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A New Synchronization Method for Time-Delay Fractional Complex Chaotic System and Its Application

Author

Listed:
  • Junmei Guo

    (School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Chunrui Ma

    (School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Xinheng Wang

    (School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China)

  • Fangfang Zhang

    (School of Electrical Engineering and Automation, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250353, China
    Shandong Computer Science Center (National Supercomputer Center in Jinan), Shandong Artificial Intelligence Institute, Jinan 250101, China)

  • Michaël Antonie van Wyk

    (School of Electrical and Information Engineering, University of the Witwatersrand, Johannesburg 2000, South Africa)

  • Lei Kou

    (Institute of Oceanographic Instrumentation, Qilu University of Technology (Shandong Academy of Sciences), Qingdao 266000, China)

Abstract

This paper proposes a class of time-delay fractional complex L u ¨ system and utilizes the adomian decomposition algorithm to study the dynamics of the system. Firstly, the time chaotic attractor, coexistence attractor and parameter space are studied. The bifurcation diagram and complexity are used to analyze the dynamic characteristics of the system. Secondly, the definition of modified fractional projective difference function synchronization (MFPDFS) is introduced. The corresponding synchronous controller is designed to realize the MFPDFS of the time-delay fractional complex L u ¨ system. Thirdly, based on the background of wireless speech communication system (WSCs), the MFPDFS controller is used to realize the secure speech transmission. Finally, the effectiveness of the controller is verified by numerical simulation. The signal-noise ratio (SNR) analysis of speech transmission is given. The performance of secure communication is verified by numerical simulation.

Suggested Citation

  • Junmei Guo & Chunrui Ma & Xinheng Wang & Fangfang Zhang & Michaël Antonie van Wyk & Lei Kou, 2021. "A New Synchronization Method for Time-Delay Fractional Complex Chaotic System and Its Application," Mathematics, MDPI, vol. 9(24), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3305-:d:705824
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    References listed on IDEAS

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    1. Gao, Xin & Yu, Juebang, 2005. "Chaos in the fractional order periodically forced complex Duffing’s oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 1097-1104.
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    Cited by:

    1. Lingling Xie & Jiahao Shi & Junyi Yao & Di Wan, 2022. "Research on the Period-Doubling Bifurcation of Fractional-Order DCM Buck–Boost Converter Based on Predictor-Corrector Algorithm," Mathematics, MDPI, vol. 10(12), pages 1-13, June.

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