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Modelling the active cochlea as a fully-coupled system of subwavelength Hopf resonators

by H. Ammari and B. Davies

(Report number 2019-20)

Abstract
We combine recent breakthroughs in coupled resonator mechanics with the theory of cochlear Hopf resonators in order to better understand the active cochlea. We model the acoustic pressure on the surface of the basilar membrane, offering an understanding of how this couples the array of subwavelength resonators and the implications for cochlear mechanics. By decomposing the behaviour over the system's resonant modes, we are able to offer explanations for several of the inner ear's key properties, including its frequency selectivity, nonlinear amplification and two-tone response. A truncated multipole expansion is used to give efficient numerical computations.

Keywords: subwavelength resonance, coupled Hopf resonators, active cochlear mechanics, hybridisation, nonlinear cochlear amplifier, two-tone interference

@Techreport{AD19_824,
  author = {H. Ammari and B. Davies},
  title = {Modelling the active cochlea as a fully-coupled system of subwavelength Hopf resonators},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2019-20},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2019/2019-20.pdf },
  year = {2019}
}

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