The cochlea uses active amplification to capture faint sounds. It has been proposed that the amplifier comprises a set of self-tuned critical oscillators: each hair cell contains a force-generating dynamical system that is maintained at the threshold of an oscillatory instability, or Hopf bifurcation. While the active response to a pure tone provides frequency selectivity, exquisite sensitivity, and wide dynamic range, its intrinsic nonlinearity causes tones of different frequency to interfere with one another in the cochlea. Here we determine the response to two tones, which provides a framework for understanding how the ear processes the more complex sounds of speech and music. Our calculations of two-tone suppression and the spectrum of distortion products generated by a critical oscillator accord with experimental observations of basilar membrane motion and the nervous response. We discuss how the response of a set of self-tuned oscillators, covering a range of characteristic frequencies, represents the structure of a complex sound. The frequency components of the stimulus can be inferred from the timing of neural spikes elicited by the vibrating hair cells. Passive prefiltering by the basilar membrane improves pitch discrimination by reducing interference between tones. Our analysis provides a general framework for examining the relation between the physical nature of the peripheral detection apparatus and psychophysical phenomena such as the sensation of dissonance and auditory illusions.

To capture faint sounds, the ear uses an active system of amplification. We and our colleagues have put forward the idea that the amplifier comprises a set of 'self-tuned critical oscillators': each hair cell contains a force-generating dynamical system which is maintained at the threshold of an oscillatory instability, or Hopf bifurcation. The active response to a pure tone is perfectly suited to the ear's needs, since it provides frequency selectivity, exquisite sensitivity and wide dynamic range. However, the intrinsic nonlinearity of the mechanism causes tones of different frequency to interfere with one another in the cochlea. In order to provide a framework for understanding how the ear processes the more complex sounds of speech and music, we have examined the response of a critical Hopf oscillator to two tones. Our calculations indicate how the response to one tone is suppressed by the presence of a second tone of similar frequency. They also show how a characteristic spectrum of distortion products is generated. The results are in accord with experimental observations of basilar membrane motion. Given the complexity of the nonlinear response, how does the ear distinguish the frequency components of a sound source? We propose a simple model of pitch extraction based on the timings of neural spikes, and investigate to what extent psychophysical phenomena such as the sensation of dissonance and auditory illusions can be attributed to the physical nature of the peripheral detection apparatus.

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Waves propagating along the basilar membrane are amplified by an active nonlinear process. The general aspects of the active amplification of periodic signals can be discussed in the framework of critical oscillators. Here, we show how the concepts of a traveling wave and of critical oscillators can be combined to describe the main features of nonlinear wave propagation, energy flow and reflections in the cochlea.