On fractional discrete financial system: Bifurcation, chaos, and control

doi:10.1088/1674-1056/ad5d96

中国物理B ›› 2024, Vol. 33 ›› Issue (10): 100201-100201.doi: 10.1088/1674-1056/ad5d96

• • 下一篇

On fractional discrete financial system: Bifurcation, chaos, and control

Louiza Diabi¹, Adel Ouannas², Amel Hioual^3,†, Shaher Momani^4,5, and Abderrahmane Abbes⁶

1 Laboratory of Dynamical Systems and Control, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria;
2 Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria;
3 Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria;
4 Nonlinear Dynamics Research Center, Ajman University, Ajman 346, United Arab Emirates;
5 Department of Mathematics, The University of Jordan, Amman 11942, Jordan;
6 Laboratory of Mathematics, Dynamics and Modelization, University Badji Mokhtar, Annaba 23000, Algeria

收稿日期:2024-05-22 修回日期:2024-06-19 接受日期:2024-07-02 出版日期:2024-10-15 发布日期:2024-10-15
通讯作者: Amel Hioual E-mail:amel.hioual@univ-oeb.dz

On fractional discrete financial system: Bifurcation, chaos, and control

Louiza Diabi¹, Adel Ouannas², Amel Hioual^3,†, Shaher Momani^4,5, and Abderrahmane Abbes⁶

1 Laboratory of Dynamical Systems and Control, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria;
2 Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria;
3 Department of Mathematics and Computer Science, University of Larbi Ben M'hidi, Oum El Bouaghi 04000, Algeria;
4 Nonlinear Dynamics Research Center, Ajman University, Ajman 346, United Arab Emirates;
5 Department of Mathematics, The University of Jordan, Amman 11942, Jordan;
6 Laboratory of Mathematics, Dynamics and Modelization, University Badji Mokhtar, Annaba 23000, Algeria

Received:2024-05-22 Revised:2024-06-19 Accepted:2024-07-02 Online:2024-10-15 Published:2024-10-15
Contact: Amel Hioual E-mail:amel.hioual@univ-oeb.dz

摘要/Abstract

摘要： The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets. This paper introduces a new three-dimensional (3D) fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders. As such, we evaluate when the equilibrium points are stable or unstable at various fractional orders. We use many numerical methods, phase plots in 2D and 3D projections, bifurcation diagrams and the maximum Lyapunov exponent. These techniques reveal that financial maps exhibit chaotic attractor behavior. This study is grounded on the Caputo-like discrete operator, which is specifically influenced by the variance of the commensurate and incommensurate orders. Furthermore, we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm. Additionally, we offer nonlinear-type controllers to stabilize the fractional financial map. The numerical results of this study are obtained using MATLAB.

关键词: financial model, stability, chaos, commensurate and incommensurate orders, complexity

Abstract: The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial markets. This paper introduces a new three-dimensional (3D) fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate orders. As such, we evaluate when the equilibrium points are stable or unstable at various fractional orders. We use many numerical methods, phase plots in 2D and 3D projections, bifurcation diagrams and the maximum Lyapunov exponent. These techniques reveal that financial maps exhibit chaotic attractor behavior. This study is grounded on the Caputo-like discrete operator, which is specifically influenced by the variance of the commensurate and incommensurate orders. Furthermore, we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy algorithm. Additionally, we offer nonlinear-type controllers to stabilize the fractional financial map. The numerical results of this study are obtained using MATLAB.

Key words: financial model, stability, chaos, commensurate and incommensurate orders, complexity

中图分类号: (Control theory)

02.30.Yy

02.30.Oz (Bifurcation theory)

Louiza Diabi, Adel Ouannas, Amel Hioual, Shaher Momani, and Abderrahmane Abbes. On fractional discrete financial system: Bifurcation, chaos, and control[J]. 中国物理B, 2024, 33(10): 100201-100201.

