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

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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.
Lingua originaleEnglish
pagine (da-a)112013-N/A
RivistaChaos, Solitons and Fractals
Stato di pubblicazionePubblicato - 2022


  • Border collision bifurcation
  • Closed invariant curves
  • Cournot duopoly
  • Homoclinic bifurcation


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