**6. Conclusions**

In this paper, considering the competitive relationship between carbon emission and carbon absorption, we set up a new two-dimensional differential equation model with time delay to make some predictions and analyze whether China can achieve it under the current policy, which depends on China's technology research and development level and government policy investment. In practice, the parameters of the model are variable. In order to simplify the problem, the parameters of the model (3) are constant coefficients. At the same time, the model in this paper does not consider too many factors. The simulation process of the model may be different from the real process. For example, the peak value of the simulation will be higher than the future peak value because we have not fully considered the carbon emission reduction measures, but on the whole, the stability of our model is consistent with the actual one. In addition, we theoretically analyzed the existence and stability of the equilibrium and the existence of Hopf bifurcation, and we also derive the normal form of Hopf bifurcation for the system (3) by using the multiple time scales method. After that, we selected a set of data for numerical analysis to verify our theoretical analysis results, we find that equilibrium *E*<sup>3</sup> of system (3) is locally asymptotically stable when *τ* = 0. When *τ* = 3.61, the system (3) has a stable periodic solution near the equilibrium *E*<sup>3</sup> and we find from Figure 4 that the optimization and adjustment of industrial structure and energy structure has an important impetus to China's realization of peak carbon dioxide emissions and carbon neutrality. When the industrial structure is optimized and the energy structure is improved, the time for China to reach peak carbon dioxide emissions will be shortened (see Figure 4).

Next, our numerical analysis also shows that when the natural growth rate of carbon absorption increases, the time for China to achieve carbon peak carbon dioxide emissions will be shortened and the peak value will also decrease (see from Figure 5). From Figure 5, we predict that when the natural growth rate of carbon absorption is 0.3, China will achieve carbon neutrality before 2060. As the natural growth rate of carbon absorption is actually too high, we also need to deepen the industrial reform and optimize the energy structure to reduce the natural growth rate of China's carbon emissions. Therefore, based on the above research, this paper emphasizes planting trees and improving the level of carbon storage technology to improve the natural growth rate of carbon absorption and carbon emission reduction technology, and improving the development and application technology of new energy to achieve in-depth industrial structure adjustment and energy structure optimization. The above measures are of great significance to China's realization of peak carbon dioxide emissions by 2030 and carbon neutrality by 2060.

**Author Contributions:** Writing—original draft preparation: L.H. and H.S.; funding acquisition: L.H., H.S. and Y.D.; methodology and supervision: Y.D. All authors have read and agreed to the published version of the manuscript.

**Funding:** This study was funded by Fundamental Research Funds for the Central Universities of China (No. 2572022DJ06) and College Students Innovations Special Project funded by Northeast Forestry University of China (No. 202210225155).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The authors confirm that the date supporting the findings of this study are available within the article.

**Conflicts of Interest:** All authors declare no conflict of interest in this paper.
