Synchronization of a forced self-sustained Duffing oscillator

TL;DR

This paper investigates the synchronization behavior of a self-sustained Duffing oscillator with feedback, revealing that nonlinearities can expand the synchronization range, with potential applications in microscale time-keeping devices.

Contribution

It provides a detailed analysis of autonomous and synchronized motions in a feedback-driven Duffing oscillator, highlighting a novel nonlinear effect on synchronization range.

Findings

Synchronization range widens with amplitude in certain regimes

Nonlinearities influence the oscillator's frequency response

Potential applications in microscale time-keeping devices

Abstract

We study the dynamics of a mechanical oscillator with linear and cubic forces -the Duffing oscillator- subject to a feedback mechanism that allows the system to sustain autonomous periodic motion with well-defined amplitude and frequency. First, we characterize the autonomous motion for both hardening and softening nonlinearities. Then, we analyze the oscillator's synchronizability by an external periodic force. We find a regime where, unexpectedly, the frequency range where synchronized motion is possible becomes wider as the amplitude of oscillations grows. This effect of nonlinearities may find application in technological uses of mechanical Duffing oscillators -for instance, in the design of time-keeping devices at the microscale- which we briefly review.