Almost‐Periodic Response Determination for Models of the Basilar Membrane

Electrical networks consisting of linear passive elements and many nonlinear resistors are often used to model the basilar membrane. The inputs to these networks are typically a sum of sinusoids switched on at t = 0, and the resulting quantities of interest because of their interpretation as analogs of experimental observables are the steady‐state response components of a certain current and of certain voltages. In this paper, recently obtained mathematical results concerning the input‐output representation of nonlinear systems are used to give, for the first time, a locally convergent expansion for all of the steady‐state quantities of interest. Also given is a good deal of information concerning general properties of the expansion, and this establishes important properties of the nonlinear network's response. Of particular practical interest is a term in the expansion that contains a component whose frequency is (2f₁ — f₂) when the network's input consists of a sum of two sinusoids, with frequencies f₁ and f₂. One of our main results is an explicit expression for this (2f₁ — f₂) component.