Louiza Diabi, Adel Ouannas, Amel Hioual, Shaher Momani, and Abderrahmane Abbes. On fractional discrete financial system: Bifurcation, chaos, and control[J]. Chin. Phys. B, 2024, 33(10): 100201-100201.

参考文献

[1] Diouf M and Sene N 2020 Complexity 1 9845031
[2] Jahanshahi H, Yousefpour A, Wei Z, Alcaraz R and Bekiros S 2019 Chaos, Solitons. Fractals 126 66
[3] Hu Y and Hu G 2023 Mathematics 11 2994
[4] Akhmet M, Akhmetova Z and Fen M O 2014 Journal of Economic Behavior. Organization 106 95
[5] Desogus M and Venturi B 2023 Journal of Risk and Financial Management 16 171
[6] Zhou S S, Jahanshahi H, Din Q, Bekiros S, Alcaraz R, Alassafi M O and Chu Y M 2021 Chaos. Solitons. Fractals 142 110378
[7] Chen Q, Sabir Z, Raja M A Z, Gao W and Baskonus H M 2023 Alexandria Engineering Journal 65 761
[8] Wu Y, Wu W, Xing C, Zhou M and Li Z 2016 arXiv:1612.01627
[9] Liu J, Wang Z, Shu M, Zhang F, Leng S and Sun X 2019 Complexity 2019 7242791
[10] Tejado I, Valério D and Valério N 2014 Proceedings of the ICFDA’14th International Conference on Fractional Differentiation and Its Applications, June, 2014, The Portuguese case. pp. 1-6
[11] Alzaid S S, Kumar A, Kumar S and Alkahtani B S T 2023 Fractals 31 2340056
[12] Chu Y M, Bekiros S, Zambrano-Serrano E, Orozco-López O, Lahmiri S, Jahanshahi H and Aly A A 2021 Chaos, Solitons. Fractals 145 110776
[13] Pourrahimian E, Salhab D, Shehab L, Hamzeh F and AbouRizk S 2024 Application of Chaos Theory in Project Management, Construction Research Congress, 2024, March 25-27, 2024, Arlington, Virginia, USA, p. 601
[14] Batiha I M, Djenina N, Ouannas A, Oussaeif T E, Aoua L B and Momani S 2023 Control of chaos in incommensurate fractional order discrete system, 2023 International Conference on Fractional Differentiation and Its Applications (ICFDA), March 13-15, 2023, Paris, France, p. 1
[15] Ouannas A, Khennaoui A A, Batiha I M and Pham V T 2022 Stabilization of different dimensional fractional chaotic maps (San Diego: Academic Press) pp. 123-155
[16] Almatroud A O, Ouannas A, Grassi G, Batiha I M, Gasri A and AlSawalha M M 2021 Archives of Control Sciences 31 765
[17] Ouannas A, Batiha I M and Pham V T 2023 Fractional discrete chaos: theories, methods and applications (Vol. 3) (Singapore: World Scientific)
[18] Hioual, A, Oussaeif, T E, Ouannas, A, Grassi, G, Batiha, I M and Momani S 2022 Alexandria Engineering Journal 61 10359
[19] Hamadneh, T, Hioual, A, Alsayyed, O, Al-Khassawneh, Y A, AlHusban, A and Ouannas A 2023 Fractal and Fractional 7 616
[20] Khennaoui A A, Almatroud A O, Ouannas A, Al-sawalha M M, Grassi G and Pham V T 2021 Discrete. Continuous Dynamical Systems-Series B 26 4549
[21] Abbes A, Ouannas A and Shawagfeh N 2023 Chin. Phys. B 32 030203
[22] Wu J and Xia L 2024 Economics 1 4
[23] Khennaoui A A and Ouannas A 2021 International Conference on Recent Advances in Mathematics and Informatics (ICRAMI), September 10-12, 2021, Constantine, Algeria, p. 1
[24] Abbes A, Ouannas A, Shawagfeh N and Grassi G 2022 Results in Physics 39 105797
[25] Abualhomos M, Abbes A, Gharib G M, Shihadeh A, Al Soudi M S, Alsaraireh A A and Ouannas A 2023 Mathematics 11 4166
[26] Alsayyed O, Abbes A, Gharib G M, Abualhomos M, Al-Tarawneh H, Al Soudi M S and Ouannas A 2023 Fractal and Fractional 7 728
[27] Atici F M and Eloe P 2009 Electron. J. Qual. Theory Differ. Equ. 3 1
[28] Abdeljawad T 2011 Computers & Mathematics with Applications 62 1602
[29] Wu G C and Baleanu D 2014 Nonlinear Dyn. 75 283
[30] Čermák J, Györi I and Nechvátal L 2015 Fractional Calculus and Applied Analysis 18 651
[31] Shatnawi M T, Djenina N, Ouannas A, Batiha I M and Grassi G 2022 Alexandria Engineering Journal 61 1655
[32] Huang D and Li H 1993 Theory and method of the nonlinear economics (Chengdu: Publishing House of Sichuan University)
[33] Xin B, Chen T and Ma J 2010 Discrete Dynamics in Nature and Society 2010
[34] Wu G C and Baleanu D 2015 Communications in Nonlinear Science and Numerical Simulation 22 95
[35] Gottwald G A and Melbourne I 2016 Chaos detection and predictability pp. 221-247
[36] Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297
[37] Jakimowicz A 2020 Entropy 22 452 100201-12

