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Pinning adaptive synchronization of complex dynamical network with multi-links |
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| Authors: | Qiyang Hu Haipeng Peng Yunge Wang Zhirui Hu Yixian Yang |
| Affiliation: | 1. Information Security Center, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing, 100876, China 2. Research Center on Fictitious Economy and Data Science, Chinese Academy of Sciences, Beijing, 100190, China 3. National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing, 100876, China 4. Department of Automation, Tsinghua University, Beijing, 100084, China |
| Abstract: | Networks with multi-links are universal in the real world such as communication networks, transport networks, and social networks. It is important for us to investigate the control of complex dynamical network with multi-links. In this paper, both local and global stabilities of dynamical network with multi-links are analyzed by applying adaptive control theory and mathematical tools, and some new criteria are proposed to ensure the pinning synchronization. We find that the number of pinned nodes satisfies an inequality for synchronization. Additionally, we solve the problem of how much the coupling strength we need to achieve network synchronization with one pinned node in the network system with multi-links. Finally, numerical examples are used to illustrate the effectiveness of the proposed method. |
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