Synchronization error dynamics of general nonidentical high-dimensional Kuramoto oscillators on unit spheres

Abstract For the general nonidentical high-dimensional Kuramoto oscillators on unit spheres, the synchronization error dynamical equations are derived, which have potential applications in the theoretical analysis of a variety of synchronization phenomena. By performing a spectral analysis of the synchronization error dynamical equations, an exponential synchronization rate of a class of high-dimensional Kuramoto oscillators coupled via a connected undirected graph is obtained. Simulations are provided to illustrate the obtained results.