Control schemes for synchronizing two subnetworks with weak couplings |
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Authors: | Zhang Jian-Bao Ma Zhong-Jun Zhang Gang |
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Affiliation: | 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 |
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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. |
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Keywords: | synchronization weak coupling star-global network control scheme |
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