= Kuramoto order parameter
{c}
{title2=$re^{i\psi}=N^{-1}\sum_j e^{i\theta_j}$}
The complex centroid of the oscillators' unit phase vectors has magnitude $r$ and argument $\psi$. A magnitude near one indicates phase coherence; zero indicates a balanced phase distribution, which need not be uniquely uniform at finite population size. Taking the imaginary part after multiplication by $e^{-i\theta_i}$ rewrites all-to-all sine coupling exactly in terms of these two collective variables.
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