On fractional discrete financial system: Bifurcation, chaos, and control

On fractional discrete financial system: Bifurcation, chaos, and control

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Jingjing Wang(王晶晶), Panlong Kong(孔攀龙), Dingmei Zhang(张定梅), Defang Gao(高德芳), Zaifu Jiang(蒋再富), and Wei Dai(戴伟). Theoretical insights into the structures and fundamental properties of pnictogen nitrides[J]. 中国物理B, 2024, 33(9): 96201-096201.
[2]	Dong-Sheng Chen(陈东升), Ting-Ting Miao(缪婷婷), Cheng Chang(常程), Xu-Yang Guo(郭旭洋), Meng-Yan Guan(关梦言), and Zhong-Li Ji(姬忠礼). Theoretical insights into thermal transport and structural stability mechanisms of triaxial compressed methane hydrate[J]. 中国物理B, 2024, 33(9): 96501-096501.
[3]	Guo-Xiao Xu(许国潇), Ning Kang(康宁), An-Le Lei(雷安乐), Hui-Ya Liu(刘会亚), Yao Zhao(赵耀), Shen-Lei Zhou(周申蕾), Hong-Hai An(安红海), Jun Xiong(熊俊), Rui-Rong Wang(王瑞荣), Zhi-Yong Xie(谢志勇), Xi-Chen Zhou(周熙晨), Zhi-Heng Fang(方智恒), and Wei Wang(王伟). Spectral characteristics of laser-plasma instabilities with a broadband laser[J]. 中国物理B, 2024, 33(8): 85204-085204.
[4]	Sihan Chen(陈思汗), Jun Li(黎俊), Keke Liu(刘可可), Xiaochen Sun(孙笑晨), Jingwei Wan(万京伟), Huiyu Zhai(翟慧宇), Xinfeng Tang(唐新峰), and Gangjian Tan(谭刚健). Defect chemistry engineering of Ga-doped garnet electrolyte with high stability for solid-state lithium metal batteries[J]. 中国物理B, 2024, 33(8): 88203-088203.
[5]	Qiuchen Wang(王秋辰), Yuli Huang(黄昱力), Jing Xu(许晶), Xiqian Yu(禹习谦), Hong Li(李泓), and Liquan Chen(陈立泉). Interface and mechanical degradation mechanisms of the silicon anode in sulfide-based solid-state batteries at high temperatures[J]. 中国物理B, 2024, 33(8): 88201-088201.
[6]	Siminda Deng(邓思敏达), Wei Ren(任伟), Jingfeng Xiang(项静峰), Jianbo Zhao(赵剑波), Lin Li(李琳), Di Zhang(张迪), Jinyin Wan(万金银), Yanling Meng(孟艳玲), Xiaojun Jiang(蒋小军), Tang Li(李唐), Liang Liu(刘亮), and Desheng Lü(吕德胜). Physics package based on intracavity laser cooling ⁸⁷Rb atoms for space cold atom microwave clock[J]. 中国物理B, 2024, 33(7): 70602-070602.
