Bifurcations and chaos in a nonlinear discrete time Cournot duopoly game |
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Authors: | Ying-hui Gao Bing Liu Wei Feng |
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Institution: | 1. School of Mathematics and System Sciences, Beihang University, LMIB of the Ministry of Education, Beijing, 100191, China 2. Department of Mathematics, Anshan Normal University, Anshan, 114007, China
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Abstract: | A nonlinear discrete time Cournot duopoly game is investigated in this paper. The conditions of existence for saddle-node bifurcation, transcritical bifurcation and flip bifurcation are derived using the center manifold theorem and the bifurcation theory. We prove that there exists chaotic behavior in the sense of Marotto’s definition of chaos. The numerical simulations not only show the consistence with our theoretical analysis, but also exhibit the complex but interesting dynamical behaviors of the model. The computation of maximum Lyapunov exponents confirms the theoretical analysis of the dynamical behaviors of the system. |
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Keywords: | discrete Cournot duopoly game bifurcation Marotto chaos |
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