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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2023, Volume 20, Issue 2, Pages 616–625
DOI: https://doi.org/10.33048/semi.2023.20.036 (Mi semr1599) 		 
Differentical equations, dynamical systems and optimal control

Resonance in oscillators with nonlinearity manifested at intermediate amplitudes

E. Pelinovskyab, I. Melnikovab

a HSE University, Bolshaya Pecherskaya str., 603155, Nizhny Novgorod, Russia
b Institute of Applied Physics, Ulyanova str., 46, 603095, Nizhny Novgorod, Russia
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DOI: https://doi.org/10.33048/semi.2023.20.036
Abstract: The present paper discusses a method for finding self-consistent external influences on a nonlinear oscillator that lead to the phenomenon of resonance as in the linear case. It is shown that for bounded nonlinear systems it is possible to find such a self-consistent external force. To illustrate the search for self-consistent external influences, the simplest system with a nonlinear term represented by the saturation function is chosen. The resonant solution stability with a small amplitude deviation of the obtained self-consistent external force is investigated.
Keywords: Nonlinear resonance, self-consistent source, oscillatory systems with bounded nonlinearity.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-1101
Russian Science Foundation 19-12-00253
The work was supported by the Laboratory of Dynamic Systems and Applications of the Higher School of Economics, grant of the Ministry of Science and Higher Education of the Russian Federation Agreement No. 075-15-2022-1101 (Section 2) and the RSF grant 19-12-00253 (Sections 3 and 4).
Received November 5, 2022, published July 21, 2023
Document Type: Article
UDC: 517.9
MSC: 34A34
Language: English
Citation: E. Pelinovsky, I. Melnikov, “Resonance in oscillators with nonlinearity manifested at intermediate amplitudes”, Sib. Èlektron. Mat. Izv., 20:2 (2023), 616–625
Citation in format AMSBIB
\Bibitem{PelMel23}
\by E.~Pelinovsky, I.~Melnikov
\paper Resonance in oscillators with nonlinearity manifested at intermediate amplitudes
\jour Sib. \`Elektron. Mat. Izv.
\yr 2023
\vol 20
\issue 2
\pages 616--625
\mathnet{http://mi.mathnet.ru/semr1599}
\crossref{https://doi.org/10.33048/semi.2023.20.036}
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