[7]	Lvjin Wang(王侣锦), Cong Wang(王聪), Linwei Zhou(周霖蔚), Xieyu Zhou(周谐宇), Yuhao Pan(潘宇浩), Xing Wu(吴幸), and Wei Ji(季威). Optimal parameter space for stabilizing the ferroelectric phase of Hf_0.5Zr_0.5O₂ thin films under strain and electric fields[J]. 中国物理B, 2024, 33(7): 76803-076803.
[8]	Mei-Ling Huang(黄美玲), Yong-Ge Yang(杨勇歌), and Yang Liu(刘洋). Performance enhancement of a viscoelastic bistable energy harvester using time-delayed feedback control[J]. 中国物理B, 2024, 33(6): 60203-060203.
[9]	Ling Xu(徐玲) and Lei Jiang(姜磊). Effects of asymmetric coupling and boundary on the dynamic behaviors of a random nearest neighbor coupled system[J]. 中国物理B, 2024, 33(6): 60503-060503.
[10]	Ruo-Shui Han(韩弱水), Wei Wang(王伟), and Tao Wang(汪涛). A proposal for detecting weak electromagnetic waves around 2.6 μm wavelength with Sr optical clock[J]. 中国物理B, 2024, 33(4): 43201-043201.
[11]	Wenjia Liang(梁文嘉), Xiaojun Xiang(向晓君), Qian Li(李倩), Hao Liang(梁浩), and Fang Peng(彭放). Stability and melting behavior of boron phosphide under high pressure[J]. 中国物理B, 2024, 33(4): 46201-046201.
[12]	Liping Zhang(张丽萍), Zongyao Sun(孙宗耀), Jiani Li(李佳妮), and Junyan Su(苏俊燕). Effect of external magnetic field on the instability of THz plasma waves in nanoscale graphene field-effect transistors[J]. 中国物理B, 2024, 33(4): 48102-048102.
[13]	Minna Hou(候敏娜), Xu Guo(郭旭), Meidouxue Han(韩梅斗雪), Juntao Zhao(赵均陶), Zhiyuan Wang(王志元), Yi Ding(丁毅), Guofu Hou(侯国付), Zongsheng Zhang(张宗胜), and Xiaoping Han(韩小平). Enhanced stability of FA-based perovskite: Rare-earth metal compound EuBr₂ doping[J]. 中国物理B, 2024, 33(4): 47802-047802.
[14]	Hong-Xia Yuan(袁红霞), Jia-Xue Li(李佳雪), Qi-Jun Ma(马奇军), Hai-Shan Tian(田海山),Yun-Yang Ye(叶云洋), Wen-Xin Luo(罗文昕), Xing-Hua Wu(吴杏华), and Le-Yong Jiang(蒋乐勇). Controllable optical bistability in a Fabry-Pérot cavity with a nonlinear three-dimensional Dirac semimetal[J]. 中国物理B, 2024, 33(3): 34213-034213.
[15]	Liu Li(李柳), Decai Li(李德才), Zhiqiang Qi(戚志强), Lu Wang(王璐), and Zhili Zhang(张志力). Wave nature of Rosensweig instability[J]. 中国物理B, 2024, 33(3): 34701-034701.