*Article* **Mathematical Modeling and Stability Analysis of a Delayed Carbon Absorption-Emission Model Associated with China's Adjustment of Industrial Structure**

**Leilei Han, Haokun Sui and Yuting Ding \***

Department of Mathematics, Northeast Forestry University, Harbin 150040, China **\*** Correspondence:dingyt@nefu.edu.cn

**Abstract:** Global warming has brought about enormous damage, therefore, some scholars have begun to conduct in-depth research on peak carbon dioxide emissions and carbon neutrality. In this paper, based on the background of China's upgrading industrial structure and energy structure, we establish a delayed two-dimensional differential equation model associated with China's adjustment of industrial structure. Firstly, we analyze the existence of the equilibrium for the model. We also analyze the characteristic roots of the characteristic equation at each equilibrium point for the model, then, we analyze the stability of the equilibrium point for the model according to the characteristic root, and discuss the existence of Hopf bifurcation of the system by using bifurcation theory. Secondly, we derive the normal form of Hopf bifurcation by using the multiple time scales method. Then, through the official real data, we present the range of some parameters in the model, and determine a set of parameters by reasonable analysis. The validity of the theoretical results is verified by numerical simulations. Finally, we use the real data to forecast the time of peak carbon dioxide emissions and carbon neutralization. Eventually, we put forward some suggestions based on the current situation of carbon emission and absorption in China, such as planting trees to increase the growth rate of carbon absorption, deepening industrial reform and optimizing energy structure to reduce carbon emissions.

**Keywords:** carbon absorption-emission model; time delay; multiple time scales method; normal form; Hopf bifurcation

**MSC:** 34K18; 37L10
