Dynamical behavior of fractional‐order energy‐saving and emission‐reduction system and its discretization

Abstract

AbstractThis paper attempts to explore dynamical behavior and mathematical properties of the three‐dimensional fractional‐order energy‐saving and emission‐reduction system. Theoretically, the conditions of local stability of fractional‐order system's equilibrium points are obtained. Numerical investigations on the dynamics of this system are carried out, and the existence of the asymptotically stable attractor is found. Combined with the fractional‐order subsystem, we discuss the relationship between energy‐saving and emission‐reduction and economic growth, and carbon emissions and economic growth. Furthermore, we discretize the fractional‐order system and give necessary and sufficient conditions of its stabilization. It is shown that the stability of the discretization system is impacted by the system's fractional parameter. Numerical simulations show the richer dynamical behavior of the fractional‐order system and verify the theoretical results.Recommendations for Resource Managers The impact of carbon emissions on economic growth is one of the main reasons for energy‐saving and emission‐reduction. Control measures on people's low‐carbon life through government intervention are required to protect the natural environment. New energy‐saving and emission‐reduction technologies should be implemented to achieve sustainable social and economic development.