中国物理B ›› 2013, Vol. 22 ›› Issue (7): 70504-070504.doi: 10.1088/1674-1056/22/7/070504

• GENERAL • 上一篇    下一篇

Generalized projective synchronization of two coupled complex networks with different sizes

李科赞a, 何恩a, 曾朝蓉b, 谢智刚c   

  1. a School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China;
    b School of Business, Guilin University of Electronic Technology, Guilin 541004, China;
    c Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
  • 收稿日期:2012-11-27 修回日期:2013-02-02 出版日期:2013-06-01 发布日期:2013-06-01
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61004101, 11161013, and 61164020) and the Natural Science Foundation of Guangxi Province, China (Grant Nos. 2011GXNSFB018059, 2011GXNSFA018136, and 2011GXNSFA018134).

Generalized projective synchronization of two coupled complex networks with different sizes

Li Ke-Zan (李科赞)a, He En (何恩)a, Zeng Zhao-Rong (曾朝蓉)b, Chi K. Tse (谢智刚)c   

  1. a School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China;
    b School of Business, Guilin University of Electronic Technology, Guilin 541004, China;
    c Department of Electronic and Information Engineering, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China
  • Received:2012-11-27 Revised:2013-02-02 Online:2013-06-01 Published:2013-06-01
  • Contact: Li Ke-Zan E-mail:lkzzr@guet.edu.cn
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 61004101, 11161013, and 61164020) and the Natural Science Foundation of Guangxi Province, China (Grant Nos. 2011GXNSFB018059, 2011GXNSFA018136, and 2011GXNSFA018134).

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摘要： We investigate a new generalized projective synchronization (GPS) between two complex dynamical networks of different sizes. To the best of our knowledge, most current studies on the projective synchronization have dealt with coupled networks with the same size. By generalized projective synchronization, we mean that the states of nodes in each network can realize complete synchronization, and the states of pair nodes from both networks can achieve projective synchronization. By using the stability theory of dynamical system, several sufficient conditions for guaranteeing the existence of the generalized projective synchronization under feedback control and adaptive control are obtained. As an example, we use Chua's circuits to demonstrate the effectiveness of our proposed approach.

关键词: complex network, projective synchronization, adaptive control

Abstract: We investigate a new generalized projective synchronization (GPS) between two complex dynamical networks of different sizes. To the best of our knowledge, most current studies on the projective synchronization have dealt with coupled networks with the same size. By generalized projective synchronization, we mean that the states of nodes in each network can realize complete synchronization, and the states of pair nodes from both networks can achieve projective synchronization. By using the stability theory of dynamical system, several sufficient conditions for guaranteeing the existence of the generalized projective synchronization under feedback control and adaptive control are obtained. As an example, we use Chua's circuits to demonstrate the effectiveness of our proposed approach.

Key words: complex network, projective synchronization, adaptive control

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Gg (Control of chaos, applications of chaos) 89.75.Hc (Networks and genealogical trees)