Bifurcations and Chaos in a Nonlinear Discrete Time Cournot Duopoly Game  

作　　者：Ying-hui GAO Bing LIU Wei FENG 

机构地区：[1]School of Mathematics and System Sciences,Beihang University,LMIB of the Ministry of Education [2]Department of Mathematics,Anshan Normal University

出　　处：《Acta Mathematicae Applicatae Sinica》2014年第4期951-964,共14页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Nos.11101021,11372017);the National Scholarship Fund of China(201303070219)

摘　　要：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.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.

关 键 词：discrete Cournot duopoly game BIFURCATION Marotto chaos 

分 类 号：O225[理学—运筹学与控制论]