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

doi:10.1088/1674-1056/ad7afb

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.

Keywords: FOFR system dynamical analysis control boundedness forecasting

Received: 06 July 2024
Revised: 06 September 2024
Accepted manuscript online: 14 September 2024

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Jn	(High-dimensional chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: 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).

Corresponding Authors: Song Zheng
E-mail: szh070318@zufe.edu.cn

Cite this article:

Kehao Yang(杨轲皓), Song Zheng(郑松), Tianhu Yu(余天虎), Aceng Sambas, Muhamad Deni Johansyah, Hassan Saberi-Nik, and Mohamad Afendee Mohamed Dynamical analysis, control, boundedness, and prediction for a fractional-order financial risk system 2024 Chin. Phys. B 33 110501

[1] Podlubny I 1999 Fractional differential equations (New York: Academic Press) pp. 41-120
[2] Petráš I 2011 Fractional-Order Nonlinear Systems: Modeling, Analysis and Simulation (Berlin: Springer Science & Business Media) pp. 7-42
[3] Yuan L, Zheng S and Wei Z 2022 Eur. Phys. J. Spec. Top. 231 2477
[4] Chen L, Wu X, António M L, Li X, Li P and Wu R 2023 Commun. Nonlinear Sci. Numer. Simul. 125 107365
[5] Zhou X, Jiang D, Nkapkop J, Ahmad M, Fossi J, Tsafack N and Wu J 2024 Chin. Phys. B 33 040506
[6] Jin M X, Sun K H and He S B 2023 Chin. Phys. B 32 060501
[7] Zhang Y, Xiao M, Cao J and Zheng W 2022 IEEE Trans. Syst. Man Cyber.: Syst. 52 1731
[8] Xu C, Liu Z, Liao M and Yao L 2022 Expert Syst. Appl. 199 116859
[9] El-Mesady A, Elsonbaty A and Adel W 2022 Chaos, Solitons and Fractals 164 112716
[10] Partohaghighi M, Yusuf A and Bayram M 2022 Int. J. Appl. Comput. Math. 8 86
[11] Chen L, Yin H, Huang T, Yuan L, Zheng S and Yin L 2020 Neural Netw. 125 174
[12] Cui L, Luo W and Ou Q 2021 Chin. Phys. B 30 020501
[13] He S, Wang H and Sun K 2022 Chin. Phys. B 31 060501
[14] Vignesh D, He S and Banerjee S 2023 Appl. Math. Comput. 455 128111
[15] Tang Z, He S, Wang H, Sun K, Yao Z and Wu X 2024 Chin. Phys. B 33 030503
[16] Wang X, Xu B, Shi P and Li S 2022 IEEE Tran. Neural Net. Lear. Syst. 33 445
[17] Wu X, Fu L, He S, Yao Z, Wang H and Han J 2023 Resul. Phys. 52 106866
[18] Leonov G, Bunin A and Koksch N 1987 Z. Angew. Math. Mech. 67 649
[19] Leonov G and Kuznetsov N 2013 Int. J. Bifurc. Chaos 23 1330002
[20] Swinnerton-Dyer P 2001 Phys. Lett. A 281 161
[21] Liao X 2004 Sci. China Ser. E, Inform. Sci. 34 1404
[22] Jian J, Wu K and Wang B 2020 Physica A 540 123166
[23] Peng Q and Jian J 2021 Chaos, Solitons and Fractals 150 111072
[24] Ren L, Lin M, Abdulwahab A, Ma J and Saberi-Nik H 2023 Chaos, Solitons and Fractals 169 113275
[25] Zhang X, Liu X, Zheng Y and Liu C 2013 Chin. Phys. B 22 030509
[26] Tacha O, Volos C, Kyprianidis I, Stouboulos I, Vaidyanathan S and Pham V 2016 Appl. Math. Comput. 276 200
[27] Tacha O, Munoz-Pacheco J, Zambrano-Serrano E, Stouboulos I and Pham V 2018 Nonlinear Dyn. 94 1303
[28] Jahanshahi H, Sajjadi S, Bekiros S and Aly A 2021 Chaos, Solitons and Fractals 144 110698
[29] Festag S, Denzler J and Spreckelsen C 2022 J. Biomed. Inform. 129 104058
[30] Maleki M, Mahmoudi M, Wraith D and Pho K 2022 Travel Med. Infect. Dis. 37 101742
[31] Puri C, Kooijman G, Vanrumste B and Luca S 2022 IEEE J Biomed. Health Inform. 26 6126
[32] Chimmula V and Zhang L 2022 Chaos, Solitons and Fractals 135 109864
[33] Wang W, Shao J and Jumahong H 2023 Sci. Rep. 13 20359
[34] Maass W, Natschläger T and Markram H 2002 Neural Comput. 14 2531
[35] Jaeger H and Haas H 2004 Science 304 78
[36] Du C, Cai F, Zidan M, Ma W, Lee S and Lu W 2017 Nat. Commun. 8 1
[37] Song Q, Zhao X, Feng Z, An Y and Song B 2021 CCDC 3893-3897
[38] Na X, Ren W, Liu M, Han M 2023 IEEE Trans. Neural Netw. Lear. Syst. 34 9302
[39] Staniczenko P, Lee C and Jones N 2009 Phys. Rev. E 79 011915
[40] Shen E, Cai Z and Gu F 2005 Appl. Math. Mech. 26 1188
[41] Gottwald G and Melbourne I 2004 Proc. Roy. Soc. A-Math. Phys. Eng. Sci. 460 603
[42] Muhamad D, Aceng S, Zheng S, Khaled B, Sundarapandian V, Mohamed M and Mamat M 2023 Chaos, Solitons and Fractals 177 114283
[43] Cherruault Y and Adomian G 1993 Math. Comput. Model. 18 103

