Characterizing Nonlinear Dynamics of Sound Detection in the Auditory System via Entrainment Analysis

The biophysics of hearing relies on active processes that are fundamentally nonlinear, enabling sensitive and robust sound detection. We present an analytical framework to characterize these nonlinear dynamics using stimulus-frequency otoacoustic emissions (SFOAEs) to probe the ear near a spontaneous otoacoustic emission (SOAE) peak. A primary experimental challenge is that the recorded signal is an inseparable superposition of the external drive and the system's response, further complicated by linear scattering from surrounding structures. Our method resolves this limitation by focusing on how the SOAE peak entrains to the external tone, revealing the underlying bifurcation structure of the active oscillator. From this entrainment behavior, we identify signatures of saddle-node infinite period (SNIPER) and supercritical Hopf bifurcations. We also explore the entrainment signatures of chaos in hearing. This framework provides a general strategy for uncovering nonlinear dynamics in hearing and other active systems where stimulus and response are inseparable at the detector.