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Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System

Author

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  • Lina Wang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

  • Hui Chang

    (College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
    Key Laboratory for Robot and Intelligent Technology of Shandong Province, Shandong University of Science and Technology, Qingdao 266590, China)

  • Yuxia Li

    (College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
    Key Laboratory for Robot and Intelligent Technology of Shandong Province, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract

Based on Hastings and Powell’s research, this paper extends a three-species food-chain system to fractional-order form, whose dynamics are analyzed and explored. The necessary conditions for generating chaos are confirmed by the stability theory of fractional-order systems, chaos is characterized by its phase diagrams, and bifurcation diagrams prove that the dynamic behaviors of the fractional-order food-chain system are affected by the order. Next, the chaotic control of the fractional-order system is realized by the feedback control method with a good effect in a relative short period. The stability margin of the controlled system is revealed by the theory and numerical analysis. Finally, the results of theory analysis are verified by numerical simulations.

Suggested Citation

  • Lina Wang & Hui Chang & Yuxia Li, 2020. "Dynamics Analysis and Chaotic Control of a Fractional-Order Three-Species Food-Chain System," Mathematics, MDPI, vol. 8(3), pages 1-15, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:409-:d:331855
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    References listed on IDEAS

    as
    1. Younghae Do & Hunki Baek & Yongdo Lim & Dongkyu Lim, 2011. "A Three-Species Food Chain System with Two Types of Functional Responses," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-16, March.
    2. Singh, Anuraj & Gakkhar, Sunita, 2015. "Controlling chaos in a food chain model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 115(C), pages 24-36.
    3. Ji, Guilin & Ge, Qing & Xu, Jiabo, 2016. "Dynamic behaviors of a fractional order two-species cooperative systems with harvesting," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 51-55.
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    Cited by:

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