| This paper studies the dynamic evolution of the Cournot duopoly model,the Cournot-Bertrand triopoly model,and the multi-market Cournot duopoly model based on the technology licensing.It focus on the impact of parameters such as royalty fees,technology innovation degree,and constant marginal cost on patent-holding firm and patent-accepting firm.Based on relevant research results at home and abroad,this paper applies Game Theory,Dynamic Economics Theory,and nonlinear dynamics theory,starting from two aspects of theoretical and numerical simulation,and analyzes the local and global properties.The main research results and innovative contents of this paper are as follows:1.Taking the technology licensing as the background,based on the assumption of bounded rationality,the duopoly model of producing homogeneous products and using output as a decision variable is analyzed.Theoretically,we discuss the local stability of equilibrium point and give the local stability inequality condition for Nash equilibrium point.From the aspect of numerical simulation,it mainly discusses the global dynamic results about the changes in the degree of technological innovation and royalty fees to the whole model.The first is to study the emergence of two types of intermittent chaos with the change of technological innovation,namely PM-I type intermittent chaos and crisis-induced intermittent chaos.The appearance of intermittent chaos means that the market economy has a self-regulating mechanism and can be adjusted to a stable state without external forces.Secondly,it analyzes the influence of the degree of technological innovation on the change law of the feasible trajectory boundary.In the process of increasing the degree of technological innovation,the feasible trajectory boundary tends to be larger in the direction of abscissa and ordinate axes.However,there are "holes" inside the feasible trajectory.Finally,there is the impact of the royalty fees on the system.It is found that the coexistence of attractors.After the contact bifurcation between the attractor and the attractor basin,a group of attractors disappear,but there are still "ghost" attractors in the basin,and accompanied by the transient phenomenon.2.We focused on the emergence of patent-holding firm and patent-accepting firm in the the Cournot-Bertrand triopoly model with different decision.Through theoretical analysis,the local stability of the fixed point is discussed.The condition of local stability of the Nash equilibrium point is given by using the Jury criterion.Two-dimensional phase diagrams are used to explore the two paths of the model to chaos,namely the halving-period bifurcation and the Neimark-Sacker bifurcation.The numerical simulation fully reflects the characteristics of the different paths to chaos with the one-dimensional bifurcation diagram and the largest Lyapunov exponent diagram of the fee.In addition,the evolution of the attractor when the Neimark-Sacker bifurcation occurs is also analyzed.On the other hand,considering that technology-owned firm occupy absolute advantages in market competition,and two technology-accepting firms are equal,this paper mainly analyzes the synchronization phenomenon between the two technology-accepting firms.Four chaotic attractors appear on the diagonal.Even if the initial conditions are not on the diagonal,they will converge to the diagonal after a infinite number of iterations.With the change of royalty fees,the stability of the constant space changes,and accompanied by On-off intermittent phenomena.3.Study a multi-market duopoly model.Due to the different quality of the products produced by the two firms,they compete in the A and B markets respectively.Theoretically,the local stability of the fixed point is discussed.Because the local stability of the four-dimensional Nash equilibrium is more complicated,the conditions of local stability of the Nash equilibrium are given by using the Schur-Cohn criterion.On the other hand,the effects of royalty fees and constant marginal costs on the dynamic evolution of the A and B markets are studied from numerical simulations.Among them,the firm signed a royalty licensing in the A market.From the perspective of the one-dimensional bifurcation diagram group,the increase in the royalty fee will allow the A market to maintain a stable state in a larger range.Although the large royalty fee is not good for firm 2,it means that firm 1 has an absolute advantage in the A market.For the study of the B market,from the analysis of the two-dimensional bifurcation diagram and the one-dimensional bifurcation diagram,the smaller constant marginal cost will make decision makers more uncertain about the changing laws of the economic market.In fact,this also implies that the B market of the two firms are in a relatively equal in the market competition.Finally,the Delayed Feedback Control is used to chaos control the entire market.As long as appropriate control parameters are obtained,the market can obtain effective chaos control. |
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