On the Nonlinear Sensitivity of Phononic Frequency Combs to Physical Perturbations

Phononic frequency combs offer a rich platform for nonlinear sensing, yet how their observable properties respond to changes in physical parameters remains poorly understood. Using a reduced two-mode autoparametric resonance model, we investigate how primary and secondary detuning, drive amplitude, and relative damping jointly shape amplitude and frequency sensitivity across the nonlinear parameter space. We find that sensitivity is far from uniform: primary detuning shifts the comb response smoothly, secondary detuning produces sharply localized transitions near resonance manifolds, and drive amplitude concentrates peak sensitivity close to the activation threshold rather than deep within the comb state. The relative damping redistributes energy continuously between modes without introducing discontinuities. The nonlinear sensitivity of amplitude and frequency observables across all parameters points to a common physical origin in autoparametric resonance, nonlinear saturation, and coupling-induced synchronization, offering a coherent basis for designing nonlinear sensing platforms with deliberate, parameter-aware sensitivity engineering.