Complete phase synchronization of nonidentical high-dimensional Kuramoto model (Q2096916)

The authors consider a high-dimensional generalisation of the Kuramoto model of coupled oscillators, for which the intrinsic frequency of a phase oscillator is replaced by a real skew-symmetric matrix. The network's connectivity is given a strongly-connected directed graph. The authors give a necessary and sufficient condition for complete phase synchronisation, for which the states of all oscillators approach a common value as \(t\to\infty\). Such synchronisation is not possible in the standard Kuramoto model with non-identical frequencies, but is possible in higher-dimensional models of non-identical oscillators. Several simulations of 5 oscillators connected in a directed cycle are given, illustrating the results.