Global Bifurcations in Duopoly When the Cournot Point Is Destabilized via a Subcritical Neimark Bifurcation

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.

Financial fragility and global dynamics

“…5c,d ) the attractor may seem to "cross" its basin boundary, but of course this is only due to our way of representing in the same plane both the attractors and the basins of a 4-dimensional system. to the constraint K * = 1, which seems very similar to the one described in [6]. What is remarkable is that the new attractor appears abruptly, and its basin of attraction becomes wider and wider as α increases, while on the other hand the basin of the steady state is gradually reduced to a small neighborhood (Figs.…”

Nonlinear dynamics in a Cournot duopoly with relative profit delegation

“…For this reason β plays an important role in determining the dynamic properties of the symmetric map, while being responsible of the existence of local and global phenomena which are usually observed in asymmetric maps (e.g., different production costs, see . From a mathematical point of view, it is relevant to stress the presence of the parameter β (which we recall it represents the relative degree of collusion or competition between managers in our context) which multiplies the mixed term Kopel, 1996;Agiza, 1999;Bischi and Naimzada, 2000;Bischi and Kopel, 2001;Agliari et al, 2005;Agliari, Gardini and Puu, 2006). 9 We note that Dixit (1986) introduces a time-adjustment mechanism of quantities in a continuous-time Cournot model.…”

Two different routes to complex dynamics in an heterogeneous triopoly game

“…In the literature, many papers are devoted to the development and the analysis of the simplest oligopolistic case: duopoly. Both homogeneous and heterogeneous firms cases are considered 1 (see [2,7,9,11,17,20,21,26] for a few papers on homogeneous duopolies, [10] for a recent survey and [4,5,8,24] for heterogeneous duopolies). The authors of these papers underscore the complicated (and complex) dynamics that may emerge whenever firms have some degree of bounded rationality.…”