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Fractional quantum Julia set

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  • Wang, Yupin

Abstract

This paper proposes fractional quantum Julia sets based on a fractional q-difference map and preliminarily investigates their fractal dynamic characteristics by numerical methods and graphical explorations. The influence of parameters on the novel fractal sets is performed by dimension analysis. Memory and scale mainly affect the appearance and existence of the sets, respectively. The robustness of the sets to three types of dynamic noise perturbations is discussed by the Julia deviation tools. In particular, the deviation index is fitted concerning noise intensity. Several extensive numerical experiments are done to support the main conclusions.

Suggested Citation

  • Wang, Yupin, 2023. "Fractional quantum Julia set," Applied Mathematics and Computation, Elsevier, vol. 453(C).
    • Handle: RePEc:eee:apmaco:v:453:y:2023:i:c:s0096300323002461
    DOI: 10.1016/j.amc.2023.128077
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    References listed on IDEAS

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    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. 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).
    3. Luo, Cheng & Liu, Bao-Qing & Hou, Hu-Shuang, 2021. "Fractional chaotic maps with q–deformation," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    4. Wang, Yupin & Liu, Shutang & Li, Hui & Wang, Da, 2019. "On the spatial Julia set generated by fractional Lotka-Volterra system with noise," Chaos, Solitons & Fractals, Elsevier, vol. 128(C), pages 129-138.
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