Resonance in oscillators with nonlinearity manifested at intermediate amplitudes

Siberian Electronic Mathematical Reports. 2023. Vol. 20. No. 2. P. 616–625.

Пелиновский Е. Н., Melnikov I.

The present paper discusses a method for nding selfconsistent
external inuences 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 nd such a self-consistent
external force. To illustrate the search for self-consistent external inuences,
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.

Ключевые слова: нелинейный резонанс, nonlinear resonance

ПУБЛИКАЦИЯ ПОДГОТОВЛЕНА ПО РЕЗУЛЬТАТАМ ПРОЕКТА: Теория динамических систем и ее приложения (2023)