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Order parameter analysis of synchronization transitions on star networks

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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.

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Acknowledgements

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.

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Authors and Affiliations

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

    Hong-Bin Chen & Zhi-Gang Zheng

  2. College of Information Science and Engineering, Huaqiao University, Xiamen, 361021, China

    Hong-Bin Chen & Zhi-Gang Zheng

  3. Department of Physics and the Beijing-Hong Kong-Singapore Joint Centre for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing, 100875, China

    Yu-Ting Sun, Jian Gao & Can Xu

Authors
  1. Hong-Bin Chen
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  2. Yu-Ting Sun
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  3. Jian Gao
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  4. Can Xu
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  5. Zhi-Gang Zheng
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Correspondence to Can Xu or Zhi-Gang Zheng.

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Chen, HB., Sun, YT., Gao, J. et al. Order parameter analysis of synchronization transitions on star networks. Front. Phys. 12, 120504 (2017). https://doi.org/10.1007/s11467-017-0651-4

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