Complex Dynamics Analysis Of Duopoly Game Model Under Technology Authorization

With the rapid development of economy,the market demand for enterprises is more and more strict,and the production enterprises need to meet the requirements of low cost,high output and environmental protection.Therefore,it is a great challenge for enterprises in terms of production technology.Many enterprises adapt to development through technological innovation.However,most enterprises cannot meet the conditions of self-technological innovation,so the issue of technology authorization has been widely concerned.In this paper,relevant knowledge of nonlinear dynamics and game theory is used to study technology authorization in Cournot Duopoly model.The main contents are as follows:1.Based on bounded rationality,the output competition model of green production enterprises with social welfare is established,and the influence of each parameter on the stability of equilibrium point of the system is explored theoretically.The effects of the parameters on the stability of the system are studied by using the 1-D bifurcation diagram,the attractor and the evolution of the basins of attraction obtained by numerical simulation.Through the 2-D bifurcation diagram,it is observed that the path into chaos can be Flip bifurcation or Neimark-Sacker bifurcation.Through the study of the 1-D bifurcation,it is found that the faster the enterprise adjusts the output of the next period,the higher the degree of privatization of the enterprise,it may cause market chaos.The increase of carbon emission level in the production process is easy to fall into an unpredictable state for the game market.Attractors coexist at the jump point of the 1-D bifurcation diagram.By making small changes to government subsidies,the pattern of attractors changes dramatically.2.We discuss the duopoly game model of partially privatized firm and fully privatized firm producing homogeneous products based on bounded rationality.Partially privatised enterprises receive technology authorizing and spend less money in the production process.The stability conditions of each equilibrium point are discussed.The authorizing cost,production cost,enterprise privatization degree,enterprise adjustment speed influence on the system is discussed,through 1-D bifurcation diagram,2-D bifurcation diagram,the basins of attraction,etc..It is found from the bifurcation curve that the stability region of Nash equilibrium decreases obviously with smaller authorization cost.In addition,when the authorization cost is used as the bifurcation parameter,contact bifurcation occurs between the attractor boundary and the critical boundary,resulting in "holes" in the basins of attraction.When the attractor and the boundary of basins of attraction contact,"boundary crisis" occurs.At the same time,by observing the two parameters bifurcation diagram,it is found that there are stray points near chaos,and the attractors coexist phenomenon is verified.Small adjustments in the parameters,the reaction in the system is dramatic.3.Cournot duopoly model with isoelastic demand function is established.One is a technology research and development company chooses to license new technology to another company in order to reduce production costs.Firstly,the local stability of the equilibrium points is discussed and the stability conditions of three practical equilibrium points are calculated.Secondly,through numerical simulation,1-D bifurcation diagram,2-D bifurcation diagram and the basins of attraction are used to vividly demonstrate the impact of authorization cost and adjustment speed on the system.Finally,when the adjustment speeds of the two enterprises are adjusted at the same time,the change of the critical boundary leads to the change of the overall shape of the basins of attraction and the evolution process of the "holes" in the basins of attraction is caused by the contact bifurcation of the system.When the parameter exceeds the critical value,the final bifurcation will occur.It is found that the greater the authorizing cost of the technology owner enterprise,the more detrimental to the stable operation between the two enterprises.When two enterprises adjust the output of the next period of time too fast or too slow,it is not conducive to establish a win-win competitive environment.