分数阶金融风险系统的动力学和函数投影同步化

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals Pub Date : 2024-10-05 DOI:10.1016/j.chaos.2024.115599

Zhao Xu , Kehui Sun , Huihai Wang

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引用次数: 0

摘要

现实金融市场具有长期记忆性和复杂性的特点。为了描述更真实的金融风险管理过程，本文引入 Caputo 分数导数来构建分数阶金融风险系统（FFRS）。应用 Adomian 分解法得到 FFRS 的数值解。通过分岔图、Lyapunov 指数谱和谱熵复杂度研究了阶数和参数对系统动力学的影响。结果表明，在合适的阶数和参数下，混沌状态的范围变小或最大的 Lyapunov 指数减小。这些动态结果可以用真实的金融风险管理过程来解释。此外，还讨论了 FFRS 的状态转换现象。为了控制和预测处于混沌状态的系统，应用了函数投影同步法。系统的动态性和同步性对金融风险管理具有参考意义。

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Dynamics and function projection synchronization for the fractional-order financial risk system

The real financial market has long-term memory and complexity characteristics. To describe a more realistic financial risk management process, this paper introduces Caputo fractional derivative to construct a fractional-order financial risk system (FFRS). Adomian decomposition method is applied to get numerical solutions of the FFRS. The effects of order and parameters on system dynamics are investigated through bifurcation diagrams, Lyapunov exponents spectrum and spectral entropy complexity. The results show the range of chaotic state is smaller or the largest Lyapunov exponent is reduced at suitable order and parameters. The dynamic results are explained by real financial risk management process. In addition, state transition phenomenon of the FFRS is discussed. To control and predict the system in chaotic state, the function projection synchronization is applied. Dynamics and synchronization of the system have reference significance for financial risk management.

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来源期刊

Chaos Solitons & Fractals 物理-数学跨学科应用

CiteScore

13.20

自引率

10.30%

发文量

1087

审稿时长

9 months

期刊介绍： Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.