Influence of discretization error on instability of cochlear model

The instability derived from the cochlear model is a phenomenon used to characterize its active processing, which is one of the fundamentals of hearing. This processing relates to the activities of outer hair cells (OHCs) lining in the cochlea. The decline of this processing function is accounted for by the spatially irregular activities of OHCs. Current cochlear models show excessive instability when cochlea containing the irregular activity of the OHCs is simulated. To explain this phenomenon, there are two possibilities. First, excessive instability may be essential to the model. Second, discretized errors may affect the instability of the model in numerical calculation. To investigate these possibilities, a state space model of two-dimensional cochlear mechanics is developed and applied to a high-accuracy scheme of numerical calculation. As a result of this simulation, the basilar membrane responses include the discretization error, which depends on the modeling accuracy. Furthermore, the transfer function and the temporal response show more instability with higher modeling accuracy, with the irregularity of the feedback gain corresponding to the activities of the OHCs. Therefore, when the discretization error is large, the instability is weakened. Consequently, this paper concludes that excessive instability is an essential feature of the cochlear model.