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Fractional chaotic maps with q–deformation

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  • Luo, Cheng
  • Liu, Bao-Qing
  • Hou, Hu-Shuang

Abstract

q–deformation of fractional chaotic maps is investigated in this study. Some deformation results in difference equations or chaotic maps are revisited first. Fractional differences and q–deformations are then introduced. New fractional chaotic maps are proposed with a q–parameter. Chaotic behaviors are discussed in both one and two dimensional cases, respectively. Finally, stability analysis of generalized Hénon maps is provided and numerical results are demonstrated.

Suggested Citation

  • Luo, Cheng & Liu, Bao-Qing & Hou, Hu-Shuang, 2021. "Fractional chaotic maps with q–deformation," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    • Handle: RePEc:eee:apmaco:v:393:y:2021:i:c:s0096300320307128
    DOI: 10.1016/j.amc.2020.125759
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    References listed on IDEAS

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    1. Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
    2. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    3. Wu, Fei & Gao, Renbo & Liu, Jie & Li, Cunbao, 2020. "New fractional variable-order creep model with short memory," Applied Mathematics and Computation, Elsevier, vol. 380(C).
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    Cited by:

    1. Wang, Yupin & Li, Xiaodi & Wang, Da & Liu, Shutang, 2022. "A brief note on fractal dynamics of fractional Mandelbrot sets," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    2. Sabe, Naval R. & Pakhare, Sumit S. & Gade, Prashant M., 2024. "Synchronization transitions in coupled q-deformed logistic maps," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    3. 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).
    4. Cánovas, Jose S. & Rezgui, Houssem Eddine, 2023. "Revisiting the dynamic of q-deformed logistic maps," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    5. Dang, Rongqi & Chen, Yiming, 2021. "Fractional modelling and numerical simulations of variable-section viscoelastic arches," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    6. Wang, Yupin, 2023. "Fractional quantum Julia set," Applied Mathematics and Computation, Elsevier, vol. 453(C).

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