中国物理B ›› 2009, Vol. 18 ›› Issue (1): 106-118.doi: 10.1088/1674-1056/18/1/018

• GENERAL • 上一篇    下一篇

Cost and effect of pinning control for network synchronization

李嵘, 段志生, 陈关荣   

  1. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
  • 收稿日期:2008-07-05 修回日期:2008-09-04 出版日期:2009-01-20 发布日期:2009-01-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 60674093) and the Foundation for Key Program of Ministry of Education, China (Grant No 107110).

Cost and effect of pinning control for network synchronization

Li Rong(李嵘)† , Duan Zhi-Sheng(段志生), and Chen Guan-Rong(陈关荣)   

  1. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, China
  • Received:2008-07-05 Revised:2008-09-04 Online:2009-01-20 Published:2009-01-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 60674093) and the Foundation for Key Program of Ministry of Education, China (Grant No 107110).

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摘要： The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabási--Albert model and various star-shaped networks are performed for verification and illustration.

Abstract: The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabási--Albert model and various star-shaped networks are performed for verification and illustration.

Key words: complex dynamical network, pinning control, exponential stability

中图分类号:  (Networks and genealogical trees)

  • 89.75.Hc
05.45.Xt (Synchronization; coupled oscillators)