| In this paper,the dynamic game models of innovative enterprises and general enterprises are studied,and the stability characteristics and global bifurcation behaviors of the system are taken as the research focus.The roles of enterprise adjustment speed,R&D spillover coefficients and product differentiation degree on the local and global bifurcation behaviors of the model are analyzed.The main contents include:1.Based on the hypothesis of bounded rationality,a Cournot duopoly game model with nonlinear inverse demand function and R&D spillover is established.Numerical simulation shows that the Nash equilibrium of the system can only enter chaos via a flip bifurcation.The complexity of the model is analyzed by means of two-dimensional bifurcation diagrams,largest Lyapunov exponent,critical curves and basin of attraction.The results show that for the identical enterprise,a small disturbance of parameters will lead to the asymptotically synchronous or asynchronous system,and the appearance and disappearance of coexisting attractors are also related to the change of parameters.The evolution of the global properties of the system with the change of parameters is analyzed by the critical curves.2.A duopoly model with nonlinear demand and cost about R&D spillover is studied.The system is symmetric when two firms have same economic environments,and it is proved that the diagonal and coordinate axes are one-dimensional invariant manifolds of system.The results show that Milnor attractor of system can be obtained through transverse Lyapunov exponents.The synchronization scenarios are verified by the basins.The parameters adjustment speed and R&D spillovers are discussed respectively.The topological structures of attracting basin are analyzed by critical curves technique,and the evolution process of "holes" in the feasible region is numerically simulated.Various global bifurcation behaviors are shown,such as two kinds of contact bifurcation and the blowout bifurcation caused by the transverse Lyapunov exponent changing sign.3.Based on technology licensing and mixed competition,a three oligarch game model is established,in which enterprise 1 is assumed to obtain a technology breakthrough and a patent first.Enterprise 1 implements a patent licensing strategy that does not allow bargaining between enterprise 2 and enterprise 3.Numerical results are used to reveal the complex dynamic evolution behaviors of the system when the equilibrium loses stability.It is found that in the quasi-periodic region,with increasing the adjustment speed parameter,the periodic oscillation evolves progressively intense.Through a series of numerical simulations such as the basin of attraction,the local synchronous dynamic behaviors of firm 2 and firm 3 are discussed.The critical curve,which is a tool for studying the global dynamics of two-dimensional noninvertible map,is applied to the study of chaotic synchronization and its related riddlled attracting domain,generation and disappearance of attractors and switching intermittence under three-dimensional noninvertible maps.4.A Cournot duopoly model with equal elastic demand and different levels of costs is studied.Because the system loses its smoothness,the local properties of the system produce a series of dynamic phenomena with the change of many factors.The main research tools are2-D bifurcation diagram,3-D maximum Lyapunov exponent diagram and so on.In the control plane of these parameters,chaotic oscillation and periodic behaviors generate alternately,forming the self similar structure of the system.The results display the stability of the system increases by increasing adjustment speed,and the smaller it is,the more complex the final state of the system is.The whole system is unstable,the amplitude and system loss are large,and the risk of the whole market becoming uncontrollable is high.The evolution process is deterministic and irregular,and the internal structure of the strange attractor is gradually complicated by the evolution of the reverse flip bifurcation. |
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