On synchronization in Kuramoto models on spheres

We analyze two classes of Kuramoto models on spheres that have been introduced in previous studies. Our analysis is restricted to ensembles identical oscillators with the global coupling. In such a setup, an additional assumption initial distribution uniform sphere, one can derive equations for order parameters closed form. The rate synchronization real model depends dimension sphere. Specifically, faster higher-dimensional spheres. On other side, parameter complex always satisfies same ODE, regardless dimension. derivation based recently unveiled connections these geometries unit balls. Simulations system several hundreds yield perfect fits theoretical predictions, are obtained by solving parameter.