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. References S. Camalet, T. Duke, F. Julicher, and J. Prost, Auditory Sensitivity Provided by Self-Tuned Critical Oscillations of Hair Cells. Proceedings of the National Academy of Sciences of the United States of America 97, 2000, pp. 3183--3188. V. M. Eguiluz, M. Ospeck, Y. Choe, A. J. Hudspeth, and M. O. Magnasco, Essential Nonlinearities in Hearing. Physical Review Letters 84, 2000, 5232--5235. E. Fragniere, Analogue VLSI Emulation of the Cochlea, Doctoral Thesis, Departement d'electricite, EPFL, Lausanne, 1998. http://library.epfl.ch/en/theses/?nr=1796 T. J. Hamilton, C. Jin, A. van Schaik, and J. Tapson, An Active 2-D Silicon Cochlea. Biomedical Circuits and Systems, IEEE Transactions on 2, 2008, 30--43. T. J. Hamilton, J. Tapson, C. Jin, and A. van Schaik, Analogue VLSI implementations of two dimensional, nonlinear, active cochlea models, Biomedical Circuits and Systems Conference, 2008. IEEE, 2008, pp. 153--156. A. Kern, J.-J. van der Vyver, and R. Stoop, Towards a biomorphic silicon Hopf cochlea, Proceedings of the 10th IEEE conference on nonlinear dynamics of electronic systems, 2, 2002. A. Kern, and R. Stoop, Essential Role of Couplings between Hearing Nonlinearities, Physical Review Letters 91 (12) 2003, 128101. M. O. Magnasco, A Wave Traveling over a Hopf Instability Shapes the Cochlear Tuning Curve, Physical Review Letters 90 (5) 2003, 058101. C. J. Plack, The Sense of Hearing, Lawrence Erlbaum Associates, Inc., New Jersey, 2005. M. A. Ruggero, Responses to sound of the basilar membrane of the mammalian cochlea. Current Opinion in Neurobiology 2, 1992, 449--456. S. H. Strogatz, Nonlinear Dynamics and Chaos, Westview Press, Cambridge, 1994. J. Tapson, T. J. Hamilton, C. Jin, and A. van Schaik, Self-Tuned Regenerative Amplification and the Hopf Bifurcation, IEEE International Symposium on Circuits and Systems (ISCAS), Seattle, USA, 2008. A. van Schaik, and E. Fragniere, Pseudo-voltage domain implementation of a 2-dimensional silicon cochlea, International Symposium on Circuits and Systems (ISCAS), Sydney, Australia, 2001, pp. 185--188 vol. 2 doi:10.1109/ISCAS.2001921277
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