Taking the middle ear system as the research object

the nonlinear vibration characteristics of the human ear under narrow-band random acoustic excitation were studied.According to the three-degree-of-freedom nonlinear model of the middle ear

the nonlinear random vibration equation was established and the regular matrix was introduced to obtain the nonlinear vibration equation in the regular coordinate.The amplitude-frequency characteristic equation of the first-order primary resonance of the middle ear system was obtained by the multi-scale method.Through the bifurcation diagram and the maximum Lyapunov index

it was found that the middle ear system produces different motions under different excitations.The Ito stochastic dif⁃ferential equation of the middle ear system was derived

the approximate expression of the second-order moment of the system was obtained by using the rectangular method

and the influence of the random disturbance intensity on the middle ear system was verified.The results show that the resonance area of the system increases with the increase of the external excitation.When the random disturbance intensity increases

the thickness of the limit cycle of the phase diagram becomes thicker.