Neimark–Sacker bifurcation and the generate cases of Kopel oligopoly model with different adjustment speed

Abstract

In this paper, bifurcations and chaotic behaviours of Kopel oligopoly model with different adjustment speed are discussed. The results imply that the Kopel oligopoly model undergoes flip bifurcation, Neimark-Sacker bifurcation, 1:3 and 1:4 resonances, which could induce complex dynamics, especially global behaviours between different orbits. The conditions for the occurrence of three different kinds of bifurcation are derived. Furthermore, the numerical simulations provide us the case study of theoretical analysis and the corresponding dynamical behaviours, especially the occurrence of global orbits.

Influence of rationality levels on dynamics of heterogeneous Cournot duopolists with quadratic costs

“…Cavalli et al [10] studied a heterogeneous nonlinear duopoly with an LMA player and a gradient adjustment player, where multiple stable attractors coexist. Other related work includes [11] , [12] , [13] , [14] , [15] , [16] , [17] , [18] , [19] , [20] , [21] , [22] , [23] , [24] , etc.…”

Analysis of stability and bifurcation for two heterogeneous triopoly games with the isoelastic demand

“…However, in the real world, it is more possible that a market supplied by two, three, or even four companies, which is called a duopoly, a triopoly, or a quadropoly, respectively. Among them, the duopoly is most intensively studied, see, e.g., [1,2,5,8,14,19,21,25,33,36,37,44]. Furthermore, the reader can refer to [4,12,24,26,38,39] for the explorations of triopoly games, which are also the topic of our concern in this paper.…”