A state space model for cochlear mechanics

The stability of a linear model of the active cochlea is difficult to determine from its calculated frequency response alone. A state space model of the cochlea is presented, which includes a discretized set of general micromechanical elements coupled via the cochlear fluid. The stability of this time domain model can be easily determined in the linear case, and the same framework used to simulate the time domain response of nonlinear models. Examples of stable and unstable behavior are illustrated using the active micromechanical model of Neely and Kim. The stability of this active cochlea is extremely sensitive to abrupt spatial inhomogeneities, while smoother inhomogeneities are less likely to cause instability. The model is a convenient tool for investigating the presence of instabilities due to random spatial inhomogeneities. The number of unstable poles is found to rise sharply with the relative amplitude of the inhomogeneities up to a few percent, but to be significantly reduced if the spatial variation is smoothed. In a saturating nonlinear model, such instabilities generate limit cycles that are thought to produce spontaneous otoacoustic emissions. An illustrative time domain simulation is presented, which shows how an unstable model evolves into a limit cycle, distributed along the cochlea.