Complex Dynamics Of Game Model With Heterogeneous Players

This artical investigates the complex dynamical behaviors of the chaotic game modelin the economic system with heterogeneous players. Firstly, duopoly game chaos modeland triopoly game chaotic model are established.Secondly,utilizing the discrete-time dy-namic system theory, it gets the existence and local stability of the fixed points in theduopoly game chaos model when ν = 0, 0 < ν < 1 and ν = 1, giving the correspondingparameter conditions of it. Thirdly, strictly prove that there is a Flip bifurcation at theNash equilibrium point but no Neimark-Sacker bifurcation.In addition, this paper utilizesthe Jacobi algorithm to calculated the Lyapunov exponent spectrum of the system, andconclude that there is chaos in the system by numerical simulation. At the same time, weuse theory analysis strictly proving the existence and the stability of the fixed point of thetriopoly game chaotic model. Besides, by the numerical simulation, we find that there isa Flip bifurcation at the Nash equilibrium point.After that we find the existence of chaosin the system based on its Lyapunov exponent and the 0-1test. the strictly provings inthis paper improve the quality of the empirical research and can better serve the decisionmakers.The main contents of this paper are as follows.The first chapter introduces the background, significance of the research and themajor works.It outlines a brief review of research and development history of the dynamicsystem, as well as its bifurcation and chaos.Then it gives the basic concepts of the dynamicsystem, the local bifurcation theory, as well as the concept and determination methodsof chaos. On the other hand, it gives a short introduce of the utilization of discrete-timesystem dynamics in the economic and the research status of Oligopoly game model.The second chapter gives the duopoly game chaos model and triopoly game chaoticmodel.The third chapter investigates the local dynamics analysis and chaos existence ofthe duopoly game chaos model when ν = 0, 0 < ν < 1 and ν = 1. It show that thesystem becomes the Logstic system when ν = 0 and gets the corresponding dynamicsproperties.At the same time,we gets the the existence and local stability of the fixed pointsand the corresponding parameter conditions when 0 < ν < 1.moreover,it strictly provesthe existence of the Flip bifurcationat and no Neimark-Sacker bifurcation.moreover,wegives the local dynamics analysis of the system when ν = 1.In addition,it gives theLyapunov exponent spectrum of the system utilizing the Jacobi algorithm, and thenshows the chaos.existence numerically.The last chapter studies the local dynamics analysis and chaos existence of the tri-opoly game chaotic model. it strictly proves the existence of the boundary equilibriumpoint and Nash equilibrium point and discusses the stability of the equilibrium points.Strictly proving shows that there is a Flip bifurcation at the Nash equilibrium point.Itgives the Lyapunov exponent spectrum and Flip bifurcation diagrams.In addition, Lya-punov exponent and 0-1 chaos test are utilized to find out the existence of chaos.