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

Anna Agliari, Nicolò Pecora and Alina Szuz

Chaos, Solitons & Fractals, 2022, vol. 158, issue C

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.

Keywords: Cournot duopoly; Closed invariant curves; Border collision bifurcation; Homoclinic bifurcation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.chaos.2022.112013

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