Abstract
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 (2f 1-f 2) when the network’s input consists of a sum of two sinusoids, with frequencies f 1 and f 2. One of our main results is an explicit expression for this (2f 1-f 2) component.
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© 1986 Springer-Verlag Berlin Heidelberg
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Sandberg, I.W., Allen, J.B. (1986). Steady-State Response Determination for Models of the Basilar Membrane. In: Allen, J.B., Hall, J.L., Hubbard, A.E., Neely, S.T., Tubis, A. (eds) Peripheral Auditory Mechanisms. Lecture Notes in Biomathematics, vol 64. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50038-1_42
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DOI: https://doi.org/10.1007/978-3-642-50038-1_42
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