Abstract
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.
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Published in Neliniini Kolyvannya, Vol. 7, No. 2, pp. 255–262, April–June, 2004.
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Stepanenko, O., Maistrenko, Y. & Yousefi, S. Complicated dynamics of an interacting economic model. Nonlinear Oscill 7, 254–261 (2004). https://doi.org/10.1007/s11072-005-0010-1
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DOI: https://doi.org/10.1007/s11072-005-0010-1