Investigating cochlear instabilities using structured stochastic uncertainty

Possible sources of instabilities in the cochlea are investigated by letting the cochlear active gain be a stochastic process which enters the dynamics multiplicatively. The theory of structured stochastic uncertainty in dynamical systems is employed by reformulating a generalized class of biomechanical models of the cochlea as an LTI system in feedback with a diagonal stochastic gain. A simulation-free, Mean Square Stability (MSS) analysis is then carried out to predict possible unstable basilar membrane vibration modes. These modes suggest a mechanism explaining the frequencies of linearized instabilities that give rise to limit cycles due to a spatially varying inhomogeneity and temporal perturbations along the cochlear partition. In fact, we show that the range of unstable frequencies is controlled by the shape of the nominal cochlear active gain. This analysis suggests an explanation of vibrations in the ear that occur in the absence of any stimulus such as Spontaneous Otoacoustic Emissions (SOAEs) and tinnitus.