A Nonhyperbolic Toy Model of Cochlear Dynamics

Cochlea displays complex and highly nonlinear behavior in response to wide-ranging auditory stimuli. While there have been many recent advancements in the modeling of cochlear dynamics, it remains unclear what mathematical structures underlie the essential features of the extended cochlea. We construct a dynamical system consisting of a series of strongly coupled critical oscillators to show that high-dimensional nonhyperbolic dynamics can account for high-order compressive nonlinearities, amplification of weak input, frequency selectivity, and traveling waves of activity. As a single Hopf bifurcation generically gives rise to features of cochlea at a local level, the nonhyperbolicity mechanism proposed in this paper can be seen as a higher-dimensional analogue for the entire extended cochlea.