formulas for properties of the amplitude and frequency of the driver when the autoresonant behavior of the nonlinear oscillator is observed. Also, we find the measure of autoresonant asymptotic behaviors for such a driven nonlinear oscillator.

Keywords: nonlinear oscillator, autoresonance, perturbations

DOI: https://doi.org/10.20537/nd190314

Full text: PDF file (525 kB)
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MSC: 34E10, 34C29
Received: 07.05.2019
Accepted:20.09.2019

Citation: O. M. Kiselev, “Conditions for Phase Locking and Dephasing of Autoresonant Pumping”, Nelin. Dinam., 15:3 (2019), 381–394

Citation in format AMSBIB
\Bibitem{Kis19}
\by O. M. Kiselev
\paper Conditions for Phase Locking and Dephasing of Autoresonant Pumping
\jour Nelin. Dinam.
\yr 2019
\vol 15
\issue 3
\pages 381--394
\mathnet{http://mi.mathnet.ru/nd667}
\crossref{https://doi.org/10.20537/nd190314}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4021377}


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