Comparing Longitudinal Coupling and Temporal Delay in a Transmission‐Line Model of the Cochlea

In this paper we compare and contrast the effects of longitudinal coupling and temporal delay on a fluid‐structure transmission‐line model of the mammalian cochlea. This work is based on recent reports that, in order to qualitatively explain experimental data, models of the basilar membrane impedance must include an exponential term that represents a time‐delayed feedback.

There are also models that include, e.g., a spatial feed‐forward mechanism, whose solution is often approximated by replacing the feed‐forward coupling by an exponential term. We show that there is no direct equivalence between the time‐delay and the longitudinal coupling mechanisms, although qualitatively similar results can be achieved, albeit in very different regions of parameter space.

An investigation of the steady‐state outputs shows that both models can display sharp tuning, but that the time‐delay model requires negative damping for such an effect to occur. Conversely, the longitudinal coupling model provides the most promising results with small positive damping. These results are extended by a careful stability analysis.

We find that, whereas a small time delay can stabilize an unstable transmission‐line model (with negative damping), that the longitudinal coupling model is stable when the damping is positive. The techniques developed in the paper are directed towards a more comprehensive analysis of nonlinear models.