  Coupled phase-oscillators are important models related to synchronization.
Recently, Ott-Antonsen(OA) ansatz is developed and used to get low-dimensional
collective behaviors in coupled oscillator systems. In this paper, we develop a
simple and concise approach based on the equations of order parameters, namely,
order parameter analysis, with which we point out that the OA ansatz is rooted
in the dynamical symmetry of the order parameters. With our approach the scope
of the OA ansatz is identified as two conditions, i.e., infinite size of the
system and only three nonzero Fourier coefficients of the coupling function.
Coinciding with each of the conditions, a distinctive system out of the scope
is taken into account and discussed with the order parameter analysis. Two
approximation methods are introduced respectively, namely the ensemble approach
and the dominating-term assumption.
