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- Agliari, Anna, et al.
(författare)
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Global Bifurcations in Duopoly when the Cournot Point is Destabilized through a Subcritical Neimark Bifurcation
- 2003
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive Cournot fixed point.
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- Agliari, Anna, et al.
(författare)
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Global bifurcations of basins in a triopoly game
- 2002
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Ingår i: International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. - 0218-1274. ; 12:10, s. 2175-2207
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Tidskriftsartikel (refereegranskat)abstract
- A Cournot model based on bounded inverse demand function and constant marginal production costs is studied. The case of three producers is considered and the adjustment process reduces to a three-dimensional noninvertible map in the output of competitors. The analysis of the dynamical behavior of the map is performed by the "critical curve method", extended to the critical surfaces in 3D. By this method, we explain the different bifurcations in the basins of attraction and in the attracting sets. In particular, given the economic application, feasible trajectories are focused, starting from the simple situation of two identical producers and extending the results to the generic case.
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- Agliari, Anna, et al.
(författare)
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Some global bifurcations related to the appearance of closed invariant curves
- 2005
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Ingår i: Mathematics and Computers in Simulation. - : Elsevier BV. - 0378-4754 .- 1872-7166. ; 68:3, s. 201-219
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we consider a two-dimensional map (a duopoly game) in which the fixed point is destabilized via a subcritical Neimark–Hopf (N–H) bifurcation. Our aim is to investigate, via numerical examples, some global bifurcations associated with the appearance of repelling closed invariant curves involved in the Neimark–Hopf bifurcations. We shall see that the mechanism is not unique, and that it may be related to homoclinic connections of a saddle cycle, that is to a closed invariant curve formed by the merging of a branch of the stable set of the saddle with a branch of the unstable set of the same saddle. This will be shown by analyzing the bifurcations arising inside a periodicity tongue, i.e., a region of the parameter space in which an attracting cycle exists.
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- Agliari, Anna, et al.
(författare)
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The dynamics of a triopoly Cournot game
- 2000
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Ingår i: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 11:15, s. 2531-2560
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Tidskriftsartikel (refereegranskat)abstract
- This paper reconsiders the Cournot oligopoly (noncooperative) game with iso-elastic demand and constant marginal costs, one of the rare cases where the reaction functions can be derived in closed form. It focuses the case of three competitors, and so also extends the critical line method for non-invertible maps to the study of critical surfaces in 3D. By this method the various bifurcations of the attractors and their basins are studied. As a special case the restriction of the map to an invariant plane when two of the three firms are identical is focused.
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