Almost global convergence to practical synchronization in the generalized Kuramoto model on networks over the n-sphere

Abstract

The Kuramoto model describes how collective synchronization appears spontaneously in a population of rhythmic units and is typically studied on a one dimensional circle. Here, the authors generalise the Kuramoto model on higher-dimensional manifolds and show that it achieves almost global convergence to synchronization and, in even dimensions, the fully synchronized state is attainable for nonidentical frequencies, in sharp contrast with the classical one-dimensional model.