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18 February 2025
 
  » arxiv » 1508.0080

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Order parameter analysis for low-dimensional behaviors of coupled phase-oscillators
Jian Gao ; Yuting Sun ; Can Xu ; Zhigang Zheng ;
Date 1 Aug 2015
AbstractCoupled 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 system. 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, infinite size of the system and only three Fourier coefficients of coupling function nonzero. 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 method and the dominate-term method.
Source arXiv, 1508.0080
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