Complicated dynamics of an interacting economic model
We study an N-dimensional dynamical system that defines interacting economic models (a so-called quantity-setting oligopoly). Parameter regions of stability of the Nash equilibrium are obtained, and the phase diagram for the stability of the synchronized motion is investigated. We also consider the problem of cluster formation. In particular, the 2-cluster state is studied extensively. A locally stable Nash equilibrium and quasiperiodic motions are present in this state. The regions of stability and the bifurcations of stable trajectories are investigated, and the corresponding bifurcation diagram is obtained.
KeywordsDifferential Equation Dynamical System Phase Diagram Partial Differential Equation Ordinary Differential Equation
Unable to display preview. Download preview PDF.
- 1.Puu, T. 2000Attractors, Bifurcations, and Chaos. Nonlinear Phenomena in EconomicsSpringerBerlinGoogle Scholar
- 2.Rand, D. 1978Exotic phenomena in games and duopoly modelsJ. Math. Econ.5173178Google Scholar
- 3.Ahmed, E., Agiza, H. N. 1998Dynamics of a Cournot game with n competitorsChaos, Solutions Fractals915131517Google Scholar
- 4.Kopel, M. 1996Simple and complex adjustment dynamics in Cournot duopoly modelsChaos, Solutions Fractals720312048Google Scholar
- 5.Agiza, H. N., Bischi, G. I., Kopel, M. 1999Multistability in a dynamic Cournot game with three oligopolistsMath. Comput. Simulat.516390Google Scholar