*5.1. Determination of Parameter Values*

Firstly, we present the carbon emissions from 2000 to 2018 (see Table 2).


**Table 2.** Annual carbon emission data (the unit of carbon emission is 102 million ton).

Based on the data in Table 2, we analyze the peak value and peak time of China's carbon emissions and also predict the amount of carbon emissions in 2022. We use carbon emissions data from 2000 to 2018 (Table 2) to simulate a quadratic function of carbon emissions over time, as shown in Figure 1. Figure 1 shows that the maximum value will appear around 2029, with a value of 13.8135 billion tons. Each hollow red circle in Figure 1 represents the real data of annual carbon emissions, the black curve represents the quadratic function simulation of these data, and the red hollow five pointed star represents the simulated maximum value. Then, we assume that the predicted maximum value is the peak value of carbon emissions, namely, maximum = *m*. We have also reasonably predicted the carbon emissions in 2022, which will be 13.2087 billion tons. In this way, the peak of carbon emissions can be achieved before 2030, which is consistent with the national policy requirements.

**Figure 1.** Carbon emission data from 2000 to 2018 and fitting curve.

Therefore, because the meaning of parameter *m* in model (3) is the maximum peak value of carbon emissions, combined with Figure 1, we take *m* = 138.135.

Next, we assume that this year's natural growth rate is the difference between this year's carbon emissions and last year's carbon emissions divided by last year's carbon emissions, that is, *<sup>a</sup>*1,*<sup>j</sup>* <sup>=</sup> *xj*−*xj*−<sup>1</sup> *xj* (*<sup>j</sup>* = 2001, 2002, ···), and we calculated the annual natural growth rate of carbon emissions and simulated it with a first-order function curve. Each blue asterisk in Figure 2 represents the natural growth rate of carbon emissions each year, and the blue line represents the simulation image of a function of these data, as shown in Figure 2.

**Figure 2.** Analysis of the natural growth rate of carbon emissions and fitting curve.

Figure 2 shows that 2029 is the last year when the natural growth rate of carbon emissions is positive with 0.09%, and it turns negative by 2030 with −0.35%.

It is common sense that the maximum capacity of carbon emissions should be greater than the peak of carbon emissions, carbon absorption is the same, so we choose *N*<sup>1</sup> = 2*m* = 276.27, *N*<sup>2</sup> = 1.1*m* = 151.9485, whose units are both 10<sup>2</sup> million ton. Since we chose a competitive model, we chose competition factors of *S*<sup>1</sup> = 2 and *S*<sup>2</sup> = 0.5 to make carbon emissions and carbon sequestration competitive. We assume natural growth rate of carbon emissions of between 0.14 and 0.05, thus, we choose *a*<sup>1</sup> = 0.14, *a*<sup>2</sup> = 0.2, *k* = 0.5. Based on the above analysis, we take one group of parameters as follows,

$$a\_1 = 0.14, \ a\_2 = 0.2, \ k = 0.5 \text{ S}\_1 = 2 \text{ S}\_2 = 0.5 \text{ N}\_1 = 276.27, \ N\_2 = 151.9485, \ m = 138.135.$$
