On equivalence of locally active models of the cochlea

In the literature on locally active models of the cochlea several forms of the model have been worked out in which elements of the organ of Corti are assumed to produce acoustical energy. In these models use is made of a secondary resonance or a place-dependent delay to achieve activity over a limited part of the length of the basilar membrane, and outer hair cells are postulated as sources of energy production. In the present paper it will be shown that several of these models are formally equivalent. That means that they can be reduced to a standard form, and that the only difference resides in the choice and meaning of the parameters. The results of the analysis serve to facilitate the analysis of function and structure in cochlear models containing sources of local activity. In particular, questions of positive versus negative feedback, and the parts played by resonance and impedance-level differences can be resolved unambiguously. The treatment can be extended to models with higher dimensionality, and can also serve to obtain insight in nonlinear phenomena occurring in cochlear models.