中国物理B ›› 2009, Vol. 18 ›› Issue (10): 4187-4192.doi: 10.1088/1674-1056/18/10/019

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Synchronization transition of limit-cycle system with homogeneous phase shifts

郑志刚1, 张廷宪2   

  1. (1)Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China; (2)Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China;College of Physics and Electronic Engineering, Qujing Normal University, Qujing 655011,
  • 收稿日期:2008-12-31 修回日期:2009-03-05 出版日期:2009-10-20 发布日期:2009-10-20
  • 基金资助:
    Project supported in part by the National Natural Science Foundation of China (Grant No 10875011), the 973 Programme (Grant No 2007CB814805), and the Foundation of Doctoral Training of China (Grant No 20060027009).

Synchronization transition of limit-cycle system with homogeneous phase shifts

Zhang Ting-Xian(张廷宪)a)b) and Zheng Zhi-Gang(郑志刚)a)†   

  1. a Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Beijing), Beijing Normal University, Beijing 100875, China; b College of Physics and Electronic Engineering, Qujing Normal University, Qujing 655011, China
  • Received:2008-12-31 Revised:2009-03-05 Online:2009-10-20 Published:2009-10-20
  • Supported by:
    Project supported in part by the National Natural Science Foundation of China (Grant No 10875011), the 973 Programme (Grant No 2007CB814805), and the Foundation of Doctoral Training of China (Grant No 20060027009).

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摘要： The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated when phase shifts are considered. In the system of coupled oscillators, phase shifts are the same between different oscillators. Synchronization and synchronization transition are revealed with different phase shifts. Phase shifts play an important role for this kind of system. When the phase shift α<0.5π, the synchronization state can be attained by increasing the coupling, and the system cannot reach the synchronization state while α≥q0.5π. A clear scaling between complete synchronization critical coupling strength K_pc and α-0.5π is found.

Abstract: The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated when phase shifts are considered. In the system of coupled oscillators, phase shifts are the same between different oscillators. Synchronization and synchronization transition are revealed with different phase shifts. Phase shifts play an important role for this kind of system. When the phase shift $\alpha<0.5\pi$, the synchronization state can be attained by increasing the coupling, and the system cannot reach the synchronization state while $\alpha\geqslant 0.5\pi$. A clear scaling between complete synchronization critical coupling strength $K_{pc}$ and $\alpha-0.5\pi$ is found.

Key words: nonlinear dynamics, coupled limit-cycle system, synchronization transition, phase shift

中图分类号:  (Synchronization; coupled oscillators)

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