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Stochastic synchronization of complex networks via a novel adaptive composite nonlinear feedback controller

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Abstract

In this paper, a novel adaptive composite nonlinear feedback controller is designed to synchronize complex networks. The proposed adaptive composite nonlinear feedback controller consists of an adaptive linear feedback control law and an adaptive nonlinear feedback control law. The adaptive linear feedback control part is designed to achieve a quick response. However, too fast convergent speed may cause overshoot or oscillations. So in order to achieve precise control, we design the adaptive nonlinear feedback control law to reduce the overshoot or oscillations caused by the adaptive linear feedback part. By using the properties of Weiner process and adding the proposed control strategy to the nodes, stochastic synchronization of complex networks with quickly convergent speed and high control precision can be achieved. Numerical simulations demonstrate the superior performance of this novel adaptive composite nonlinear feedback controller as compared to the conventional adaptive linear feedback controller.

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Acknowledgments

The authors would like to thank all the anonymous reviewers for their helpful advices. This paper is supported by the National Natural Science Foundation of China (Grant Nos. 61170269, 61121061), the Beijing Natural Science Foundation (Grant No. 4142016), the Asia Foresight Program under NSFC Grant (Grant No. 61161140320), and the Beijing Higher Education Young Elite Teacher Project (Grant No. YETP0449).

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Weiping Wang & Jinghua Xiao

  2. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Lixiang Li, Haipeng Peng & Yixian Yang

  3. Potsdam Institute for Climate Impact Research, 14473, Potsdam, Germany

    Jürgen Kurths

  4. National Engineering Laboratory for Disaster Backup and Recovery, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yixian Yang

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  1. Weiping Wang
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  2. Lixiang Li
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  3. Haipeng Peng
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  4. Jürgen Kurths
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  5. Jinghua Xiao
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  6. Yixian Yang
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Correspondence to Lixiang Li.

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Wang, W., Li, L., Peng, H. et al. Stochastic synchronization of complex networks via a novel adaptive composite nonlinear feedback controller. Nonlinear Dyn 80, 363–374 (2015). https://doi.org/10.1007/s11071-014-1874-3

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  • DOI: https://doi.org/10.1007/s11071-014-1874-3

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