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Improving dynamics of integer-order small-world network models under fractional-order PD control

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Abstract

The optimal control of dynamics is a popular topic for small-world networks. In this paper, we address the problem of improving the behavior of Hopf bifurcations in an integer-order model of small-world networks. In this study, the time delay is used as the bifurcation parameter. We add a fractional-order proportional-derivative (PD) scheme to an integer-order Newman-Watts (N-W) small-world model to better control the Hopf bifurcation of the model. The most important contribution of this paper involves obtaining the stability of the system and the variation of the conditions of the Hopf bifurcation after a fractional PD controller is added to the integer-order small-world model. The results demonstrate that the designed PD controller can be used to restrain or promote the occurrence of Hopf bifurcations by setting appropriate parameters. We also describe several simulations to verify our research results.

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Acknowledgements

This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61573194, 51775284, 61877033), Natural Science Foundation of Jiangsu Province of China (Grant Nos. BK20181389, BK20181387), Key Project of Philosophy and Social Science Research in Colleges and Universities in Jiangsu Province (Grant No. 2018SJZDI142), and Postgraduate Research & Practice Innovation Program of Jiangsu Province (Grant No. KYCX18_0924).

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Authors and Affiliations

  1. College of Automation, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Huaifei Wang, Min Xiao, Binbin Tao & Fengyu Xu

  2. School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, 266061, China

    Min Xiao

  3. College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210003, China

    Zhengxin Wang

  4. School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000, China

    Chengdai Huang

  5. School of Automation and Electrical Engineering, Linyi University, Linyi, 276005, China

    Jianlong Qiu

Authors
  1. Huaifei Wang
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  2. Min Xiao
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  3. Binbin Tao
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  4. Fengyu Xu
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  5. Zhengxin Wang
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  6. Chengdai Huang
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  7. Jianlong Qiu
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Correspondence to Min Xiao.

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Wang, H., Xiao, M., Tao, B. et al. Improving dynamics of integer-order small-world network models under fractional-order PD control. Sci. China Inf. Sci. 63, 112206 (2020). https://doi.org/10.1007/s11432-018-9933-6

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  • DOI: https://doi.org/10.1007/s11432-018-9933-6

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