On coupled oscillators modeling bio-inspired acoustic sensors: Bifurcation analysis toward tunability enhancement

Oscillators exhibiting an Andronov-Hopf bifurcation are candidates to mimic the functionality of the cochlea, since the transfer response of these oscillators is compressive and frequency selective. The former implies that small stimuli are amplified and strong stimuli are attenuated, while the latter means that the oscillator only reacts in a (small) frequency band. However, this implies that many oscillators are needed to cover a relevant frequency band. By introducing the notion of tunable characteristic frequencies, i.e., the characteristic frequency can be adjusted by a controllable input, the number of oscillators can be eventually reduced. Subsequently, the tunability enhancement of coupled oscillators is investigated by analyzing the local dynamics of a network of oscillators. For this, necessary conditions for the emergence of Andronov-Hopf bifurcations are determined for networks consisting of two groups, i.e., a group is a network of identical oscillators. By choosing the eigenvalues of the product of the cross-coupling matrix as bifurcation parameters and exploiting the structure of the transfer matrix of this network, the critical points and, thus, the characteristic frequency at this point can be derived. Tunability of the characteristic frequency is then enabled by controlling the asymmetry between the groups of oscillators.