| As the main body of our country’s economy,the manufacturing industry has been plagued with high pollution and energy dissipation.Encouraging manufacturing enterprises to adopt low-carbon innovation technology is the only way for our country to realize low-carbon economic development.The formation process of enterprise strategy is a process of constant adjustment and trial and error.Enterprise decision makers will formulate basic strategic direction based on previous experience as the basis of adjustment and trial and error.Enterprise decision-making process not only has the characteristics of irrationality,but also has the characteristics of long memory.In this paper,a fractional evolutionary game model for green low-carbon innovation in manufacturing enterprises is established,and the fractional replication dynamic equation is used to describe the process of learning and adjusting strategies of the finite rational game parties.This model is closer to reality and conforms to the actual law.In Chapter 1,it mainly introduces the research background and significance,analyzes the research status of enterprise low-carbon innovation technology decision and the research status of fractional calculus application.Secondly,it expounds the main innovation points of the article.Finally,it introduces the basic theoretical knowledge,including the basic theory of evolutionary game and the basic concept of fractional differential equation.In Chapter 2,the fractional evolutionary game model of green low-carbon innovation in manufacturing enterprises is constructed,and the dynamic characteristics of the model are analyzed.Firstly,the existence and uniqueness of evolutionary dynamic solutions are proved by using the principle of compression mapping.Secondly,the local asymptotic stability of equilibrium points of fractional order system is analyzed according to Matignon condition,and the evolutionary stability strategy of game is found out.Finally,Lyapunov function is constructed and Caputo fractional Lyapunov inequality is used to analyze the global stability of equilibrium points.In Chapter 3,he discretization form of fractional evolutionary game model for green low-carbon innovation in manufacturing enterprises is studied,and the evolutionarily stable strategy of the discretization game is found out.At the same time,sensitivity equation is established to analyze the parameters of the system.Finally,the influence of the change of key parameters on the evolutionary stability strategy is analyzed by numerical simulation.From the phase diagram and bifurcation diagram of different parameters,it is found that only by obtaining excess returns through green and low-carbon innovation technology can enterprises develop into a stable situation in which all enterprises adopt green and low-carbon innovation technology.The results also show that reducing the fractional order increases the rate of evolution to an evolutionarily stable strategy.In Chapter 4,the full text is summarized and the future work is prospected. |
