A generalization of the van-der-Pol oscillator underlies active signal amplification in Drosophila hearing.

The antennal hearing organs of the fruit fly Drosophila melanogaster boost their sensitivity by an active mechanical process that, analogous to the cochlear amplifier of vertebrates, resides in the motility of mechanosensory cells. This process nonlinearly improves the sensitivity of hearing and occasionally gives rise to self-sustained oscillations in the absence of sound. Time series analysis of self-sustained oscillations now unveils that the underlying dynamical system is well described by a generalization of the van-der-Pol oscillator. From the dynamic equations, the underlying amplification dynamics can explicitly be derived. According to the model, oscillations emerge from a combination of negative damping, which reflects active amplification, and a nonlinear restoring force that dictates the amplitude of the oscillations. Hence, active amplification in fly hearing seems to rely on the negative damping mechanism initially proposed for the cochlear amplifier of vertebrates.

Role of transient processes for reconstruction of model equations from time series.

We perform a global reconstruction of differential and difference equations, which model an object in a wide domain of a phase space, from a time series. The efficiency of using time realizations of transient processes for this purpose is demonstrated. Time series of transients are shown to have some advantages for the realization of a procedure of model structure optimization.