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Application and research of fractional differential equations in dynamic analysis of supply chain financial chaotic system

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  • Ma, Yutian
  • Li, Wenwen

Abstract

This paper first introduces the numerical solution of fractional differential equations and the method of discriminating chaos, which lays a mathematical foundation for the later study of fractional-order chaotic systems. Secondly, the thesis uses the theoretical knowledge of fractional differential to construct a new three-dimensional supply chain fractional differential game model. The numerical simulation analysis of the complex dynamic behavior of the model is carried out to investigate the influence of the output adjustment velocity parameters on the dynamic behavior of the system. The parameter control method is used to chaotic control of the multi-period bifurcation and unstable periodic orbit of the producer’s production decision, so that the chaotic model is re-stabilized to the Nash equilibrium state. Finally, the paper constructs a new financial model of fractional time delay and analyzes the basic dynamics of the system in detail. In addition, the stability analysis of the system is carried out by using Lyapunov stability theory, and then the controller is designed to realize the chaotic control of the system, which provides theoretical guidance for the stable development of the financial market.

Suggested Citation

  • Ma, Yutian & Li, Wenwen, 2020. "Application and research of fractional differential equations in dynamic analysis of supply chain financial chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    • Handle: RePEc:eee:chsofr:v:130:y:2020:i:c:s0960077919303583
    DOI: 10.1016/j.chaos.2019.109417
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    Cited by:

    1. Abdullahi, Auwal, 2021. "Modelling of transmission and control of Lassa fever via Caputo fractional-order derivative," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    2. Hamede Karami & Saleh Mobayen & Marzieh Lashkari & Farhad Bayat & Arthur Chang, 2021. "LMI-Observer-Based Stabilizer for Chaotic Systems in the Existence of a Nonlinear Function and Perturbation," Mathematics, MDPI, vol. 9(10), pages 1-15, May.
    3. Bekiros, Stelios & Yao, Qijia & Mou, Jun & Alkhateeb, Abdulhameed F. & Jahanshahi, Hadi, 2023. "Adaptive fixed-time robust control for function projective synchronization of hyperchaotic economic systems with external perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    4. Ya-Ru Zhu & Zhong-Xuan Mao & Jing-Feng Tian & Ya-Gang Zhang & Xin-Ni Lin, 2022. "Oscillation and Nonoscillatory Criteria of Higher Order Dynamic Equations on Time Scales," Mathematics, MDPI, vol. 10(5), pages 1-17, February.
    5. Lei Xie & Hongshuai Han, 2020. "Capacity Sharing and Capacity Investment of Environment-Friendly Manufacturing: Strategy Selection and Performance Analysis," IJERPH, MDPI, vol. 17(16), pages 1-20, August.
    6. Liu, Donghui & Gao, Xiangyun & An, Haizhong & Jia, Nanfei & Wang, Anjian, 2024. "Exploring market instability of global lithium resources based on chaotic dynamics analysis," Resources Policy, Elsevier, vol. 88(C).

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