February 05, 2010, 1171 Chem

Mammalian hearing has a complex physiology that is still not completely understood. One of its most studied aspects is the cochlear amplification. In vivo experiments suggest that the cochlear amplifier is compressively nonlinear, has sharp tuning and prone to otoacoustic emissions. It is hypothesized in the literature that all of these features can be modeled by the so-called Hopf oscillator. However, the Hopf normal form is a local model not designed to be forced by a large variation of amplitudes and it has to be tuned near instability whose mechanism remains to be uncovered. In this talk we present alternative models that reproduce the experimental observations equally well as the Hopf oscillator. In fact, one can build a phenomenological model without the need to be tuned near a bifurcation. We also introduce two physiological models, one of them is an outer hair cell model proposed by Ó Maoiléidigh and Jülicher that accounts for features such as hair bundle movement, adaptation and charge movement inside the cell. We find that it is not necessary to tune this model into the region where Hopf bifurcations occur to reproduce the characteristic nonlinearity. Our final model uses the essence of the outer hair cell model and adds features like mechanical feedback that yield the desired sharp tuning and nonlinear compression. (Joint work with D. O’Maleidigh, A.R. Champneys, N.P. Cooper, H. Kennedy and M. Homer).

Robert Szalai is a postdoctoral researcher at the Bristol Centre for Applied Nonlinear Mathematics at the University of Bristol since 2006. He received his MSc (2002) and PhD (2006) in Mechanical Engineering from Budapest University of Technology and Economics. He has held a Fulbright Fellowship at the MIT in 2004 – 2005 and a visiting fellowship at the University of Bristol in 2004. His research interests are in the mechanics of mammalian hearing, machine-tool vibrations, piecewise-smooth systems, delay equations and invariant manifolds.