Order parameter analysis of synchronization transitions on star networks  

作　　者：Hong-Bin Chen Yu-Ting Sun Jian Gao Can Xu Zhi-Gang Zheng 

机构地区：[1]Institute of Systems Science, Huaqiao University, Xiamen 361021, China [2]CoUege of Information Science and Engineering, Huaqiao University, Xiamen 361021, China [3]Department of Physics and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China

出　　处：《Frontiers of physics》2017年第6期11-20,共10页物理学前沿（英文版）

基　　金：This work was partially supported by the National Natural Science Foundation of China （Grant Nos. 11075016 and 11475022） and the Scientific Research Funds of Huaqiao University.

摘　　要：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 oscil- lators 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 ensem- ble 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.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 oscil- lators 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 ensem- ble 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.

关 键 词：Kuramoto model SYNCHRONIZATION order parameter Ott-Antonsen ansatz star network 

分 类 号：O4[理学—物理]