Order parameter analysis of synchronization transitions on star networks

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• 作者：Hong-Bin Chen ; Yu-Ting Sun ; Jian Gao ; Can Xu ; Zhi-Gang Zheng
• 关键词：Kuramoto model ; synchronization ; order parameter ; Ott–Antonsen ansatz ; star network
• 刊名：Frontiers of Physics
• 出版年：2017
• 出版时间：December 2017
• 年：2017
• 卷：12
• 期：6
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Atomic, Molecular, Optical and Plasma Physics; Condensed Matter Physics; Particle and Nuclear Physics; Astronomy, Astrophysics and Cosmology;
• 出版者：Higher Education Press
• ISSN：2095-0470
• 卷排序：12

文摘

The collective behaviors of populations of coupled oscillators have attracted significant attention in recent years. In this paper, an order parameter approach is proposed to study the low-dimensional dynamical mechanism of collective synchronizations, by adopting the star-topology of coupled oscillators as a prototype system. The order parameter equation of star-linked phase oscillators can be obtained in terms of the Watanabe–Strogatz transformation, Ott–Antonsen ansatz, and the ensemble order parameter approach. Different solutions of the order parameter equation correspond to the diverse collective states, and different bifurcations reveal various transitions among these collective states. The properties of various transitions in the star-network model are revealed by using tools of nonlinear dynamics such as time reversibility analysis and linear stability analysis.