Modelling the Cochlear Partition with Coupled van der Pol Oscillators

Abstract

Within the context of interest in analyzing `active' and nonlinear processes in the cochlea we have been studying a model cochlea in which the local membrane impedance is described by a Van der Pol-oscillator. The behaviour of the undriven and sinusoidally driven discretized model is examined numerically. The undriven model describes the behaviour of a discrete number of coupled oscillators, which, if uncoupled, would have limit cycles gradually differing in frequency. In the coupled case the limit cycle behaviour is less predictable: it appears to exhibit quasi stochastic properties. In the driven model a sufficiently strong stimulus causes entrainment to the stimulus, and odd order harmonics appear. In the range where the driven response is small compared with the average limit cycle, the response is almost linear. The strict Van der Pol-damping function, which is parabolic in velocity, produces strong saturation. A generalized Van der Pol-damping term, which causes small-amplitude instability and large-amplitude stability, produces much the same general behaviour, but the intensity response can be modelled more realistically.