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 stabil -ity, 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 influ-ence 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 enter-prises 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 sys-tem will decrease.(c) 2022 THE AUTHORS. Published by Elsevier BV on behalf of Faculty of Engineering, Alexandria University This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/ licenses/by-nc-nd/4.0/).