IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v188y2024ics0960077924011512.html
   My bibliography  Save this article

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

Author

Listed:
  • Xu, Zhao
  • Sun, Kehui
  • Wang, Huihai

Abstract

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.

Suggested Citation

  • Xu, Zhao & Sun, Kehui & Wang, Huihai, 2024. "Dynamics and function projection synchronization for the fractional-order financial risk system," Chaos, Solitons & Fractals, Elsevier, vol. 188(C).
    • Handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924011512
    DOI: 10.1016/j.chaos.2024.115599
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924011512
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115599?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Li, Qinnan & Li, Ruihong & Huang, Dongmei, 2023. "Dynamic analysis of a new 4D fractional-order financial system and its finite-time fractional integral sliding mode control based on RBF neural network," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. He, Ke & Shi, Jianping & Fang, Hui, 2024. "Bifurcation and chaos analysis of a fractional-order delay financial risk system using dynamic system approach and persistent homology," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 223(C), pages 253-274.
    3. Paul Yaovi Dousseh & Cyrille Ainamon & Clément Hodévèwan Miwadinou & Adjimon Vincent Monwanou & Jean Bio Chabi Orou & Guillermo Huerta Cuellar, 2021. "Chaos in a Financial System with Fractional Order and Its Control via Sliding Mode," Complexity, Hindawi, vol. 2021, pages 1-15, July.
    4. Zhang, Tianxian & Zhao, Yongqi & Xu, Xiangliang & Wu, Si & Gu, Yujuan, 2024. "Solution and dynamics analysis of fractal-fractional multi-scroll Chen chaotic system based on Adomain decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    5. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    6. Johansyah, Muhamad Deni & Sambas, Aceng & Zheng, Song & Benkouider, Khaled & Vaidyanathan, Sundarapandian & Mohamed, Mohamad Afendee & Mamat, Mustafa, 2023. "A novel financial system with one stable and two unstable equilibrium points: Dynamics, coexisting attractors, complexity analysis and synchronization using integral sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. Xinggui Li & Ruofeng Rao & Shouming Zhong & Xinsong Yang & Hu Li & Yulin Zhang, 2022. "Impulsive Control and Synchronization for Fractional-Order Hyper-Chaotic Financial System," Mathematics, MDPI, vol. 10(15), pages 1-13, August.
    8. Chen, Shu-Bo & Jahanshahi, Hadi & Alhadji Abba, Oumate & Solís-Pérez, J.E. & Bekiros, Stelios & Gómez-Aguilar, J.F. & Yousefpour, Amin & Chu, Yu-Ming, 2020. "The effect of market confidence on a financial system from the perspective of fractional calculus: Numerical investigation and circuit realization," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    9. Altan, Aytaç & Karasu, Seçkin & Bekiros, Stelios, 2019. "Digital currency forecasting with chaotic meta-heuristic bio-inspired signal processing techniques," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 325-336.
    10. Cao, Yanli, 2020. "Chaotic synchronization based on fractional order calculus financial system," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    11. Lin, Xiaoran & Wang, Yachao & Wang, Jifang & Zeng, Wenxian, 2022. "Dynamic analysis and adaptive modified projective synchronization for systems with Atangana-Baleanu-Caputo derivative: A financial model with nonconstant demand elasticity," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    12. Ahmed, E. & Elgazzar, A.S., 2007. "On fractional order differential equations model for nonlocal epidemics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 379(2), pages 607-614.
    13. Shi, Jianping & He, Ke & Fang, Hui, 2022. "Chaos, Hopf bifurcation and control of a fractional-order delay financial system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 194(C), pages 348-364.
    14. Bo Wang & Hadi Jahanshahi & Stelios Bekiros & Yu-Ming Chu & J. F. Gã“Mez-Aguilar & Fawaz E. Alsaadi & Madini O. Alassafi, 2021. "Tracking Control And Stabilization Of A Fractional Financial Risk System Using Novel Active Finite-Time Fault-Tolerant Controls," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(06), pages 1-20, September.
    15. Karasu, Seçkin & Altan, Aytaç, 2022. "Crude oil time series prediction model based on LSTM network with chaotic Henry gas solubility optimization," Energy, Elsevier, vol. 242(C).
    16. Yousefpour, Amin & Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Wei, Zhouchao, 2020. "A fractional-order hyper-chaotic economic system with transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    17. Paul Yaovi Dousseh & Cyrille Ainamon & Clément Hodévèwan Miwadinou & Adjimon Vincent Monwanou & Jean Bio Chabi Orou, 2021. "Corrigendum to “Chaos in a Financial System with Fractional Order and Its Control via Sliding Modeâ€," Complexity, Hindawi, vol. 2021, pages 1-16, November.
    18. Paul C. Godfrey & Craig B. Merrill & Jared M. Hansen, 2009. "The relationship between corporate social responsibility and shareholder value: an empirical test of the risk management hypothesis," Strategic Management Journal, Wiley Blackwell, vol. 30(4), pages 425-445, April.
