## 4 Result and Discussion
### Stability Analysis
The specific situation is shown in Figure 2.  
Situation 1: when \(H<0\), \(I<0\), \(S<0\), \(T<0\), there exists a unique evolutionary stabilization strategy (0,0), (0,1) and (1,0) are the saddle points of the system, and (1,1) is the point of instability. Situation 2: when \(H<0\), \(I<0\), \(S>0\), \(T<0\), there exists a unique evolutionary stabilization strategy (0,0), (0,1) and (1,1) are the saddle points of the system, and (1,0) is the point of instability. Situation 3: when \(H>0\), \(I<0\), \(S<0\), \(T<0\), there exists a unique evolutionary stabilization strategy (0,0), (1,0), and (1,1) are the saddle points of the system, and (0,1) is the point of instability. Inference 1: When \(I<0\), \(T<0\), the evolutionarily stable strategy of the system is (0,0), excluding the case where \(H>0\), \(I>0\). For the local government, if the value-perceived benefit of performing deregulation is greater than the benefit of choosing strict regulation, then the local government will tend to perform deregulation. For the coal mining enterprise, the perceived benefit of not implementing intelligent construction is greater than that of full implementation. When the government does not tighten control, and the external social attention is at the bottom, the enterprise will tend not to implement intelligent construction. The final evolutionary stable strategy is [not implemented, deregulation], and the specific evolutionary trend is shown in Figure 3a,c,i. For the local government, as long as the central government enhances the monitoring of the local government and actively pushes the enforcement of the relevant policies, the perceived benefit of strict supervision by the local government is greater than the benefit of relaxed supervision, and the local government will choose the strategy of strict supervision. For coal mining enterprises, although the local government strictly enforces the relevant policies and regulations, the relevant reward and punishment mechanism is set up in vain, coupled with the external society's lower concern for the internal administration of the enterprise, then the perceived benefit of the enterprise choosing not to carry out the intelligent construction is greater than the benefit of the active construction. The coal mining enterprise will tend to refrain from conducting intelligent construction. The final evolutionary stable strategy is [not implemented, strict supervision], and the specific evolutionary trend is shown in Figure 3b,d,h. Inference 3: When \(H>0\) and \(S>0\), the evolutionary stability strategy for the system can be expressed as (1,1), except for the case where \(I<0\) and \(S<0\). In the context of local government, if the higher government department demonstrates a high level of attention to the operation and construction of the local government and enhances the management and standardization of the system, the value gained by the local government in implementing strict regulation is greater than the gain of deregulation. Consequently, the local government will opt for strict regulation. In the context of coal mining enterprises, the value gain of a fully implemented intelligent construction system outweighs that of a negative implementation. This is particularly true when the local government strictly regulates and integrates a reward and punishment system. Consequently, the enterprise will choose to implement intelligent construction fully. The final evolutionary stabilization strategy is [full implementation, strict regulation], and the specific evolutionary trend is shown in Figure 3l,o,p. Inference 4: When \(I>0\), \(S<0\), and excluding the case where \(H<0\) and \(T>0\), the evolutionarily stable strategy of the system is (1,0). Figure 3: Phase diagram of coal mine replicator dynamics equation. (**a**) is the case where \(H\), \(I\), \(S\) and \(T\) are all less than zero. (**b**) is the case where \(H\), \(I\), \(S\) are all less than zero; \(T\) is greater than zero. (**c**) is the case where \(H\), \(I\), \(T\) are all less than zero; \(S\) is greater than zero.