A Generalized Van Der Pol-Oscillator Cochlea Model

  • M. P. M. G. van den Raadt
  • H. Duifhuis
Part of the Lecture Notes in Biomathematics book series (LNBM, volume 87)


Over the last decade it has become clear that active and nonlinear behavior of the cochlea is to a certain extent similar to that of a Van der Poloscillator. This was first proposed by Johannesma (1980). It was worked out in more detail by several groups (e.g., van Netten and Duifhuis, 1983, Duifhuis et al., 1985, Jones et al., 1986, Diependaal et al., 1987, van Dijk and Wit, 1988). We have been working on a cochlea model with many active components, i.e. self-sustained oscillators. Initially this was set up with spatial parameters that varied smoothly. The classical parabolic damping profile was used. Our major emphasis, however, shifted toward potentially more realistic biophysical models. For the damping term we now use a function in which two parts can be discerned. First, a passive (positive) part with exponential “tails”, which provides response behavior with a log-like characteristic for external stimuli. Secondly, there is an active (negative) part that, if sufficiently strong, produces net active (negative damping = energy production) behavior. In order to model spontaneous emissions, we also introduced spatial discontinuities in the damping parameters.


Basilar Membrane1 Strong Oscillator Spatial Discontinuity Dominant Oscillator Cochlear Partition 


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  1. Diependaal, R. J., Duifhuis, H., Hoogstraten, H. W., and Viergever, M. A. (1987). “Numerical methods for solving one–dimensional cochlear models in the time domain”, J. Acoust. Soc. Am. 82, 1655–1666.Google Scholar
  2. Duifhuis, H. (1988). “Cochlear macromechanics”, in Auditorl/ Function. Neurobiological basis 0/ hearing, edited by G. M. Edelman, W. E. Gall, and W. M. Cowan, chapter 6, pp. 189–211 (A Neurosciences Institute Publication, Wiley, New York).Google Scholar
  3. Duifhuis, H., Hoogstraten, H. W., van Netten, S. M., Diependaal, R. J., and Bialek, W. (1985). “Modelling the cochlear partition with coupled Van der Pol oscillators”, in Peripheral Auditor Mechanisms, edited by J. B. Alien, J. L. Hall, A. E. Hubbard, S. T. Neely, and A. Tubis (Springer, New York), pp. 290–297.Google Scholar
  4. Johannesma, P. I. M. (1980). “Narrow band filters and active resonators. Comments on papers by D. T. Kemp & R. A. Chum, and H. P. Wit & R. J. Ritsma“, in physiological, and behavioural Itudie. in hearing, edited by G. van den Brink and F. A. Bilsen (Delft University PreBB, Delft), pp. 62–63.Google Scholar
  5. Jones, K., Tubis, A., Long, G. R., Burns, E. M., and Strickland, E. A. (1986). “Interactions among multiple spontaneous otoacoustic emissions”, in Peripheral Auditory Mechanisms, edited by J. B. Allen, J. L. Hall, A. Hubbard, S. T. Neely, an . 18 (Springer–Verlag Berlin) pp. 266–273.Google Scholar
  6. van Netten, S. M., and Duifhuis, H. (1983). Modelling an active nonlinear cochlea, In Mechanics of Hearing, edited by E. de Boer and M. A. Viergever (Nijhoff/Delft Univ. Press, Netherlands), pp. 143–151.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • M. P. M. G. van den Raadt
    • 1
  • H. Duifhuis
    • 1
  1. 1.Biophysics DepartmentRijksuniversiteit Groningenthe Netherlands

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