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Article overview
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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 | 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 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 | Services: | Forum | Review | PDF | Favorites |
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