IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v126y2019icp66-77.html
   My bibliography  Save this article

A financial hyperchaotic system with coexisting attractors: Dynamic investigation, entropy analysis, control and synchronization

Author

Listed:
  • Jahanshahi, Hadi
  • Yousefpour, Amin
  • Wei, Zhouchao
  • Alcaraz, Raúl
  • Bekiros, Stelios

Abstract

This paper is concerned with dynamic and entropy analyses of a hyperchaotic financial system, as well as with its hyperchaos suppression and synchronization. The dynamic behaviour of the system is analyzed for several parameters and initial conditions making use of bifurcation diagrams, Lyapunov exponents and phase portraits. Moreover, entropy from resulting time series is also characterized by estimating ordinal pattern distributions. These analyses have been able to determine and locate accurately chaotic and periodic attractors in the system, thus enabling successful design of its control. In general, financial systems are not always completely synchronized; therefore, some robust synchronization technique should be considered. This study proposes a novel fuzzy disturbance-observer based integral terminal sliding mode control method for the hyperchaotic financial system. The presented control technique guarantees robustness against uncertainties, external disturbances and control input saturation. Fuzzy rules are employed to adaptively tune the gains of the proposed control scheme. Also, the fuzzy inference engine avoids the chattering problem in the system response. Simulation results illustrate the efficient performance of the proposed control technique in the presence of dynamic uncertainties, external disturbances and control input saturation.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:126:y:2019:i:c:p:66-77
    DOI: 10.1016/j.chaos.2019.05.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077919301882
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2019.05.023?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. Shukla, Manoj Kumar & Sharma, B.B., 2017. "Stabilization of a class of fractional order chaotic systems via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 56-62.
    2. Chen, Aimin & Lu, Junan & Lü, Jinhu & Yu, Simin, 2006. "Generating hyperchaotic Lü attractor via state feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 103-110.
    3. Jajarmi, Amin & Hajipour, Mojtaba & Baleanu, Dumitru, 2017. "New aspects of the adaptive synchronization and hyperchaos suppression of a financial model," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 285-296.
    4. Hołyst, Janusz A & Urbanowicz, Krzysztof, 2000. "Chaos control in economical model by time-delayed feedback method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 587-598.
    5. 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.
    6. Dadras, Sara & Momeni, Hamid Reza, 2010. "Control of a fractional-order economical system via sliding mode," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2434-2442.
    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. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    2. Jajarmi, Amin & Hajipour, Mojtaba & Baleanu, Dumitru, 2017. "New aspects of the adaptive synchronization and hyperchaos suppression of a financial model," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 285-296.
    3. Vasily E. Tarasov, 2019. "On History of Mathematical Economics: Application of Fractional Calculus," Mathematics, MDPI, vol. 7(6), pages 1-28, June.
    4. Deepika, Deepika & Kaur, Sandeep & Narayan, Shiv, 2018. "Uncertainty and disturbance estimator based robust synchronization for a class of uncertain fractional chaotic system via fractional order sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 196-203.
    5. 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.
    6. Song Xu & Hui Lv & Heng Liu & Aijing Liu, 2019. "Robust Control of Disturbed Fractional-Order Economical Chaotic Systems with Uncertain Parameters," Complexity, Hindawi, vol. 2019, pages 1-13, October.
    7. H. Norouzi Nav & M. R. Jahed Motlagh & A. Makui, 2017. "Robust controlling of chaotic behavior in supply chain networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(6), pages 711-724, June.
    8. Veronika Novotná & Vladěna Štěpánková, 2015. "Parameter Estimation for Dynamic Model of the Financial System," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 63(6), pages 2051-2055.
    9. Akhmet, Marat & Akhmetova, Zhanar & Fen, Mehmet Onur, 2014. "Chaos in economic models with exogenous shocks," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 95-108.
    10. Lai, Qiang & Norouzi, Benyamin & Liu, Feng, 2018. "Dynamic analysis, circuit realization, control design and image encryption application of an extended Lü system with coexisting attractors," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 230-245.
    11. Chien, Fengsheng & Inc, Mustafa & Yosefzade, Hamidreza & Saberi Nik, Hassan, 2021. "Predicting the chaos and solution bounds in a complex dynamical system," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    12. Askar, S.S., 2018. "Tripoly Stackelberg game model: One leader versus two followers," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 301-311.
    13. Laarem, Guessas, 2021. "A new 4-D hyper chaotic system generated from the 3-D Rösslor chaotic system, dynamical analysis, chaos stabilization via an optimized linear feedback control, it’s fractional order model and chaos sy," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    14. Ding, Yuting & Jiang, Weihua & Wang, Hongbin, 2012. "Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay," Chaos, Solitons & Fractals, Elsevier, vol. 45(8), pages 1048-1057.
    15. 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).
    16. Tchitnga, R. & Mezatio, B.A. & Fozin, T. Fonzin & Kengne, R. & Louodop Fotso, P.H. & Fomethe, A., 2019. "A novel hyperchaotic three-component oscillator operating at high frequency," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 166-180.
    17. Yassen, M.T., 2008. "Synchronization hyperchaos of hyperchaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 465-475.
    18. Peng, Yu & Lu, Qian, 2015. "Complex dynamics analysis for a duopoly Stackelberg game model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 259-268.
    19. Yu, Weisheng & Yu, Yu, 2014. "The complexion of dynamic duopoly game with horizontal differentiated products," Economic Modelling, Elsevier, vol. 41(C), pages 289-297.
    20. Jiang, Jingfei & Guirao, Juan Luis García & Chen, Huatao & Cao, Dengqing, 2019. "The boundary control strategy for a fractional wave equation with external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 92-97.

    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:126:y:2019:i:c:p:66-77. 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.