Fractional-order evolutionary game of green and low-carbon innovation in manufacturing enterprises

Using a fractional-order replication dynamic equation to describe the process of learning and modifying strategies, this paper tries to develop a fractional-order game model of green and low-carbon (GLC) innovation evolution in manufacturing enterprises. The uniqueness, local stability, and global stability of the evolutionary dynamics are discussed to determine the evolutionary stable strategy (ESS) of the game. The discretized form of the fractional-order game model, the ESS of the discretized game, and the sensitivity analysis of parameters are studied. Then, the influence of variable parameters on the ESS is analyzed using phase diagrams and bifurcation diagrams. The results show that: manufacturing industry can develop into a stable situation where all enterprises adopt GLC innovative technologies if their incomes exceed their investment; decreasing the fractional order of the model, the convergence rate to ESS will increase, but the stability of the system will decrease.