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Chaos control in economical model by time-delayed feedback method

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  • Hołyst, Janusz A
  • Urbanowicz, Krzysztof

Abstract

A two-dimensional map describing chaotic behaviour of an economic model has been stabilized on various periodic orbits by the use of Pyragas time-delayed feedback control. The method avoids fancy data processing used in the Ott–Grebogi–Yorke approach and is based solely on the plain measurement and time lag of a scalar signal which in our case is a value of sales of a firm following an active investment strategy (Behrens–Feichtinger model). We show that the application of this control method is very straightforward and one can easily switch from a chaotic trajectory to a regular periodic orbit and simultaneously improve the system's economic properties.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:287:y:2000:i:3:p:587-598
    DOI: 10.1016/S0378-4371(00)00395-2
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    Cited by:

    1. Ding, Zhanwen & Wang, Qiao & Jiang, Shumin, 2014. "Analysis on the dynamics of a Cournot investment game with bounded rationality," Economic Modelling, Elsevier, vol. 39(C), pages 204-212.
    2. Salarieh, Hassan & Alasty, Aria, 2008. "Delayed feedback control via minimum entropy strategy in an economic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 851-860.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Lin, Jinchai & Fan, Ruguo & Tan, Xianchun & Zhu, Kaiwei, 2021. "Dynamic decision and coordination in a low-carbon supply chain considering the retailer's social preference," Socio-Economic Planning Sciences, Elsevier, vol. 77(C).
    8. 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.
    9. Yu, Weisheng & Yu, Yu, 2014. "The complexion of dynamic duopoly game with horizontal differentiated products," Economic Modelling, Elsevier, vol. 41(C), pages 289-297.
    10. Peng, Yu & Lu, Qian & Xiao, Yue, 2016. "A dynamic Stackelberg duopoly model with different strategies," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 128-134.
    11. 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.
    12. Junhai Ma & Lijian Sun & Xueli Zhan, 2017. "Study on Triopoly Dynamic Game Model Based on Different Demand Forecast Methods in the Market," Complexity, Hindawi, vol. 2017, pages 1-12, July.
    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. Xin, Baogui & Chen, Tong, 2011. "On a master-slave Bertrand game model," Economic Modelling, Elsevier, vol. 28(4), pages 1864-1870, July.
    15. Qiuxiang Li & Mengnan Shi & Yimin Huang, 2019. "A Dynamic Price Game Model in a Low-Carbon, Closed-Loop Supply Chain Considering Return Rates and Fairness Concern Behaviors," IJERPH, MDPI, vol. 16(11), pages 1-21, June.
    16. 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.
    17. 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.
    18. Qiuxiang Li & Xingli Chen & Yimin Huang, 2019. "The Stability and Complexity Analysis of a Low-Carbon Supply Chain Considering Fairness Concern Behavior and Sales Service," IJERPH, MDPI, vol. 16(15), pages 1-21, July.
    19. Ding, Zhanwen & Li, Qiang & Jiang, Shumin & Wang, Xuedi, 2015. "Dynamics in a Cournot investment game with heterogeneous players," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 939-950.
    20. S. S. Askar, 2020. "Duopolistic Stackelberg game: investigation of complex dynamics and chaos control," Operational Research, Springer, vol. 20(3), pages 1685-1699, September.
    21. 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.
    22. Askar, S.S., 2018. "Tripoly Stackelberg game model: One leader versus two followers," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 301-311.
    23. Costea, Carmen, 2006. "Comments on the use of network structures to analyse commercial companies’ evolution and their impact on economic behaviour," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 140-144.

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