title: Order parameter analysis for low-dimensional behaviors of coupled phase-oscillators.
abstract: 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 equations of order parameters, namely, order parameter analysis, with which we point out that OA ansatz is rooted in the dynamical symmetry of order parameters. With our approach the scope of OA ansatz is identified as two conditions, i.e., the limit of infinitely many oscillators 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 expectation assumption and the dominating-term assumption.
authors.affiliation: College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.|Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China.
authors.forename: Jian
authors.initials: J
authors.lastname: Gao
authors.affiliation: Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China.
authors.forename: Can
authors.initials: C
authors.lastname: Xu
authors.affiliation: Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China.
authors.forename: Yuting
authors.initials: Y
authors.lastname: Sun
authors.affiliation: College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China.
authors.forename: Zhigang
authors.initials: Z
authors.lastname: Zheng