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Hidden and self-excited attractors in a heterogeneous Cournot oligopoly model

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  • Danca, Marius-F.
  • Lampart, Marek

Abstract

In this paper it is numerically shown that the dynamics of a heterogeneous Cournot oligopoly model depending on two bifurcation parameters can exhibit hidden and self-excited attractors. The system has a single equilibrium and a line of equilibria. The bifurcation diagrams show that the system admits several attractor coexistence windows, where the hidden attractors can be found. Depending on the parameters ranges, the coexistence windows present combinations of periodic, quasiperiodic and chaotic attractors.

Suggested Citation

  • Danca, Marius-F. & Lampart, Marek, 2021. "Hidden and self-excited attractors in a heterogeneous Cournot oligopoly model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s0960077920307657
    DOI: 10.1016/j.chaos.2020.110371
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    References listed on IDEAS

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    1. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 133-134.
    2. Lorenzo Cerboni Baiardi & Ahmad K. Naimzada, 2019. "An evolutionary Cournot oligopoly model with imitators and perfect foresight best responders," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 458-475, July.
    3. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    4. Lampart, Marek, 2012. "Stability of the Cournot equilibrium for a Cournot oligopoly model with n competitors," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1081-1085.
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    Cited by:

    1. Wang, Chun & Pi, Jinxiu & Zhou, Die & Tang, Wei & Yang, Guanghui, 2023. "Dynamics of n-person Cournot games with asymmetric information and heterogeneous expectations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 618(C).
    2. Zhao, Heqi & Ma, Xindong & Yang, Weijie & Zhang, Zhao & Bi, Qinsheng, 2023. "The mechanism of periodic and chaotic bursting patterns in an externally excited memcapacitive system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Danca, Marius-F., 2021. "Hopfield neuronal network of fractional order: A note on its numerical integration," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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