| Based on the advantages of quantum game theory that classical games do not have,this paper establishes a nonlinear oligopoly dynamic model under quantum game.The influence of different parameters on the local and global stability of the established model is analyzed,and the complex dynamic behavior in the evolution of the system is studied in detail.The main contents of this paper are as follows:1.Under the introduction of quantum entanglement parameter,a dynamic oligopoly game model based on linear demand is established.Through calculation,it is concluded that there are four equilibrium points in the model,and the local stability of the four equilibrium points is analyzed by stability theory.The influence of different parameters on the stability of the system is analyzed by numerical simulation,and the bifurcation behavior of the system is studied in detail.The final asymptotic behavior of the system is discussed using the attractor,and the gradual change of parameters can lead to the complexity of the final behavior for the system.In addition,the evolution of the co-existing attractor is studied using the basin of attraction.The boundary of the feasible region is studied through the theory of critical boundary and irreversible mapping,and the formation of "hole" in the basin of attraction is deeply analyzed.2.Based on the isoelastic demand function,the static quantum Cournot duopoly game model is first established,and the relationship between corporate profits and quantum entanglement is analyzed theoretically,supplemented by the profit change diagram for verification.Then the gradient adjustment mechanism is used to establish a dynamic game model,and the Jury criterion is used to analyze the stability conditions of Nash equilibrium point.The type of bifurcation curves is proved by the theory of conic curve and verified numerically.The path of the system to chaos is analyzed by using two-parameter bifurcation graph,single-parameter graph and maximum Lyapunov exponent graph.The multistable state and contact bifurcation behavior are analyzed using the basin of attraction.In addition,theoretical and numerical aspects of the developed model are compared with other models.3.Establish a quantum Cournot oligopoly game model with quadratic costs when two firms produce differentiated products.By studying the nonnegativity of the equilibrium point,the existence of the equilibrium point is proved and its stability condition is analyzed.The local bifurcation behavior of the system is studied using two-dimensional and singleone-dimensional graphs.Through the single-parameter graph,we analyze the influence of each parameter on the system state,and analyze the change of enterprise profit.The multi-stability of the system is analyzed by the basin of attraction and the critical boundary,and the specific evolution。In addition,the dynamical behavior of the system in the case of symmetric information is discussed.The invariant set and the natural transversely Lyapunov exponent are used to study the synchronization behavior,find the weak attractor in the sense of Milnor,and also analyze the complex structure of the attractor. |
