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Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method

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  • Zhang, Tianxian
  • Zhao, Yongqi
  • Xu, Xiangliang
  • Wu, Si
  • Gu, Yujuan

Abstract

In recent years, newly proposed fractal-fractional calculus operators have been used to predict the chaotic behavior of some attractors, and the new operators can capture self-similarity in the studied chaotic attractors. The results of varying with fractal order and fractional order are interesting, however, the dynamics are barely analyzed in these studies, and the law of fractal order and fractional order on the system is not clear. In this paper, the fractal-fractional differential operators with inverse operator property are redefined in the Caputo sense, and a new numerical scheme is proposed based on the sixth-order Adomain decomposition method. Then the dynamics of the new multi-scroll Chen chaotic system and its three degradation modes are analyzed completely in the fractal-fractional sense. The influence of the change of fractal order and fractional order on the chaotic system is revealed. Finally, a new physical phenomenon of the fractal-fractional chaotic system is captured by observing the coexistence of multi-scroll and two-scroll chaotic attractors of the new system through a wood-grain-like attractor basin, as well as transient chaos, chaotic jumps, and complex state transition behaviors. It is shown that fractal-fractional multi-scroll Chen system has complex and specific dynamical behaviors.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:178:y:2024:i:c:s0960077923011700
    DOI: 10.1016/j.chaos.2023.114268
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    References listed on IDEAS

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    1. Yan Cui & Hongjun He & Guan Sun & Chenhui Lu, 2019. "Analysis and Control of Fractional Order Generalized Lorenz Chaotic System by Using Finite Time Synchronization," Advances in Mathematical Physics, Hindawi, vol. 2019, pages 1-12, July.
    2. Lei Zhang & Shabir Ahmad & Aman Ullah & Ali Akgãœl & Esra Karatas Akgãœl, 2022. "Analysis Of Hidden Attractors Of Non-Equilibrium Fractal-Fractional Chaotic System With One Signum Function," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(05), pages 1-16, August.
    3. Atangana, Abdon & Qureshi, Sania, 2019. "Modeling attractors of chaotic dynamical systems with fractal–fractional operators," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 320-337.
    4. 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.
    5. Zou, Chengye & Wang, Xingyuan & Zhou, Changjun & Xu, Shujuan & Huang, Chun, 2022. "A novel image encryption algorithm based on DNA strand exchange and diffusion," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    6. Mishra, Jyoti, 2019. "Modified Chua chaotic attractor with differential operators with non-singular kernels," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 64-72.
    7. Atangana, Abdon & Shafiq, Anum, 2019. "Differential and integral operators with constant fractional order and variable fractional dimension," Chaos, Solitons & Fractals, Elsevier, vol. 127(C), pages 226-243.
    8. Atangana, Abdon & Bouallegue, Ghaith & Bouallegue, Kais, 2020. "New multi-scroll attractors obtained via Julia set mapping," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    9. Atangana, Abdon, 2017. "Fractal-fractional differentiation and integration: Connecting fractal calculus and fractional calculus to predict complex system," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 396-406.
    10. Saifullah, Sayed & Ali, Amir & Franc Doungmo Goufo, Emile, 2021. "Investigation of complex behaviour of fractal fractional chaotic attractor with mittag-leffler Kernel," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    11. Mohamed Elbadri & Mohamed A. Abdoon & Mohammed Berir & Dalal Khalid Almutairi, 2023. "A Numerical Solution and Comparative Study of the Symmetric Rossler Attractor with the Generalized Caputo Fractional Derivative via Two Different Methods," Mathematics, MDPI, vol. 11(13), pages 1-11, July.
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    Cited by:

    1. Xu, Zhao & Sun, Kehui & Wang, Huihai, 2024. "Dynamics and function projection synchronization for the fractional-order financial risk system," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    2. 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).
    3. Zhang, Jie & Zuo, Jiangang & Wang, Meng & Guo, Yan & Xie, Qinggang & Hou, Jinyou, 2024. "Design and application of multiscroll chaotic attractors based on a novel multi-segmented memristor," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).

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