Waves in viscously coupled chains of overdamped oscillators: The gecko's papilla.
The hearing organ of lizards -papilla- has been modelled as a chain of over-damped (inertia-less) bio-mechanical self-oscillators mutually coupled by a combination of viscous and elastic forces. In the extreme case when the elastic ones are negligible the combination of viscous coupling and overdamping leads to the study of unusual class of extended dynamical systems defined by a nonlocal spatial operator. In other words, the lack of inertia in the dynamics of the individual oscillators effectively mutates the original, locally defined coupling into one defined by a global, albeit exponentially weakening, prescription. In this talk we present a number of counterintuitive consequences of this phenomenon on the propagation of perturbations along the media, as well as on the expected synchronization behaviour of the chain. Other characteristics of papillae is tonotopy: the oscillators proper frequencies are arranged in an increasing order along the chain. The combination of different types of couplings and tonotopy, produces characteristic collective frequency spectra that one could associate with distinguishably stable spontaneous otoacoustic emissions observed in individual of certain lizards’ species like tokkai gecko for instance. We explore this phenomenon in simple settings.