IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i10p1670-d420957.html
   My bibliography  Save this article

Chaos Control and Anti-Control of the Heterogeneous Cournot Oligopoly Model

Author

Listed:
  • Marek Lampart

    (IT4Innovations, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 708 00 Ostrava, Czech Republic
    Department of Applied Mathematics, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 708 00 Ostrava, Czech Republic
    These authors contributed equally to this work.)

  • Alžběta Lampartová

    (IT4Innovations, VSB-Technical University of Ostrava, 17. listopadu 2172/15, 708 00 Ostrava, Czech Republic
    These authors contributed equally to this work.
    PRIGO University, V. Nezvala 801/1, 73601 Havířov, Czech Republic.)

Abstract

The main aim of this paper focuses on chaos suppression (control) and stimulation (anti-control) of a heterogeneous Cournot oligopoly model. This goal is reached by applying the theory of dynamical systems, namely impulsive control. The main aim was to demonstrate, through massive numerical simulations and estimation of the maximal Lyapunov exponent, the 0-1test for chaos, and bifurcation analysis, that it is possible to control the dynamical behavior of the investigated model by finding injection values under which the desired phenomena are attained. Moreover, it was shown that there are injection values for which the injected system admits a self-excited cycle or chaotic trajectory.

Suggested Citation

  • Marek Lampart & Alžběta Lampartová, 2020. "Chaos Control and Anti-Control of the Heterogeneous Cournot Oligopoly Model," Mathematics, MDPI, vol. 8(10), pages 1-13, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1670-:d:420957
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/10/1670/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/10/1670/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    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. Fang Wu & Junhai Ma, 2023. "Research Trend, Logical Structure and Outlook on Complex Economic Game," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    2. Nálepová, Veronika & Lampart, Marek, 2024. "Impact of windfall tax on market dynamics: A Cournot oligopoly model with exogenous shocks," Economic Modelling, Elsevier, vol. 137(C).

    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. Cavalli, Fausto & Naimzada, Ahmad, 2016. "Complex dynamics and multistability with increasing rationality in market games," Chaos, Solitons & Fractals, Elsevier, vol. 93(C), pages 151-161.
    2. Luca Gori & Luca Guerrini & Mauro Sodini, 2017. "A characterisation of duopoly dynamics with frictions in production adjustments," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 963-988, November.
    3. 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).
    4. Akio Matsumoto & Ferenc Szidarovszky, 2020. "Delay Stability of n -Firm Cournot Oligopolies," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
    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. Fausto Cavalli & Ahmad Naimzada & Marina Pireddu, 2015. "Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-17, May.
    7. Nálepová, Veronika & Lampart, Marek, 2024. "Impact of windfall tax on market dynamics: A Cournot oligopoly model with exogenous shocks," Economic Modelling, Elsevier, vol. 137(C).
    8. Danca, Marius-F. & Lampart, Marek, 2021. "Hidden and self-excited attractors in a heterogeneous Cournot oligopoly model," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    9. Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2015. "Heterogeneity and the (de)stabilizing role of rationality," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 226-244.

    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:gam:jmathe:v:8:y:2020:i:10:p:1670-:d:420957. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.