Search Advanced
2024 Volume 33 Issue 10
Article Contents
Previous Article Next Article

Louiza Diabi, Adel Ouannas, Amel Hioual, Shaher Momani, and Abderrahmane Abbes. 2024: On fractional discrete financial system: Bifurcation, chaos, and control, Chinese Physics B, 33(10): 100201. doi: 10.1088/1674-1056/ad5d96
Citation: Louiza Diabi, Adel Ouannas, Amel Hioual, Shaher Momani, and Abderrahmane Abbes. 2024: On fractional discrete financial system: Bifurcation, chaos, and control, Chinese Physics B, 33(10): 100201. doi: 10.1088/1674-1056/ad5d96
shu

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

  • 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 Date: 22/05/2024
    Accepted Date: 19/06/2024
  • 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.
  • 加载中
  • Diouf M and Sene N 2020 Complexity 1 9845031

    Google Scholar Pub Med

    Jahanshahi H, Yousefpour A, Wei Z, Alcaraz R and Bekiros S 2019 Chaos, Solitons. Fractals 126 66

    Google Scholar Pub Med

    Hu Y and Hu G 2023 Mathematics 11 2994

    Google Scholar Pub Med

    Akhmet M, Akhmetova Z and Fen M O 2014 Journal of Economic Behavior. Organization 106 95

    Google Scholar Pub Med

    Desogus M and Venturi B 2023 Journal of Risk and Financial Management 16 171

    Google Scholar Pub Med

    Zhou S S, Jahanshahi H, Din Q, Bekiros S, Alcaraz R, Alassafi M O and Chu Y M 2021 Chaos. Solitons. Fractals 142 110378

    Google Scholar Pub Med

    Chen Q, Sabir Z, Raja M A Z, Gao W and Baskonus H M 2023 Alexandria Engineering Journal 65 761

    Google Scholar Pub Med

    Wu Y, Wu W, Xing C, Zhou M and Li Z 2016 arXiv:1612.01627

    Google Scholar Pub Med

    Liu J, Wang Z, Shu M, Zhang F, Leng S and Sun X 2019 Complexity 2019 7242791

    Google Scholar Pub Med

    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

    Google Scholar Pub Med

    Alzaid S S, Kumar A, Kumar S and Alkahtani B S T 2023 Fractals 31 2340056

    Google Scholar Pub Med

    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

    Google Scholar Pub Med

    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

    Google Scholar Pub Med

    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

    Google Scholar Pub Med

    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

    Google Scholar Pub Med

    Almatroud A O, Ouannas A, Grassi G, Batiha I M, Gasri A and AlSawalha M M 2021 Archives of Control Sciences 31 765

    Google Scholar Pub Med

    Ouannas A, Batiha I M and Pham V T 2023 Fractional discrete chaos: theories, methods and applications (Vol. 3) (Singapore: World Scientific)

    Google Scholar Pub Med

    Hioual, A, Oussaeif, T E, Ouannas, A, Grassi, G, Batiha, I M and Momani S 2022 Alexandria Engineering Journal 61 10359

    Google Scholar Pub Med

    Hamadneh, T, Hioual, A, Alsayyed, O, Al-Khassawneh, Y A, AlHusban, A and Ouannas A 2023 Fractal and Fractional 7 616

    Google Scholar Pub Med

    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

    Google Scholar Pub Med

    Abbes A, Ouannas A and Shawagfeh N 2023 Chin. Phys. B 32 030203

    Google Scholar Pub Med

    Wu J and Xia L 2024 Economics 1 4

    Google Scholar Pub Med

    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

    Google Scholar Pub Med

    Abbes A, Ouannas A, Shawagfeh N and Grassi G 2022 Results in Physics 39 105797

    Google Scholar Pub Med

    Abualhomos M, Abbes A, Gharib G M, Shihadeh A, Al Soudi M S, Alsaraireh A A and Ouannas A 2023 Mathematics 11 4166

    Google Scholar Pub Med

    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

    Google Scholar Pub Med

    Atici F M and Eloe P 2009 Electron. J. Qual. Theory Differ. Equ. 3 1

    Google Scholar Pub Med

    Abdeljawad T 2011 Computers & Mathematics with Applications 62 1602

    Google Scholar Pub Med

    Wu G C and Baleanu D 2014 Nonlinear Dyn. 75 283

    Google Scholar Pub Med

    Čermák J, Györi I and Nechvátal L 2015 Fractional Calculus and Applied Analysis 18 651

    Google Scholar Pub Med

    Shatnawi M T, Djenina N, Ouannas A, Batiha I M and Grassi G 2022 Alexandria Engineering Journal 61 1655

    Google Scholar Pub Med

    Huang D and Li H 1993 Theory and method of the nonlinear economics (Chengdu: Publishing House of Sichuan University)

    Google Scholar Pub Med

    Xin B, Chen T and Ma J 2010 Discrete Dynamics in Nature and Society 2010

    Google Scholar Pub Med

    Wu G C and Baleanu D 2015 Communications in Nonlinear Science and Numerical Simulation 22 95

    Google Scholar Pub Med

    Gottwald G A and Melbourne I 2016 Chaos detection and predictability pp. 221-247

    Google Scholar Pub Med

    Pincus S M 1991 Proc. Natl. Acad. Sci. USA 88 2297

    Google Scholar Pub Med

    Jakimowicz A 2020 Entropy 22 452 100201-12

    Google Scholar Pub Med

  • 加载中
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Export Citation
PDF
XML

Article Metrics

Article views(125) PDF downloads(3) Cited by(0)

Access History

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

  • Received Date: 22/05/2024
  • Accepted Date: 19/06/2024

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.

    HTML

Reference (37)

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return