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Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System

Author

Listed:
  • Xinggui Li

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Ruofeng Rao

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Shouming Zhong

    (College of Mathematics, University of Electronic Science and Technology of China, Chengdu 611731, China)

  • Xinsong Yang

    (College of Electronics and Information Engineering, Sichuan University, Chengdu 610065, China)

  • Hu Li

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

  • Yulin Zhang

    (Department of Mathematics, Chengdu Normal University, Chengdu 611130, China)

Abstract

This paper reports a new global Mittag-Leffler synchronization criterion with regard to fractional-order hyper-chaotic financial systems by designing the suitable impulsive control and the state feedback controller. The significance of this impulsive synchronization lies in the fact that the backward economic system can synchronize asymptotically with the advanced economic system under effective impulse macroeconomic management means. Matlab’s LMI toolbox is utilized to deduce the feasible solution in a numerical example, which shows the effectiveness of the proposed methods. It is worth mentioning that the LMI-based criterion usually requires the activation function of the system to be Lipschitz, but the activation function in this paper is fixed and truly nonlinear, which cannot be assumed to be Lipschitz continuous. This is another mathematical difficulty overcome in this paper.

Suggested Citation

  • Xinggui Li & Ruofeng Rao & Shouming Zhong & Xinsong Yang & Hu Li & Yulin Zhang, 2022. "Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System," Mathematics, MDPI, vol. 10(15), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2737-:d:878658
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    References listed on IDEAS

    as
    1. Laskin, Nick, 2000. "Fractional market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 482-492.
    2. Bingrui Xu & Bing Li, 2022. "Event-Triggered State Estimation for Fractional-Order Neural Networks," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    3. Huang, Chengdai & Cai, Liming & Cao, Jinde, 2018. "Linear control for synchronization of a fractional-order time-delayed chaotic financial system," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 326-332.
    4. Yao, Xueqi & Zhong, Shouming, 2021. "EID-based robust stabilization for delayed fractional-order nonlinear uncertain system with application in memristive neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
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    Cited by:

    1. Yu Liu & Yan Zhou & Biyao Guo, 2023. "Hopf Bifurcation, Periodic Solutions, and Control of a New 4D Hyperchaotic System," Mathematics, MDPI, vol. 11(12), pages 1-14, June.
    2. 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).

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