Understanding the mathematics of hearing using electronic circuits

Tara Julia Hamilton, Jonathan Tapson, Michael Rapson, Craig Jin, Andre van Schaik

Abstract


The human cochlea is a fascinating transduction organ that illustrates the ingenious way in which engineering problems are solved in nature. A healthy cochlea has a dynamic range in the order of~120\,dB; that is, the difference between the roar of the engines of a Boeing~747 and the faintest whisper. We discuss the recent assertion that the cochlea is governed by the dynamics of a Hopf bifurcation. In our cochlea model we discretise the basilar membrane into resonant sections with logarithmically decreasing characteristic frequencies. We show that the observed active behaviour of the cochlea can be modelled as a change in the quality factor of the individual resonant sections in a discretised model, and that this has dynamics which embody the Hopf bifurcation.

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Keywords


cochlear modelling, Hopf bifurcation, control theory

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DOI: http://dx.doi.org/10.21914/anziamj.v51i0.2543



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