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Chin. Phys. B, 2014, Vol. 23(1): 010507    DOI: 10.1088/1674-1056/23/1/010507
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Control schemes for synchronizing two subnetworks with weak couplings

Zhang Jian-Baoa, Ma Zhong-Junb, Zhang Gangc
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
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.
Keywords:  synchronization      weak coupling      star-global network      control scheme  
Received:  12 June 2013      Revised:  02 July 2013      Accepted manuscript online: 
PACS:  05.45.Xt (Synchronization; coupled oscillators)  
  05.45.Gg (Control of chaos, applications of chaos)  
  89.75.-k (Complex systems)  
Fund: 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).
Corresponding Authors:  Ma Zhong-Jun     E-mail:  mzj1234402@163.com

Cite this article: 

Zhang Jian-Bao, Ma Zhong-Jun, Zhang Gang Control schemes for synchronizing two subnetworks with weak couplings 2014 Chin. Phys. B 23 010507

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