  Kuramoto model is one of the most prominent models for the synchronization of
coupled oscillators. It has long been a research hotspot to understand how
natural frequencies, the interaction between oscillators, and network topology
determine the onset of synchronization. In this paper, we investigate the
critical coupling of Kuramoto oscillators on deterministic dense networks,
viewed as a natural generalization from all-to-all networks of identical
oscillators. We provide a sufficient condition under which the Kuramoto model
with non-identical oscillators has one unique and stable equilibrium. Moreover,
this equilibrium is phase cohesive and enjoys local exponential
synchronization. We perform numerical simulations of the Kuramoto model on
random networks and circulant networks to complement our theoretical analysis
and provide insights for future research.
