Chin. Phys. B ›› 2014, Vol. 23 ›› Issue (1): 10507-010507.doi: 10.1088/1674-1056/23/1/010507

• GENERAL • 上一篇    下一篇

Control schemes for synchronizing two subnetworks with weak couplings

张建宝a, 马忠军b, 张刚c   

  1. a School of Science, Hangzhou Dianzi University, Hangzhou 310018, China;
    b School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China;
    c College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
  • 收稿日期:2013-06-12 修回日期:2013-07-02 出版日期:2013-11-12 发布日期:2013-11-12
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11162004, 10972011, and 11001069), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LQ12A01003 and LQ12A01002), and the Science Foundation of Guangxi Province, China (Grant No. 2013GXNSFAA019006).

Control schemes for synchronizing two subnetworks with weak couplings

Zhang Jian-Bao (张建宝)a, Ma Zhong-Jun (马忠军)b, Zhang Gang (张刚)c   

  1. a School of Science, Hangzhou Dianzi University, Hangzhou 310018, China;
    b School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, China;
    c College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, China
  • Received:2013-06-12 Revised:2013-07-02 Online:2013-11-12 Published:2013-11-12
  • Contact: Ma Zhong-Jun E-mail:mzj1234402@163.com
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant Nos. 11162004, 10972011, and 11001069), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. LQ12A01003 and LQ12A01002), and the Science Foundation of Guangxi Province, China (Grant No. 2013GXNSFAA019006).

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摘要： In this paper, we propose a well-designed network model with a parameter and study full and partial synchronization of the network model based on the stability analysis. The network model is composed of a star-coupled subnetwork and a globally coupled subnetwork. By analyzing the special coupling configuration, three control schemes are obtained for synchronizing the network model. Further analysis indicates that even if the inner couplings in each subnetwork are very weak, two of the control schemes are still valid. In particular, if the outer coupling weight parameter θ is larger than (n2-2n)/4, or the subnetwork size n is larger than θ2, the two subnetworks with weak inner couplings can achieve synchronization. In addition, the synchronizability is independent of the network size in case of 0< θ < n/(n+1). Finally, we carry out some numerical simulations to confirm the validity of the obtained control schemes. It is worth noting that the main idea of this paper also applies to any network consisting of a dense subnetwork and a sparse network.

关键词: synchronization, weak coupling, star-global network, control scheme

Abstract: In this paper, we propose a well-designed network model with a parameter and study full and partial synchronization of the network model based on the stability analysis. The network model is composed of a star-coupled subnetwork and a globally coupled subnetwork. By analyzing the special coupling configuration, three control schemes are obtained for synchronizing the network model. Further analysis indicates that even if the inner couplings in each subnetwork are very weak, two of the control schemes are still valid. In particular, if the outer coupling weight parameter θ is larger than (n2-2n)/4, or the subnetwork size n is larger than θ2, the two subnetworks with weak inner couplings can achieve synchronization. In addition, the synchronizability is independent of the network size in case of 0< θ < n/(n+1). Finally, we carry out some numerical simulations to confirm the validity of the obtained control schemes. It is worth noting that the main idea of this paper also applies to any network consisting of a dense subnetwork and a sparse network.

Key words: synchronization, weak coupling, star-global network, control scheme

中图分类号:  (Synchronization; coupled oscillators)

  • 05.45.Xt
05.45.Gg (Control of chaos, applications of chaos) 89.75.-k (Complex systems)