[1]	Simulations of superconducting quantum gates by digital flux tuner for qubits Xiao Geng(耿霄), Kaiyong He(何楷泳), Jianshe Liu(刘建设), and Wei Chen(陈炜). Chin. Phys. B, 2024, 33(7): 070305.
[2]	Bifurcation analysis and control study of improved full-speed differential model in connected vehicle environment Wen-Huan Ai(艾文欢), Zheng-Qing Lei(雷正清), Dan-Yang Li(李丹洋), Dong-Liang Fang(方栋梁), and Da-Wei Liu(刘大为). Chin. Phys. B, 2024, 33(7): 070503.
[3]	Internal phase control of fiber laser array based on photodetector array Kai-Kai Jin(靳凯凯), Jin-Hu Long(龙金虎), Hong-Xiang Chang(常洪祥), Rong-Tao Su(粟荣涛), Jia-Yi Zhang(张嘉怡), Si-Yu Chen(陈思雨), Yan-Xing Ma(马阎星), and Pu Zhou(周朴). Chin. Phys. B, 2024, 33(7): 074201.
[4]	Mechanism analysis of regulating Turing instability and Hopf bifurcation of malware propagation in mobile wireless sensor networks Xi-Xi Huang(黄习习), Min Xiao(肖敏), Leszek Rutkowski, Hai-Bo Bao(包海波), Xia Huang(黄霞), and Jin-De Cao(曹进德). Chin. Phys. B, 2024, 33(6): 060202.
[5]	Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control Mei-Ling Huang(黄美玲), Yong-Ge Yang(杨勇歌), and Yang Liu(刘洋). Chin. Phys. B, 2024, 33(6): 060203.
[6]	Enhancing quantum metrology for multiple frequencies of oscillating magnetic fields by quantum control Xin Lei(雷昕), Jingyi Fan(范静怡), and Shengshi Pang(庞盛世). Chin. Phys. B, 2024, 33(6): 060304.
[7]	Controlling the dynamic behavior of decentralized cluster through centralized approaches Daming Yuan(袁大明), Peilong Wang(王培龙), Peng Wang(王鹏), Xingyu Ma(马星宇), Chuyun Wang(汪楚云), Jing Wang(王璟), Huaicheng Chen(陈怀城), Gao Wang(王高), and Fangfu Ye(叶方富). Chin. Phys. B, 2024, 33(6): 060702.
[8]	Observer-based dynamic event-triggered control for distributed parameter systems over mobile sensor-plus-actuator networks Wenying Mu(穆文英), Bo Zhuang(庄波), and Fang Qiu(邱芳). Chin. Phys. B, 2024, 33(4): 040204.
[9]	Quantum control based on three forms of Lyapunov functions Guo-Hui Yu(俞国慧) and Hong-Li Yang(杨洪礼). Chin. Phys. B, 2024, 33(4): 040201.
[10]	Polarization control of above-threshold ionization spectrum in elliptically polarized two-color laser fields Fa-Cheng Jin(金发成), Hui-Hui Yang(杨慧慧), Xiao-Hong Song(宋晓红), Fei Li(李飞), Ling-Ling Du(杜玲玲), Hong-Jie Xue(薛红杰), Li-Min Wei(魏丽敏), Yue Bai(白悦), Hao-Xiang Liu(刘浩翔), Bing-Bing Wang(王兵兵), and Wei-Feng Yang(杨玮枫). Chin. Phys. B, 2024, 33(4): 043301.
[11]	Versatile and controlled quantum teleportation network Yao-Yao Zhou(周瑶瑶), Peng-Xian Mei(梅鹏娴), Yan-Hong Liu(刘艳红), Liang Wu(吴量), Yan-Xiang Li(李雁翔), Zhi-Hui Yan(闫智辉), and Xiao-Jun Jia(贾晓军). Chin. Phys. B, 2024, 33(3): 034209.
[12]	Oscillation of Dzyaloshinskii-Moriya interaction driven by weak electric fields Runze Chen(陈润泽), Anni Cao(曹安妮), Xinran Wang(王馨苒), Yang Liu(柳洋), Hongxin Yang(杨洪新), and Weisheng Zhao(赵巍胜). Chin. Phys. B, 2024, 33(2): 027501.
[13]	Optimal and robust control of population transfer in asymmetric quantum-dot molecules Yu Guo(郭裕), Songshan Ma(马松山), and Chuan-Cun Shu(束传存). Chin. Phys. B, 2024, 33(2): 024203.
[14]	Coexisting and multiple scroll attractors in a Hopfield neural network with a controlled memristor Qing-Qing Ma(马青青), An-Jiang Lu(陆安江), and Zhi Huang(黄智). Chin. Phys. B, 2024, 33(12): 120502.
[15]	Sliding-mode-based preassigned-time control of a class of memristor chaotic systems Jinrong Fan(樊金荣), Qiang Lai(赖强), Qiming Wang(汪其铭), and Leimin Wang(王雷敏). Chin. Phys. B, 2024, 33(11): 110205.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

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

Cite this article:

Online attention