中国物理B ›› 2024, Vol. 33 ›› Issue (11): 110501-110501.doi: 10.1088/1674-1056/ad7afb

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Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system

Kehao Yang(杨轲皓)1, Song Zheng(郑松)1,†, Tianhu Yu(余天虎)2, Aceng Sambas3,4, Muhamad Deni Johansyah5, Hassan Saberi-Nik6, and Mohamad Afendee Mohamed3   

  1. 1 School of Data Science, Zhejiang University of Finance & Economics, Hangzhou 310018, China;
    2 Department of Mathematics, Luoyang Normal University, Luoyang 471934, China;
    3 Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut Campus, 22200, Terengganu, Malaysia;
    4 Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya, Jawa Barat, 46196, Indonesia;
    5 Department of Mathematics, Universitas Padjajdaran, Jatinangor, Kabupaten Sumedang 45363, Indonesia;
    6 Department of Mathematics and Statistics, University of Neyshabur, Neyshabur 9319774400, Iran
  • 收稿日期:2024-07-06 修回日期:2024-09-06 接受日期:2024-09-14 出版日期:2024-11-15 发布日期:2024-11-15
  • 基金资助:
    Project jointly supported by the National Natural Science Foundation of China (Grant No. 12372013), Program for Science and Technology Innovation Talents in Universities of Henan Province, China (Grant No. 24HASTIT034), the Natural Science Foundation of Henan Province, China (Grant No. 232300420122), the Humanities and Society Science Foundation from the Ministry of Education of China (Grant No. 19YJCZH265), China Postdoctoral Science Foundation (Grant No. 2019M651633), First Class Discipline of Zhejiang-A (Zhejiang University of Finance and EconomicsStatistics), the Collaborative Innovation Center for Data Science and Big Data Analysis (Zhejiang University of Finance and Economics-Statistics).

Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system

Kehao Yang(杨轲皓)1, Song Zheng(郑松)1,†, Tianhu Yu(余天虎)2, Aceng Sambas3,4, Muhamad Deni Johansyah5, Hassan Saberi-Nik6, and Mohamad Afendee Mohamed3   

  1. 1 School of Data Science, Zhejiang University of Finance & Economics, Hangzhou 310018, China;
    2 Department of Mathematics, Luoyang Normal University, Luoyang 471934, China;
    3 Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Besut Campus, 22200, Terengganu, Malaysia;
    4 Department of Mechanical Engineering, Universitas Muhammadiyah Tasikmalaya, Tasikmalaya, Jawa Barat, 46196, Indonesia;
    5 Department of Mathematics, Universitas Padjajdaran, Jatinangor, Kabupaten Sumedang 45363, Indonesia;
    6 Department of Mathematics and Statistics, University of Neyshabur, Neyshabur 9319774400, Iran
  • Received:2024-07-06 Revised:2024-09-06 Accepted:2024-09-14 Online:2024-11-15 Published:2024-11-15
  • Contact: Song Zheng E-mail:szh070318@zufe.edu.cn
  • Supported by:
    Project jointly supported by the National Natural Science Foundation of China (Grant No. 12372013), Program for Science and Technology Innovation Talents in Universities of Henan Province, China (Grant No. 24HASTIT034), the Natural Science Foundation of Henan Province, China (Grant No. 232300420122), the Humanities and Society Science Foundation from the Ministry of Education of China (Grant No. 19YJCZH265), China Postdoctoral Science Foundation (Grant No. 2019M651633), First Class Discipline of Zhejiang-A (Zhejiang University of Finance and EconomicsStatistics), the Collaborative Innovation Center for Data Science and Big Data Analysis (Zhejiang University of Finance and Economics-Statistics).

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摘要： This paper delves into the dynamical analysis, chaos control, Mittag-Leffler boundedness (MLB), and forecasting a fractional-order financial risk (FOFR) system through an absolute function term. To this end, the FOFR system is first proposed, and the adomian decomposition method (ADM) is employed to resolve this fractional-order system. The stability of equilibrium points and the corresponding control schemes are assessed, and several classical tools such as Lyapunov exponents (LE), bifurcation diagrams, complexity analysis (CA), and 0-1 test are further extended to analyze the dynamical behaviors of FOFR. Then the global Mittag-Leffler attractive set (MLAS) and Mittag-Leffler positive invariant set (MLPIS) for the proposed financial risk (FR) system are discussed. Finally, a proficient reservoir-computing (RC) method is applied to forecast the temporal evolution of the complex dynamics for the proposed system, and some simulations are carried out to show the effectiveness and feasibility of the present scheme.

关键词: FOFR system, dynamical analysis, control, boundedness, forecasting

Abstract: This paper delves into the dynamical analysis, chaos control, Mittag-Leffler boundedness (MLB), and forecasting a fractional-order financial risk (FOFR) system through an absolute function term. To this end, the FOFR system is first proposed, and the adomian decomposition method (ADM) is employed to resolve this fractional-order system. The stability of equilibrium points and the corresponding control schemes are assessed, and several classical tools such as Lyapunov exponents (LE), bifurcation diagrams, complexity analysis (CA), and 0-1 test are further extended to analyze the dynamical behaviors of FOFR. Then the global Mittag-Leffler attractive set (MLAS) and Mittag-Leffler positive invariant set (MLPIS) for the proposed financial risk (FR) system are discussed. Finally, a proficient reservoir-computing (RC) method is applied to forecast the temporal evolution of the complex dynamics for the proposed system, and some simulations are carried out to show the effectiveness and feasibility of the present scheme.

Key words: FOFR system, dynamical analysis, control, boundedness, forecasting

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.45.Jn (High-dimensional chaos) 05.45.Pq (Numerical simulations of chaotic systems)