  Model reduction techniques have been widely used to study the collective
behavior of globally coupled oscillators. However, most approaches assume that
there are infinitely many oscillators. Here we propose a new ansatz, based on
the collective coordinate approach, that reproduces the collective dynamics of
the Kuramoto model for finite networks to high accuracy, yields the same
bifurcation structure in the thermodynamic limit of infinitely many oscillators
as previous approaches, and additionally captures the dynamics of the order
parameter in the thermodynamic limit, including critical slowing down that
results from a cascade of saddle-node bifurcations.
