Fig. 4: Amplitude fluctuations in the synchronization regime at the resonance frequency.

The added noise applied to the oscillator is kept fixed at 0.5 V (standard deviation). The amplitude fluctuations are normalized to that of the free-running oscillator for the same drive levels (see Fig. S4 and Supplementary Note 2). a Experimental spectral density of the amplitude fluctuations as the nonlinearity of the oscillator increases. The red line shows the theoretical position of the peak at \({{{{{{\boldsymbol{f}}}}}}}_{{{{{{{\bf{s}}}}}}}_{{{{{{\bf{peak}}}}}}}}\). b Numerical simulation associated to panel (a). c Cross-section of panels (a, b) near the carrier frequency, highlighting the reduction in amplitude fluctuations as the oscillator enters the nonlinear regime (black line: theory, blue dots: experimental results). The spectral frequency was purposely shifted by ∼100 Hz from the carrier frequency to avoid 1/f noise. The experimental data are the result of an average over 40 measurements, the error bars corresponding to the associated standard deviation. d Cross-section of panels (a, b) along 0.1 V (black, linear regime) and 0.5 V (blue, Duffing regime), presenting the evolution of the spectral density from a regime similar to that of a free-running oscillator to the nonlinear regime where the fluctuations are shifted away from the carrier frequency (dashed line: theory, continuous line: experiment).