    19. Sara S. Alzaid & Ajay Kumar & Sunil Kumar & Badr Saad T. Alkahtani, 2023. "Chaotic Behavior Of Financial Dynamical System With Generalized Fractional Operator," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(04), pages 1-20.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Li, Qinnan & Li, Ruihong & Huang, Dongmei, 2023. "Dynamic analysis of a new 4D fractional-order financial system and its finite-time fractional integral sliding mode control based on RBF neural network," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    2. Qing Ding & Oumate Alhadji Abba & Hadi Jahanshahi & Madini O. Alassafi & Wen-Hua Huang, 2022. "Dynamical Investigation, Electronic Circuit Realization and Emulation of a Fractional-Order Chaotic Three-Echelon Supply Chain System," Mathematics, MDPI, vol. 10(4), pages 1-15, February.
    3. Ávalos-Ruíz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Cortes-Campos, H.M. & Lavín-Delgado, J.E., 2023. "A RGB image encryption technique using chaotic maps of fractional variable-order based on DNA encoding," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    4. Zambrano-Serrano, Ernesto & Bekiros, Stelios & Platas-Garza, Miguel A. & Posadas-Castillo, Cornelio & Agarwal, Praveen & Jahanshahi, Hadi & Aly, Ayman A., 2021. "On chaos and projective synchronization of a fractional difference map with no equilibria using a fuzzy-based state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    5. Zhou, Shuang-Shuang & Jahanshahi, Hadi & Din, Qamar & Bekiros, Stelios & Alcaraz, Raúl & Alassafi, Madini O. & Alsaadi, Fawaz E. & Chu, Yu-Ming, 2021. "Discrete-time macroeconomic system: Bifurcation analysis and synchronization using fuzzy-based activation feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    6. Miwadinou, C.H. & Olabodé, D.L. & Monwanou, A.V. & Enjieu Kadji, H.G. & Chabi Orou, J.B., 2023. "Nonlinear dynamics and passive control of GLYCOLYTIC oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    7. Yu, Xihong & Bao, Han & Chen, Mo & Bao, Bocheng, 2023. "Energy balance via memristor synapse in Morris-Lecar two-neuron network with FPGA implementation," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    8. Li, Jun-Feng & Jahanshahi, Hadi & Kacar, Sezgin & Chu, Yu-Ming & Gómez-Aguilar, J.F. & Alotaibi, Naif D. & Alharbi, Khalid H., 2021. "On the variable-order fractional memristor oscillator: Data security applications and synchronization using a type-2 fuzzy disturbance observer-based robust control," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    9. Bekiros, Stelios & Jahanshahi, Hadi & Bezzina, Frank & Aly, Ayman A., 2021. "A novel fuzzy mixed H2/H∞ optimal controller for hyperchaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    10. Mirza, Fuat Kaan & Baykaş, Tunçer & Hekimoğlu, Mustafa & Pekcan, Önder & Tunçay, Gönül Paçacı, 2024. "Decoding compositional complexity: Identifying composers using a model fusion-based approach with nonlinear signal processing and chaotic dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    11. Chu, Yu-Ming & Bekiros, Stelios & Zambrano-Serrano, Ernesto & Orozco-López, Onofre & Lahmiri, Salim & Jahanshahi, Hadi & Aly, Ayman A., 2021. "Artificial macro-economics: A chaotic discrete-time fractional-order laboratory model," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    12. Bazán Navarro, Ciro Eduardo & Benazic Tomé, Renato Mario, 2024. "Qualitative behavior in a fractional order IS-LM-AS macroeconomic model with stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 425-443.
    13. Yan, Lisha & Wang, Zhen & Zhang, Mingguang & Fan, Yingjie, 2023. "Sampled-data control for mean-square exponential stabilization of memristive neural networks under deception attacks," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    14. Shabani, Masoume & Wallin, Fredrik & Dahlquist, Erik & Yan, Jinyue, 2022. "Techno-economic assessment of battery storage integrated into a grid-connected and solar-powered residential building under different battery ageing models," Applied Energy, Elsevier, vol. 318(C).
    15. Al-Barakati, Abdullah A. & Mesdoui, Fatiha & Bekiros, Stelios & Kaçar, Sezgin & Jahanshahi, Hadi, 2024. "A variable-order fractional memristor neural network: Secure image encryption and synchronization via a smooth and robust control approach," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    16. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    17. Yao, Qijia & Alsaade, Fawaz W. & Al-zahrani, Mohammed S. & Jahanshahi, Hadi, 2023. "Fixed-time neural control for output-constrained synchronization of second-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    18. Alsaadi, Fawaz E. & Bekiros, Stelios & Yao, Qijia & Liu, Jinping & Jahanshahi, Hadi, 2023. "Achieving resilient chaos suppression and synchronization of fractional-order supply chains with fault-tolerant control," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    19. H. Mesgarani & Y. Esmaeelzade Aghdam & A. Beiranvand & J. F. Gómez-Aguilar, 2024. "A Novel Approach to Fuzzy Based Efficiency Assessment of a Financial System," Computational Economics, Springer;Society for Computational Economics, vol. 63(4), pages 1609-1626, April.
    20. Chen, Xiaolu & Weng, Tongfeng & Yang, Huijie, 2023. "Synchronization of spatiotemporal chaos and reservoir computing via scalar signals," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:188:y:2024:i:c:s0960077924011512. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.