  We investigate instabilities in a stochastic mathematical model of cochlear
dynamics. The cochlea is modeled as a spatio-temporal dynamical system made up
of a spatially distributed array of coupled oscillators, together with the
cochlear amplification mechanism. We consider a setting where the cochlear
amplifier has relatively small spatially and temporally varying stochastic
parameters. It is shown that relatively small parameter variations (five to
four orders of magnitude smaller than the nominal values) are sufficient to
destabilize the dynamics and induce spontaneous oscillations. This extreme
sensitivity of the cochlear dynamics appears to be due to a combination of the
local cochlear amplification mechanism, as well as the spatial coupling of the
distributed resonators. We use an analysis technique which allows for a
simulation-free prediction of the stability thresholds, as well as the
statistics of the spontaneous oscillations. We verify our theoretical
predictions using full non- linear stochastic simulations which appear to be in
very good agreement with our theory.
