Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Elements of applied bifurcation theory (2nd ed.)
Elements of applied bifurcation theory (2nd ed.)
Multistability in a dynamic Cournot game with three oligopolists
Mathematics and Computers in Simulation
Complex dynamics and synchronization of a duopoly game with bounded rationality
Mathematics and Computers in Simulation
SIAM Journal on Scientific Computing
Detecting simple dynamics in Cournot-like models
Journal of Computational and Applied Mathematics
A note on the equilibria of an economic model with local competition “à la Cournot”
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
| Hi-index | 7.29 |
We consider a discrete map proposed by M. Kopel that models a nonlinear Cournot duopoly consisting of a market structure between the two opposite cases of monopoly and competition. The stability of the fixed points of the discrete dynamical system is analyzed. Synchronization of two dynamics parameters of the Cournot duopoly is considered in the computation of stability boundaries formed by parts of codim-1 bifurcation curves. We discover more on the dynamics of the map by computing numerically the critical normal form coefficients of all codim-1 and codim-2 bifurcation points and computing the associated two-parameter codim-1 curves rooted in some codim-2 points. It enables us to compute the stability domains of the low-order iterates of the map. We concentrate in particular on the second, third and fourth iterates and their relation to the period doubling, 1:3 and 1:4 resonant Neimark-Sacker points.