IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v131y2020ics0960077919304734.html
   My bibliography  Save this article

Chaos and complexity in a fractional-order financial system with time delays

Author

Listed:
  • Wang, Shaojie
  • He, Shaobo
  • Yousefpour, Amin
  • Jahanshahi, Hadi
  • Repnik, Robert
  • Perc, Matjaž

Abstract

Finance and economics are complex nonlinear systems that are affected by various external factors, including of course human action, bilateral relations, conflicts, and policy. Time delays in a financial system take into account the amount of time that passes from a particular policy or decision being made to it actually taking effect. It is thus important to consider time delays as an integral part of modeling in this field. Moreover, many features of financial systems cannot be expressed sufficiently precisely by means of integer-order calculus. Fractional-order calculus alleviates these shortcomings. The aim of this paper is therefore to study the dynamics and complexity in a fractional-order financial system with time delays. We observe fascinating transitions to deterministic chaos, including cascading period doubling, as well as high levels of complexity. This is particularly true in response to variations of derivative orders, which are thus identified as key system parameters.

Suggested Citation

  • Wang, Shaojie & He, Shaobo & Yousefpour, Amin & Jahanshahi, Hadi & Repnik, Robert & Perc, Matjaž, 2020. "Chaos and complexity in a fractional-order financial system with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304734
    DOI: 10.1016/j.chaos.2019.109521
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919304734
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.109521?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. Jahanshahi, Hadi & Yousefpour, Amin & Wei, Zhouchao & Alcaraz, Raúl & Bekiros, Stelios, 2019. "A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 66-77.
    2. De Cesare, Luigi & Sportelli, Mario, 2005. "A dynamic IS-LM model with delayed taxation revenues," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 233-244.
    3. Chen, Wei-Ching, 2008. "Nonlinear dynamics and chaos in a fractional-order financial system," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1305-1314.
    4. Larrondo, H.A. & González, C.M. & Martín, M.T. & Plastino, A. & Rosso, O.A., 2005. "Intensive statistical complexity measure of pseudorandom number generators," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 356(1), pages 133-138.
    5. Shone,Ronald, 2001. "An Introduction to Economic Dynamics," Cambridge Books, Cambridge University Press, number 9780521804783.
    6. Huang, Chengdai & Cai, Liming & Cao, Jinde, 2018. "Linear control for synchronization of a fractional-order time-delayed chaotic financial system," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 326-332.
    7. He, Shaobo & Banerjee, Santo & Sun, Kehui, 2018. "Can derivative determine the dynamics of fractional-order chaotic system?," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 14-22.
    8. 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).
    9. Shone,Ronald, 2001. "An Introduction to Economic Dynamics," Cambridge Books, Cambridge University Press, number 9780521800341.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fawaz E. Alsaadi & Amirreza Yasami & Christos Volos & Stelios Bekiros & Hadi Jahanshahi, 2023. "A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy," Mathematics, MDPI, vol. 11(2), pages 1-25, January.
    2. 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).
    3. Bekiros, Stelios & Laarem, Guessas & Mou, Jun & Al-Barakati, Abdullah A. & Jahanshahi, Hadi, 2023. "Heterogeneous agent-based modeling of endogenous boom-bust cycles in financial markets with adaptive expectations and dynamically switching fractions between contrarian and fundamental market entry st," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Dwivedi, Kushal Dhar & Singh, Jagdev, 2021. "Numerical solution of two-dimensional fractional-order reaction advection sub-diffusion equation with finite-difference Fibonacci collocation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 38-50.
    5. Bambe Moutsinga, Claude Rodrigue & Pindza, Edson & Maré, Eben, 2021. "Comparative performance of time spectral methods for solving hyperchaotic finance and cryptocurrency systems," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    6. 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.
    7. Wang, Bo & Liu, Jinping & Alassafi, Madini O. & Alsaadi, Fawaz E. & Jahanshahi, Hadi & Bekiros, Stelios, 2022. "Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    8. Shoji, Isao & Nozawa, Masahiro, 2022. "Geometric analysis of nonlinear dynamics in application to financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    9. Qijia Yao & Hadi Jahanshahi & Larissa M. Batrancea & Naif D. Alotaibi & Mircea-Iosif Rus, 2022. "Fixed-Time Output-Constrained Synchronization of Unknown Chaotic Financial Systems Using Neural Learning," Mathematics, MDPI, vol. 10(19), pages 1-14, October.
    10. 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).
    11. 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).
    12. 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).
    13. Muhammad Imran Liaqat & Ali Akgül & Hanaa Abu-Zinadah, 2023. "Analytical Investigation of Some Time-Fractional Black–Scholes Models by the Aboodh Residual Power Series Method," Mathematics, MDPI, vol. 11(2), pages 1-19, January.
    14. Li, Yue & Yuan, Mingfeng & Chen, Zengqiang, 2023. "Constructing 3D conservative chaotic system with dissipative term based on Shilnikov theorem," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    15. Jahanshahi, Hadi & Sajjadi, Samaneh Sadat & Bekiros, Stelios & Aly, Ayman A., 2021. "On the development of variable-order fractional hyperchaotic economic system with a nonlinear model predictive controller," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    16. Muhamad Deni Johansyah & Aceng Sambas & Saleh Mobayen & Behrouz Vaseghi & Saad Fawzi Al-Azzawi & Sukono & Ibrahim Mohammed Sulaiman, 2022. "Dynamical Analysis and Adaptive Finite-Time Sliding Mode Control Approach of the Financial Fractional-Order Chaotic System," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    17. 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.
    18. Ren, Lei & Lin, Ming-Hung & Abdulwahab, Abdulkareem & Ma, Jun & Saberi-Nik, Hassan, 2023. "Global dynamical analysis of the integer and fractional 4D hyperchaotic Rabinovich system," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    19. Wang, Zhen & Hu, Weipeng, 2021. "Resonance analysis of a single-walled carbon nanotube," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    20. Peng, Yaohao & Nagata, Mateus Hiro, 2020. "An empirical overview of nonlinearity and overfitting in machine learning using COVID-19 data," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    21. 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).
    22. Gomez, Ledys Llasmin Salazar & Torres, Soledad & Kiseľák, Jozef & Fuders, Felix & Ishimura, Naoyuki & Yoshizawa, Yasukazu & Stehlík, Milan, 2022. "Long memory estimation in a non-Gaussian bivariate process," Applied Mathematics and Computation, Elsevier, vol. 420(C).

