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On the dynamics of fractional q-deformation chaotic map

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  • Ran, Jie
  • Li, Yu-Qin
  • Xiong, Yi-Bin

Abstract

In this paper, the dynamical behaviors of fractional q-deformation chaotic map are analyzed. Firstly, the fractional q-deformation chaotic map is proposed by employing the Caputo delta difference operator. Secondly, the rich dynamical behaviors, such as numerically stable period (NSP) attractor, quasi-periodic attractor, strange nonchaotic attractor, and chaotic attractor, of the proposed map are discussed by utilizing bifurcation diagram, phase diagram, and 0–1 test. Thirdly, two controllers are designed to study the chaos control and synchronization of the fractional q-deformation chaotic map. Finally, numerical simulations are presented to demonstrate the findings.

Suggested Citation

  • Ran, Jie & Li, Yu-Qin & Xiong, Yi-Bin, 2022. "On the dynamics of fractional q-deformation chaotic map," Applied Mathematics and Computation, Elsevier, vol. 424(C).
    • Handle: RePEc:eee:apmaco:v:424:y:2022:i:c:s0096300322001394
    DOI: 10.1016/j.amc.2022.127053
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    References listed on IDEAS

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    1. Luo, Cheng & Liu, Bao-Qing & Hou, Hu-Shuang, 2021. "Fractional chaotic maps with q–deformation," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    2. Marius-F. Danca & Nikolay Kuznetsov, 2021. "Hidden Strange Nonchaotic Attractors," Mathematics, MDPI, vol. 9(6), pages 1-19, March.
    3. Khennaoui, Amina-Aicha & Ouannas, Adel & Bendoukha, Samir & Grassi, Giuseppe & Lozi, René Pierre & Pham, Viet-Thanh, 2019. "On fractional–order discrete–time systems: Chaos, stabilization and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 150-162.
    4. Baleanu, Dumitru & Wu, Guo–Cheng & Zeng, Sheng–Da, 2017. "Chaos analysis and asymptotic stability of generalized Caputo fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 99-105.
    5. M. Higazy & George Maria Selvam & R. Janagaraj, 2021. "Chaotic Dynamics Of A Novel 2d Discrete Fractional Order Ushiki Map," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-11, December.
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    Cited by:

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