Resonance in oscillators with nonlinearity manifested at intermediate amplitudes

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.