Fig. 2

Duffing nonlinearity in the resonator. a, b The amplitude responses and phase responses of the device under different AC driving voltages. The responses convert from linear to stiffness-hardening nonlinear when the AC driving voltage increases from 50 mV to 800 mV (left to right). c The real-time oscillation amplitude (blue solid line) and oscillation frequency (red solid line) of the resonator when it generated self-sustained oscillation in a phase-locked loop. The AC driving voltage was first increased from 400 to 800 mV in steps of 50 mV and then decreased from 800 to 400 mV in steps of 50 mV. The inset shows the oscillation frequency of the device when the AC driving voltage was increased from 450 to 500 mV. The device can re-stabilize within 0.48 s. d The experimental and theoretical quadratic dependence of oscillation frequency on AC driving voltage