Three-frequency resonances in single-mode systems

Abstract

We review recent results on the interaction of low- and high-frequency oscillations that lead to arising of three-frequency resonances in nonlinear oscillators. The Duffing oscillator and the Van der Pol oscillator both with modulated natural frequency and a high-frequency harmonic forcing are considered as examples to illustrate and study this phenomenon. It is shown that such interaction enables an efficient control of the oscillators dynamics and their properties. The formation of bistable states and synchronous oscillations is considered in detail.