中国物理B ›› 2023, Vol. 32 ›› Issue (6): 60503-060503.doi: 10.1088/1674-1056/acc808

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Stability and multistability of synchronization in networks of coupled phase oscillators

Yun Zhai(翟云)1,2,3, Xuan Wang(王璇)2,3, Jinghua Xiao(肖井华)1, and Zhigang Zheng(郑志刚)2,3,†   

  1. 1 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
    2 Institute of Systems Science, Huaqiao University, Xiamen 361021, China;
    3 College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
  • 收稿日期:2023-02-13 修回日期:2023-03-01 接受日期:2023-03-28 出版日期:2023-05-17 发布日期:2023-05-17
  • 通讯作者: Zhigang Zheng E-mail:zgzheng@bnu.edu.cn
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No. 11875135).

Stability and multistability of synchronization in networks of coupled phase oscillators

Yun Zhai(翟云)1,2,3, Xuan Wang(王璇)2,3, Jinghua Xiao(肖井华)1, and Zhigang Zheng(郑志刚)2,3,†   

  1. 1 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China;
    2 Institute of Systems Science, Huaqiao University, Xiamen 361021, China;
    3 College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
  • Received:2023-02-13 Revised:2023-03-01 Accepted:2023-03-28 Online:2023-05-17 Published:2023-05-17
  • Contact: Zhigang Zheng E-mail:zgzheng@bnu.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No. 11875135).

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摘要： Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we study the stability of the synchronous state in coupled phase oscillators. It is found that numerical integration of differential equations of coupled phase oscillators with a finite time step may induce desynchronization at strong couplings. The mechanism behind this instability is that numerical accumulated errors in simulations may trigger the loss of stability of the synchronous state. Desynchronization critical couplings are found to increase and diverge as a power law with decreasing the integral time step. Theoretical analysis supports the local stability of the synchronized state. Globally the emergence of synchronous state depends on the initial conditions. Other metastable ordered states such as twisted states can coexist with the synchronous mode. These twisted states keep locally stable on a sparse network but lose their stability when the network becomes dense.

关键词: synchronization, coupled phase oscillators, complex networks, multistability

Abstract: Coupled phase oscillators usually achieve synchronization as the coupling strength among oscillators is increased beyond a critical value. The stability of synchronous state remains an open issue. In this paper, we study the stability of the synchronous state in coupled phase oscillators. It is found that numerical integration of differential equations of coupled phase oscillators with a finite time step may induce desynchronization at strong couplings. The mechanism behind this instability is that numerical accumulated errors in simulations may trigger the loss of stability of the synchronous state. Desynchronization critical couplings are found to increase and diverge as a power law with decreasing the integral time step. Theoretical analysis supports the local stability of the synchronized state. Globally the emergence of synchronous state depends on the initial conditions. Other metastable ordered states such as twisted states can coexist with the synchronous mode. These twisted states keep locally stable on a sparse network but lose their stability when the network becomes dense.

Key words: synchronization, coupled phase oscillators, complex networks, multistability

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Ra (Coupled map lattices)