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Appearance of closed invariant curves in a piecewise Cournot model with advertising

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  • Agliari, Anna
  • Pecora, Nicolò
  • Szuz, Alina

Abstract

In the present paper we investigate two cases which can explain what happens when the Cournot equilibrium of a duopoly model loses stability through a Neimark-Sacker bifurcation of subcritical type. This kind of bifurcation involves complex dynamics which lead to the appearance of closed invariant curves. We analyze a Cournot model where competitors hold different plants and compete on advertising quantities. The model is described by a two-dimensional piecewise map in discrete time. Making use of analytical results and numerical simulations, we show that the appearance/disapearance of closed invariant curves is directly related to two different mechanisms, namely homoclinic bifurcations and border collision bifurcations.

Suggested Citation

  • Agliari, Anna & Pecora, Nicolò & Szuz, Alina, 2022. "Appearance of closed invariant curves in a piecewise Cournot model with advertising," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002235
    DOI: 10.1016/j.chaos.2022.112013
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    References listed on IDEAS

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    1. Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2010. "Global bifurcations in a piecewise-smooth Cournot duopoly game," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 15-24.
    2. Anna Agliari & Laura Gardini & Tonu Puu, 2006. "Global Bifurcations In Duopoly When The Cournot Point Is Destabilized Via A Subcritical Neimark Bifurcation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 1-20.
    3. Kind, Christoph, 1999. "Remarks on the economic interpretation of Hopf bifurcations," Economics Letters, Elsevier, vol. 62(2), pages 147-154, February.
    4. Agliari, Anna, 2006. "Homoclinic connections and subcritical Neimark bifurcation in a duopoly model with adaptively adjusted productions," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 739-755.
    5. Agliari, Anna & Gardini, Laura & Puu, Tönu, 2005. "Some global bifurcations related to the appearance of closed invariant curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(3), pages 201-219.
    6. Foroni, Ilaria & Agliari, Anna, 2011. "Complex dynamics associated with the appearance/disappearance of invariant closed curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1640-1655.
    7. Agliari, Anna & Rillosi, Francesco & Vachadze, George, 2015. "Credit market imperfection, financial market globalization, and catastrophic transition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 41-62.
    8. Gaunersdorfer, Andrea & Hommes, Cars H. & Wagener, Florian O.O., 2008. "Bifurcation routes to volatility clustering under evolutionary learning," Journal of Economic Behavior & Organization, Elsevier, vol. 67(1), pages 27-47, July.
    9. Agliari, Anna & Hommes, Cars H. & Pecora, Nicolò, 2016. "Path dependent coordination of expectations in asset pricing experiments: A behavioral explanation," Journal of Economic Behavior & Organization, Elsevier, vol. 121(C), pages 15-28.
    10. Ingrid Kubin & Laura Gardini, 2013. "Border collision bifurcations in boom and bust cycles," Journal of Evolutionary Economics, Springer, vol. 23(4), pages 811-829, September.
    11. Michael D. Whinston, 1988. "Exit with Multiplant Firms," RAND Journal of Economics, The RAND Corporation, vol. 19(4), pages 568-588, Winter.
    12. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
    13. Puu, Tonu & Tramontana, Fabio, 2019. "Can Bertrand and Cournot oligopolies be combined?," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 97-107.
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