An array of coupled nonlinear oscillators as a model for amplitude variations in intermodulation distortions from the auditory system

Abstract

The response of a nonlinear oscillator driven by two or more forces displays several frequency components corresponding to the linear combinations of the driving frequencies, known as intermodulation distortions (IMDs). The auditory system of all classes of vertebrates produces strong IMDs in the presence of sounds of two tones. This phenomenon is attributed to the nonlinearity of the biological acoustic sensors within the inner ear. In this work, we developed a numerical model to investigate the total IMDs generated by a chain of coupled nonlinear oscillators. Total nonlinear distortions exhibited variations in amplitudes with respect to the stimulus frequency. The variation profile was sensitive to the magnitude of the driving forces and the difference in the two driving frequencies. We found that the arrangement of the oscillators’ characteristic frequencies was necessary for the variations in total IMD level. Results from the numerical model agreed with measurements of IMDs from Chinese edible frog (Hoplobatrachus Rugulosus), whose inner ear is constituted by arrays of acoustic receptors with progressively increasing natural frequencies. In response to sounds of two tones, IMDs produced by the inner ear of Chinese edible frog exhibited variations in amplitudes with respect to the driving frequencies. The third-order distortion level displayed several peaks at high stimulating sound pressure level, and at large differences between the stimulus frequencies. Our findings suggest that an array of coupled nonlinear oscillator can serve as a simple model for the generation of nonlinear distortions by the inner ear.