Acta Physica Sinica, Volume. 69, Issue 8, 080502-1(2020)

Synchronization of coupled phase oscillators: Order parameter theory

Zhi-Gang Zheng1,2、*, Yun Zhai1,2,3, Xue-Bin Wang1,2, Hong-Bin Chen1,2, and Can Xu1,2、*
Author Affiliations
  • 1Institute of Systems Science, Huaqiao University, Xiamen 361021, China
  • 2College of Information Science and Engineering, Huaqiao University, Xiamen 361201, China
  • 3School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China
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    References(86)

    [1] Glass L, Mackay M C[J]. From  Clocks  to  Chaos:  The Rhythms of Life, 10(1988).

    [2] Mikhailov A S, Calenbuhr V[J]. From  Cells  to  Societies:Models of Complex Coherent Action, 127-154(2002).

    [3] Zheng Z G[J]. Spatiotemporal  Dynamics  and  Cooperative Behaviors  in  Coupled  Nonlinear  Systems, 53-85(2004).

    [4] Pikovsky A, Rosenblum M, Kurths J[J]. Synchronization, A Universal  Concept  in  Nonlinear  Sciences, 1-24(2001).

    [5] Strogatz S[J]. Sync: The Emerging Science of Spontaneous Order, 103-152(2015).

    [6] Wiener N[J]. Cybernetics or Control and Communication in the Animal and the Machine, 65(1965).

    [8] Kuramoto Y[J]. Self-entrainment  of  a  Population  of Coupled Non-linear Oscillators, in: International Symposium on  Mathematical  Problems  in  Theoretical  Physics, 420-428(1975).

    [9] Kuramoto Y[J]. Chemical Oscillations, Waves and Turbulence, 60-66(1984).

    [12] Bocaletti S, Kurths J, Osipov G, Valladares D, Zhou C[J]. Phys. Rep., 336, 1(2002).

    [15] Osipov G V, Kurths J, Zhou C S[J]. Synchronization  in Oscillatory Networks, Springer Series in Synergetics, 3-10(2007).

    [16] Balanov A, Janson N, Postnov D, Sosnovtseva O[J]. ynchronization:  From  Simle  to  Complex, 21(2009).

    [17] Zheng Z G[J]. Synchronization of Coupled Phase Oscillators, 293-327(2011).

    [22] Gomez-Gardenes J, Gomez S, Arenas A, et al[J]. Phys. Rev. Lett, 106, 12870(2011).

    [24] Peron T, , Mata A S, Rodrigues F A, Moreno Y[J]. Phys. Rev. E, 100, 042302(2019).

    [34] Zhang T X, Zheng Z G[J]. Phys. B, 18, 1674(2009).

    [43] Zheng Z G, Hu B, Hu G[J]. Phys. Rev. E, 62, 402(2000).

    [44] Hu B, Zheng Z G[J]. Int. J. Bif. & Chaos, 10, 2399(2000).

    [46] Watanabe S, Strogatz S H[J]. Phys. Rev. Lett., 70, 2391(1994).

    [51] Zheng Z G[J]. Emergence Dynamics in Complex Systems:From  Synchronization  to  Collective  Transport, 95-176(2019).

    [52] Nicolis G, Prigogine I[J]. Exploring  Complexity:  An Introduction, 21-25(1989).

    [53] Prigogine I, Nicolis G[J]. Self-Organization  in  Non-Equilibrium Systems, 63-222(1977).

    [54] Haken H[J]. Synergetics: An Introduction 3rd Ed., 191-224(1983).

    [55] Haken H[J]. Advanced Synergetics, 187-221(1983).

    [57] Tristan N[J]. Visual Complex Analysis, 1(1997).

    [59] Yao N, Zheng Z G[J]. Int. J. Mod. Phys. B, 30, 7 1630002(2016).

    [61] Liu Z H[J]. Chaotic  Dynamics  Foundation  and  Its Applications  in  Brain  functions, 234-256(2018).

    [70] Abrams D M, Strogatz S H[J]. Int. J. Bif. & Chaos, 16, 21(2006).

    [74] Gong C C[J]. arXiv 1909.07718(2019).

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    Zhi-Gang Zheng, Yun Zhai, Xue-Bin Wang, Hong-Bin Chen, Can Xu. Synchronization of coupled phase oscillators: Order parameter theory[J]. Acta Physica Sinica, 2020, 69(8): 080502-1

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    Paper Information

    Received: Dec. 26, 2019

    Accepted: --

    Published Online: Nov. 24, 2020

    The Author Email: Xu Can (xucan@hqu.edu.cn)

    DOI:10.7498/aps.69.20191968

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