Geodesic
Resonance in oscillators with nonlinearity manifested at intermediate amplitudes
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 616-625

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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. 
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     author = {E. Pelinovsky and I. Melnikov},
     title = {Resonance in oscillators with nonlinearity manifested at intermediate amplitudes},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {616--625},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a41/}
}
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E. Pelinovsky; I. Melnikov. Resonance in oscillators with nonlinearity manifested at intermediate amplitudes. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 616-625. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a41/