Reduced equations for an active model of hydroelastic waves in the cochlea

Author:

Rubinstein Jacob,Sternberg Peter

Abstract

Building upon our earlier passive models for the cochlea (see L. Peres Hari, J. Rubinstein, and P. Sternberg [Quart. Appl. Math. 74 (2016), no. 4, 647–670] and J. Rubinstein and P. Sternberg [Pure Appl. Funct. Anal. 5 (2020), no. 2, 457–471]), 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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

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