  Building upon our earlier passive models for the cochlea, here we enhance the
model with an active mechanism. Starting with a one-chamber simplification
leading to a system of a time-dependent PDE in two spatial variables for the
pressure coupled to a PDE in one spatial variable for the oscillation of the
basilar membrane, we rigorously establish the validity of a dimension reduction
to a system to two ODE's. We then present numerical simulations demonstrating
the ability of this reduced active system to distinguish and amplify
multi-frequency input signals.