    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. Jahanshahi, Hadi & Yousefpour, Amin & Munoz-Pacheco, Jesus M. & Kacar, Sezgin & Pham, Viet-Thanh & Alsaadi, Fawaz E., 2020. "A new fractional-order hyperchaotic memristor oscillator: Dynamic analysis, robust adaptive synchronization, and its application to voice encryption," Applied Mathematics and Computation, Elsevier, vol. 383(C).
    2. Wang, Shaojie & Bekiros, Stelios & Yousefpour, Amin & He, Shaobo & Castillo, Oscar & Jahanshahi, Hadi, 2020. "Synchronization of fractional time-delayed financial system using a novel type-2 fuzzy active control method," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Soradi-Zeid, Samaneh & Jahanshahi, Hadi & Yousefpour, Amin & Bekiros, Stelios, 2020. "King algorithm: A novel optimization approach based on variable-order fractional calculus with application in chaotic financial systems," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    4. 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).
    5. Çalış, Yasemin & Demirci, Ali & Özemir, Cihangir, 2022. "Hopf bifurcation of a financial dynamical system with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 343-361.
    6. 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).
    7. Andrea Vaona, 2013. "The Most Beautiful Variations on Fair Wages and the Phillips Curve," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(6), pages 1069-1084, September.
    8. 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).
    9. 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).
    10. Jahanshahi, Hadi & Orozco-López, Onofre & Munoz-Pacheco, Jesus M. & Alotaibi, Naif D. & Volos, Christos & Wang, Zhen & Sevilla-Escoboza, R. & Chu, Yu-Ming, 2021. "Simulation and experimental validation of a non-equilibrium chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    11. David, S.A. & Machado, J.A.T. & Quintino, D.D. & Balthazar, J.M., 2016. "Partial chaos suppression in a fractional order macroeconomic model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 122(C), pages 55-68.
    12. Din Prathumwan & Wannika Sawangtong & Panumart Sawangtong, 2017. "An Analysis on the Fractional Asset Flow Differential Equations," Mathematics, MDPI, vol. 5(2), pages 1-17, June.
    13. Chen, Wei-Ching, 2008. "Dynamics and control of a financial system with time-delayed feedbacks," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1198-1207.
    14. Son, Woo-Sik & Park, Young-Jai, 2011. "Delayed feedback on the dynamical model of a financial system," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 208-217.
    15. Vaona, Andrea, 2011. "Four variations on fair wages and the Phillips curve," Kiel Working Papers 1713, Kiel Institute for the World Economy (IfW Kiel).
    16. Wang, Yong-Long & Jahanshahi, Hadi & Bekiros, Stelios & Bezzina, Frank & Chu, Yu-Ming & Aly, Ayman A., 2021. "Deep recurrent neural networks with finite-time terminal sliding mode control for a chaotic fractional-order financial system with market confidence," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    17. Weiwei Zhang & Jinde Cao & Ahmed Alsaedi & Fuad Eid S. Alsaadi, 2017. "Synchronization of Time Delayed Fractional Order Chaotic Financial System," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-5, October.
    18. Stasys Girdzijauskas & Dalia Štreimikiene, 2008. "Application of logistic models for stock market bubbles analysis," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 10(1), pages 45-51, November.
    19. 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.
    20. Wang, Bo & Liu, Jinping & Alassafi, Madini O. & Alsaadi, Fawaz E. & Jahanshahi, Hadi & Bekiros, Stelios, 2022. "Intelligent parameter identification and prediction of variable time fractional derivative and application in a symmetric chaotic financial system," Chaos, Solitons & Fractals, Elsevier, vol. 154(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:131:y:2020:i:c:s0960077919304734. 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.