Controlling the oscillator frequency synchronization by a low-frequency drive

TL;DR

This paper investigates how low-frequency drives can control oscillator frequency synchronization, revealing new resonance regions through analytical and experimental methods, with implications for nonlinear oscillator control.

Contribution

It introduces a novel approach to controlling oscillator synchronization using low-frequency modulation, supported by analytical estimates and experimental validation.

Findings

Low-frequency modulation creates additional synchronization regions.

Both two- and three-frequency resonances are observed.

Experimental results confirm theoretical predictions.

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.