Mechanism of Desynchronization in the Finite-Dimensional Kuramoto Model

We study how a decrease of the coupling strength causes a desynchronization in the Kuramoto model of $N$ globally coupled phase oscillators. We show that, if the natural frequencies are distributed uniformly or close to that, the synchronized state can robustly split into any number of phase clusters with different average frequencies, even culminating in complete desynchronization. In the simplest case of $N=3$ phase oscillators, the course of the splitting is controlled by a Cherry flow. The general $N$-dimensional desynchronization mechanism is numerically illustrated for $N=5$.