  Modelling noisy oscillations of active systems is one of the current
challenges in physics and biology. Because the physical mechanisms of such
processes are often difficult to identify, we propose a linear stochastic model
driven by a non-Markovian bistable noise that is capable of generating
self-sustained periodic oscillation. We derive analytical predictions for most
relevant dynamical and thermodynamic properties of the model. This minimal
model turns out to describe accurately bistable-like oscillatory motion of hair
bundles in bullfrog sacculus, extracted from experimental data. Based on and in
agreement with these data, we estimate the power required to sustain such
active oscillations to be of the order of one hundred $k_B T$ per oscillation
cycle.
