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Multi-Direction Chain And Grid Chaotic System Based On Julia Fractal

Author

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  • XIANG-LIANG XU

    (School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China†School of Information and Software Engineering, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China)

  • GUO-DONG LI

    (School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China‡Key Laboratory of Data Analysis and Computing, Guangxi University Laboratory, Guilin 541004, China)

  • WAN-YING DAI

    (�College of Management Science, Chengdu University of Technology, Chengdu 610059, P. R. China)

  • XIAO-MING SONG

    (School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin 541004, P. R. China)

Abstract

In this paper, based on the multi-scroll chaotic system, multi-direction chain and grid chaotic attractors are generated by a new Julia fractal mapping process. The feasibility and effectiveness of the proposed method are verified by numerical simulation. This scheme not only realizes the combination of unidirectional and bidirectional distributed multi-scroll chaotic system and Julia fractal, but also applies to three-directional distributed 3D grid-like multi-scroll generalized Jerk system. This paper takes unidirectionally distributed multi-scroll chaos as an example. It discusses the influence of Julia fractals with coefficients and complex constants on the system and generalizes them to the higher-order Julia fractal mapping process. Then, three types of chaotic systems with controllable scroll numbers distributed in multiple directions are obtained. The results of the dynamic analysis method show that the post-fractal chaotic system not only increases the bifurcation interval of its parameters compared with the original chaotic system, but also increases the complexity of its sequence and the maximum Lyapunov exponent, and its attraction domain has a very complex fractal boundary. A kind of multi-directional chain chaotic attractor is realized by the Digital Signal Processors (DSP). The phase diagram of the oscilloscope is consistent with the result of numerical simulation, which verifies the possibility of this method in the digital circuit.

Suggested Citation

  • Xiang-Liang Xu & Guo-Dong Li & Wan-Ying Dai & Xiao-Ming Song, 2021. "Multi-Direction Chain And Grid Chaotic System Based On Julia Fractal," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(08), pages 1-20, December.
    • Handle: RePEc:wsi:fracta:v:29:y:2021:i:08:n:s0218348x21502455
    DOI: 10.1142/S0218348X21502455
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    Citations

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    Cited by:

    1. Zhang, Tianxian & Zhao, Yongqi & Xu, Xiangliang & Wu, Si & Gu, Yujuan, 2024. "Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Bao, H. & Gu, Y. & Xu, Q. & Zhang, X. & Bao, B., 2022. "Parallel bi-memristor hyperchaotic map with extreme multistability," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    3. Liu, Hongwei & He, Ping & Li, Guodong & Xu, Xiangliang & Zhong, Huiyan, 2022. "Multi-directional annular multi-wing chaotic system based on Julia fractals," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    4. Zhong, Huiyan & Li, Guodong & Xu, Xiangliang, 2022. "A generic voltage-controlled discrete memristor model and its application in chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Yang, Min & Dong, Chengwei & Pan, Hepeng, 2024. "Generating multi-directional hyperchaotic attractors: A novel multi-scroll system based on Julia fractal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).

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