Metastable synchronization and inertial-beating sensing in nonlinear oscillators

Abstract

Synchronization is widely used to enhance the sensitivity and noise resilience of mechanical sensors, while nonlinear operation is often assumed to substantially broaden the usable synchronization bandwidth. Here, we show that this apparent bandwidth enhancement is fundamentally metastable. In nonlinear self-oscillating systems, large portions of the nominal synchronization region are dynamically inaccessible under direct signal injection, despite being theoretically stable. We demonstrate that this breakdown originates from phase inertia, which endows phase evolution with an effective second-order response and creates inertial barriers to phase capture. As a result, nonlinear synchronization splits into a narrow dynamically accessible locking region and a much larger metastable regime in which stable phase locking exists in principle but cannot be reached in practice. Rather than suppressing this inertial unlocking behavior, we exploit it as a sensing mechanism. Near the inaccessible locking boundary, phase inertia sustains slow beating dynamics that continuously encode frequency detuning while intrinsically averaging fast phase fluctuations. The resulting inertial-beating transduction produces a continuous, history-independent sensing response and enables faster synchronization dynamics beyond the conventional locking regime. More broadly, our results reveal that synchronization bandwidth is fundamentally governed by dynamical accessibility rather than static stability, establishing phase inertia as a general organizing principle for nonlinear synchronization dynamics across driven oscillatory systems.