Exploiting Asymmetries in Diffusively Coupled Oscillators to Enable Frequency Tunability in Neuromorphic Devices

By exploiting controllable asymmetries, consensus in networks can be adjusted. In case of coupled oscillators, the characteristic frequencies of the network can be controlled. This property is called frequency tunability and it is, e.g., induced by changing the asymmetry between the damping of the oscillators or the coupling between the oscillators. Subsequently, the frequency tunability of two diffusively coupled Andronov-Hopf oscillators is investigated by analyzing the emergence of Andronov-Hopf bifurcations. This is done by investigating the local dynamics of the corresponding system. It turns out that the number of critical points of the Andronov-Hopf bifurcation is determined by analyzing a polynomial whose degree changes based on the choice of the bifurcation parameter. Thus, this polynomial is analyzed in terms of two different bifurcation parameters: (i) symmetric damping and (ii) symmetric coupling. In case of (i), the system has two critical points, which correspond to Andronov-Hopf bifurcations. In contrast to this, for (ii) the number of critical points varies between one and three depending on the asymmetric damping.