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

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  • 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
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    References listed on IDEAS

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    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.
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    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.

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