Order parameter analysis of synchronization transitions on star networks

doi:10.1007/s11467-017-0651-4

Front. Phys.

2017, Vol. 12

Issue (6) : 120504 https://doi.org/10.1007/s11467-017-0651-4

RESEARCH ARTICLE

Order parameter analysis of synchronization transitions on star networks

Hong-Bin Chen^1,²,Yu-Ting Sun³,Jian Gao³,Can Xu³(

),Zhi-Gang Zheng^1,²(

)

¹. Institute of Systems Science, Huaqiao University, Xiamen 361021, China
². College 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

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Abstract

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.

Keywords Kuramoto model synchronization order parameter Ott–Antonsen ansatz star network

Corresponding Author(s): Can Xu,Zhi-Gang Zheng

Issue Date: 09 February 2017

Cite this article:

Hong-Bin Chen,Yu-Ting Sun,Jian Gao, et al. Order parameter analysis of synchronization transitions on star networks[J]. Front. Phys. , 2017, 12(6): 120504.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-017-0651-4
https://academic.hep.com.cn/fop/EN/Y2017/V12/I6/120504

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