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Complex dynamics of Kopel model with nonsymmetric response between oligopolists

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  • Li, Bo
  • Liang, Houjun
  • Shi, Lian
  • He, Qizhi

Abstract

In this paper, complex dynamics of Kopel model with nonsymmetric response between oligopolists are discussed. The research show that for the nonsymmetric model fixed point may undergo fold, transcritical, pitchfork and Neimark–Sacker bifurcation when satisfying some specific parameter combinations. The research also show us that effects from the rivals may incur more complex dynamics than self-adjust. During the process of numerical simulation, different combinations of parameter are chosen to show multiple-period phenomenon, the change of stability and the transition of different dynamical behaviors.

Suggested Citation

  • Li, Bo & Liang, Houjun & Shi, Lian & He, Qizhi, 2022. "Complex dynamics of Kopel model with nonsymmetric response between oligopolists," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    • Handle: RePEc:eee:chsofr:v:156:y:2022:i:c:s0960077922000716
    DOI: 10.1016/j.chaos.2022.111860
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    References listed on IDEAS

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    1. Yu, Yu & Yu, Weisheng, 2021. "The stability and duality of dynamic Cournot and Bertrand duopoly model with comprehensive preference," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    2. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2018. "Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 822-843, December.
    3. Tönu Puu, 2018. "Disequilibrium Economics," Springer Books, Springer, number 978-3-319-74415-5, March.
    4. Alidousti, J. & Eskandari, Z. & Avazzadeh, Z., 2020. "Generic and symmetric bifurcations analysis of a three dimensional economic model," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Colombo, Luca & Labrecciosa, Paola, 2019. "Stackelberg versus Cournot: A differential game approach," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 239-261.
    6. Li, Hui & Zhou, Wei & Elsadany, A. A & Chu, Tong, 2021. "Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Panchuk, A. & Puu, T., 2015. "Oligopoly model with recurrent renewal of capital revisited," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 119-128.
    8. Li, Bo & Liang, Houjun & He, Qizhi, 2021. "Multiple and generic bifurcation analysis of a discrete Hindmarsh-Rose model," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    9. A. A. Elsadany & A. M. Awad, 2016. "Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 617-639, December.
    10. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    11. Puu, Tonu & Tramontana, Fabio, 2019. "Can Bertrand and Cournot oligopolies be combined?," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 97-107.
    12. Shi, Lian & Xu, Feng & Chen, Yongtai, 2021. "Quantum Cournot duopoly game with isoelastic demand function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
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