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Partial Anti-Synchronization of the Fractional-Order Chaotic Systems through Dynamic Feedback Control

Author

Listed:
  • Runlong Peng

    (School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Cuimei Jiang

    (School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Rongwei Guo

    (School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

Abstract

This paper investigates the partial anti-synchronization problem of fractional-order chaotic systems through the dynamic feedback control method. Firstly, a necessary and sufficient condition is proposed, by which the existence of the partial anti-synchronization problem is proved. Then, an algorithm is given and used to obtain all solutions of this problem. Moreover, the partial anti-synchronization problem of the fractional-order chaotic systems is realized through the dynamic feedback control method. It is noted that the designed controllers are single-input controllers. Finally, two illustrative examples with numerical simulations are used to verify the correctness and effectiveness of the proposed results.

Suggested Citation

  • Runlong Peng & Cuimei Jiang & Rongwei Guo, 2021. "Partial Anti-Synchronization of the Fractional-Order Chaotic Systems through Dynamic Feedback Control," Mathematics, MDPI, vol. 9(7), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:7:p:718-:d:524477
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    References listed on IDEAS

    as
    1. Lu, Jun Guo & Chen, Guanrong, 2006. "A note on the fractional-order Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 685-688.
    2. Xuan-Bing Yang & Yi-Gang He & Chun-Lai Li, 2018. "Dynamics Feature and Synchronization of a Robust Fractional-Order Chaotic System," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    3. Yu, Yongguang & Li, Han-Xiong & Wang, Sha & Yu, Junzhi, 2009. "Dynamic analysis of a fractional-order Lorenz chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1181-1189.
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