Controlling the oscillator frequency synchronization by a low-frequency drive

Abstract: The dynamics of an oscillator driven by both low- and high- frequency external signals is studied. It is shown that both two- and three-frequency resonances arise due to a nonlinear interaction of these harmonic forces. Conditions which must be met for oscillator synchronization under these resonances are estimated analytically by considering the Van der Pol oscillator with modulated natural frequency as mathematical model. It is demonstrated that due to the low-frequency modulation, additional synchronization regions arise in the control parameter space. Feasibility of the theoretical findings is confirmed in experiments with a Hartley-type oscillator.