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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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