A system of nonlinear differential equations modeling basilar-membrane motion.

A phenomenological model for displacement of a point on the basilar membrane is developed by formulating a system of nonlinear differential equations: ẍi(t) + 2Di[1 + ηẋi2(t)]ẋi(t) + ω0i2xi(t) = Cxi−1(t), for i = 1, 2, …, 10, where x0(t) is the input (stapes displacement) and x10(t) is the output. This model, which behaves effectively linearly at low levels and nonlinearly at high levels, shows that a single nonlinear system is adequate to account for the following frequency‐dependent nonlinear phenomena of the peripheral auditory system: (1) limiting of the output level; (2) decrease of Q with increasing input level; (3) decrease of the most effective frequency with increasing input level; (4) changes in phase angle of the output with input level; (5) changes in shape of the click response waveform with input level; (6) two‐tone suppression with f1 = CF and f2 > CF; (7) generation of the combination tone 2f1 − f2 in response to two tones f1 < f2); (8) “amplitude” nonlinearity in response to click pairs; ...