Fig. 4: Comparison of experiments and model.

a, Critical feedback strength a_crit, for the occurrence of a Hopf bifurcation without sound input (autonomous oscillations), depending on bias voltage u_d.c. obtained from experiments (black, red and blue dots) with three different sensors and from a fixed-point analysis (equation (10)) with experimental parameters f, R, Q and k (Methods). The formula describes the dependence of the critical feedback strength on the sensor properties and feedback parameter u_d.c.. b, Sensitivity of the experimental sensor system (u_d.c. = −200 mV) depending on feedback strength a for single-tone sound signals with a frequency of 14 kHz (pressure range, 0.10–0.32 Pa) as black dots. The effective quality factor depending on feedback strength a obtained from the simulations of equations (1)–(5) for different initial quality factors: Q₀ = 41.6 (red line), Q₀ = 46.5 (purple line) and Q₀ = 49.7 (green line). The comparison shows that an increase in sensitivity in the active, linear mode with increasing feedback strength a can be attributed to the change in quality factor due to feedback.