Topological bifurcations in networks of proximity Kuramoto oscillators

In this paper, we present a numerical study on a modified Kuramoto model, in which the oscillators are coupled only if in mutual proximity. In particular, we show that the onset of phase locking is associated to the phenomenon of topological bifurcation. When the coupling strength belongs to a finite interval of values, all the oscillators asymptotically share the same frequency, but the topology of the interconnection may converge towards different steady-state values. This emerging phenomenon is thoroughly analyzed for the case of 5 nodes, while preliminary results are illustrated for larger networks.