Stability and Bifurcation Analysis of a Nonlinear Cochlear Model

Hearing relies on a series of coupled electrical, acoustical (fluidic) and mechanical interactions inside the cochlea that enable sound processing. The stability of the cochlea is studied using a nonlinear, micromechanical model of the organ of Corti (OoC) coupled to the electrical potentials in the cochlear ducts. The OoC is part of the mammalian cochlea that contains auditory sensory cells that both identify fluid-born vibrations in the cochlea and amplify the cycle-by-cycle motions of the cochlear structures. This process occurs through local resonance of the OoC system. In the mammalian cochlea, an active process accounts for the ear’s exquisite sensitivity and its remarkable responsiveness for a range of frequencies and intensities. Numerical and analytical techniques are utilized to examine the stability of this system. It is observed that the cochlear active process, controls the stability. We show that instability in this model is generated through a supercritical Hopf bifurcation. Furthermore, a reduced order model of the system is approximated and it is shown that the tectorial membrane (TM) transverse mode effect on the dynamics is significant while the radial mode can be simplified from the equations. We compare the cross sectional model with the comprehensive 3-dimensional model of the cochlea. It is indicated that the global model qualitatively inherits some characteristics of the local model, but the longitudinal coupling along the cochlea enhances stability (i.e., shifts the Hopf bifurcation point).