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The Kuramoto model, which describes synchronization phenomena, is a system ofordinary differential equations on $N$-torus defined as coupled harmonicoscillators. The order parameter is often used to measure the degree ofsynchronization. In this paper, a few properties of the continuous model forthe Kuramoto model are investigated. In particular, the moments systems areintroduced for both of the Kuramoto model and its continuous model. By usingthem, it is proved that the order parameter of the $N$-dimensional Kuramotomodel converges to that of the continuous model as $N\to \infty$.

Continuous limit of the moments system for the globally coupled phase oscillators