IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v156y2022ics0960077922000716.html
   My bibliography  Save this article

Complex dynamics of Kopel model with nonsymmetric response between oligopolists

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077922000716
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2022.111860?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. 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, December.
    4. 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.
    5. 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).
    6. 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.
    7. 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).
    8. 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.
    9. 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).
    10. 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.
    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).
    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. Li, Peiluan & Han, Liqin & Xu, Changjin & Peng, Xueqing & Rahman, Mati ur & Shi, Sairu, 2023. "Dynamical properties of a meminductor chaotic system with fractal–fractional power law operator," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. Najariyan, Marzieh & Qiu, Li, 2023. "Singular fuzzy fractional quadratic regulator problem," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    3. Zorica Dodevska & Sandro Radovanović & Andrija Petrović & Boris Delibašić, 2023. "When Fairness Meets Consistency in AHP Pairwise Comparisons," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    4. Xiaoliang Li & Kongyan Chen, 2023. "Equilibria and their stability in an asymmetric duopoly model of Kopel," Papers 2301.12628, arXiv.org.
    5. Liu, Dayong, 2023. "Does green finance and natural resources agglomeration have potential for green economic growth? Evidence from Asian perspective," Resources Policy, Elsevier, vol. 84(C).
    6. Timilehin Opeyemi Alakoya & Oluwatosin Temitope Mewomo, 2023. "A Relaxed Inertial Tseng’s Extragradient Method for Solving Split Variational Inequalities with Multiple Output Sets," Mathematics, MDPI, vol. 11(2), pages 1-26, January.
    7. Xiaoliang Li & Jiacheng Fu & Wei Niu, 2023. "Complex dynamics of knowledgeable monopoly models with gradient mechanisms," Papers 2301.01497, arXiv.org.
    8. Abdelkader Moumen & Abdelaziz Mennouni, 2022. "A New Projection Method for a System of Fractional Cauchy Integro-Differential Equations via Vieta–Lucas Polynomials," Mathematics, MDPI, vol. 11(1), pages 1-14, December.
    9. Ngo, Thanh & Trinh, Hai Hong & Haouas, Ilham & Ullah, Subhan, 2022. "Examining the bidirectional nexus between financial development and green growth: International evidence through the roles of human capital and education expenditure," Resources Policy, Elsevier, vol. 79(C).
    10. Xiaoliang Li & Bo Li, 2023. "A Bertrand duopoly game with differentiated products reconsidered," Papers 2301.01007, arXiv.org.
    11. Li, Xiaoliang & Li, Bo & Liu, Li, 2023. "Stability and dynamic behaviors of a limited monopoly with a gradient adjustment mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    12. Wu, Qihan & Yan, Dong & Umair, Muhammad, 2023. "Assessing the role of competitive intelligence and practices of dynamic capabilities in business accommodation of SMEs," Economic Analysis and Policy, Elsevier, vol. 77(C), pages 1103-1114.
    13. Mohsen Mortazavi, 2023. "Selecting Sustainable Optimal Stock by Using Multi-Criteria Fuzzy Decision-Making Approaches Based on the Development of the Gordon Model: A case study of the Toronto Stock Exchange," Papers 2304.13818, arXiv.org.

    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. 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. 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).
    3. Li, Xiaoliang & Li, Bo & Liu, Li, 2023. "Stability and dynamic behaviors of a limited monopoly with a gradient adjustment mechanism," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    4. Eskandari, Z. & Avazzadeh, Z. & Khoshsiar Ghaziani, R., 2022. "Complex dynamics of a Kaldor model of business cycle with discrete-time," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    5. Wang, Chun & Tang, Wei & Pi, Jinxiu, 2024. "The stability of dynamic n-person Cournot games with strategic adjustment costs," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    6. Tian, Yi & Ma, Junhai & Xie, Lei & Koivumäki, Timo & Seppänen, Veikko, 2020. "Coordination and control of multi-channel supply chain driven by consumers’ channel preference and sales effort," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    7. Long, Jianjun & Wang, Fenglian, 2024. "Complexity of a two-stage R&D game within a cluster supply chain considering vertical R&D spillovers, effective information, and government subsidies," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 606-621.
    8. Ding, Shasha & Sun, Hao & Sun, Panfei & Han, Weibin, 2022. "Dynamic outcome of coopetition duopoly with implicit collusion," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    9. Yu Yu & Weisheng Yu, 2019. "The Complexion of Multi-period Stackelberg Triopoly Game with Bounded Rationality," Computational Economics, Springer;Society for Computational Economics, vol. 53(1), pages 457-478, January.
    10. Li Cheng & Liu Conglin, 2023. "Game analysis and pricing strategy of duopoly airlines based on service," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(3), pages 1103-1124, June.
    11. Yang, Xuenan & Peng, Yu & Xiao, Yue & Wu, Xue, 2019. "Nonlinear dynamics of a duopoly Stackelberg game with marginal costs," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 185-191.
    12. Wu, Huagan & Gu, Jinxiang & Guo, Yixuan & Chen, Mo & Xu, Quan, 2024. "Biphasic action potentials in an individual cellular neural network cell," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    13. Colombo, Luca & Labrecciosa, Paola, 2022. "Product quality differentiation in a renewable resource oligopoly," Journal of Environmental Economics and Management, Elsevier, vol. 111(C).
    14. Sameh Askar & Abdulaziz Foul & Tarek Mahrous & Saleh Djemele & Emad Ibrahim, 2021. "Global and Local Analysis for a Cournot Duopoly Game with Two Different Objective Functions," Mathematics, MDPI, vol. 9(23), pages 1-14, December.
    15. Xiaoliang Li & Kongyan Chen, 2023. "Equilibria and their stability in an asymmetric duopoly model of Kopel," Papers 2301.12628, arXiv.org.
    16. Sarah Mignot & Fabio Tramontana & Frank Westerhoff, 2024. "Complex dynamics in a nonlinear duopoly model with heuristic expectation formation and learning behavior," Annals of Operations Research, Springer, vol. 337(3), pages 809-834, June.
    17. Ilko Vrankić & Tomislav Herceg & Mirjana Pejić Bach, 2021. "Dynamics and stability of evolutionary optimal strategies in duopoly," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(3), pages 1001-1019, September.
    18. Sorin Lugojan & Loredana Ciurdariu & Eugenia Grecu, 2022. "Another Case of Degenerated Discrete Chenciner Dynamic System and Economics," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    19. Peng, Yu & Xiao, Yue & Lu, Qian & Wu, Xue & Zhao, Yueru, 2020. "Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    20. Zhang, Ling & Zhang, Zheng, 2022. "Dynamic analysis of the decision of authorized remanufacturing supply chain affected by government subsidies under cap-and-trade policies," Chaos, Solitons & Fractals, Elsevier, vol. 160(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:156:y:2022:i:c:s0960077922000716. 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.