## 4 Simulation Experiment and Analysis
### Experimental Explanation
The Impact of the Number of Control Nodes on the Anti-Destructive Ability of the Air Traffic Control Network  
In this set of experiments, when the control capacity \(n\) of the control nodes \(V_{cm}\) is determined, with the increase of the initial number of failed nodes \(N_{fail}\), the final number of failed nodes \(N_{lose}\) and the load failure threshold value \(\gamma\) of the system were compared under different numbers \(N_{cm}\) of control nodes \(V_{cm}\) when the cascading failure ended and the network reached the final steady state. Taking Figure 8a as an example, it can be analyzed that, from top to bottom, the numbers of control nodes are 2, 4, 100, and 200, respectively. With the increase of the number of control nodes, the initial cascading failure rate of the network decreases, and the fewer final failed nodes are caused under the same initial number of failed nodes. The load failure threshold value of the system is higher for the system with more control nodes. When the network is close to complete destruction, the cascading failure rate of the system with more control nodes decreases to 0 later. In summary, as shown in Figure 8a,b, when the control capacity of the control nodes in the air traffic control network is determined, with the increase of the number of control nodes, the number of control dependency edges provided by the control nodes to the air route facility network nodes increases. The cascading failure rate of the network decreases, enhancing the anti-destructive ability of the air traffic control network. The results show that, by increasing the number of control positions in the control coordination network, the cascading failure rate of the network can be reduced, which can improve the anti-destructive ability of the air traffic control network and enhance its ability to resist cascading failures. From the conclusions of Sections 4.2 and 4.3, it can be seen that, when the control capacity of the control nodes is enhanced and the number of control nodes is increased, it is equivalent to increasing the control cost of the air traffic control network from two different aspects, which is beneficial to improving the anti-destructive ability of the air traffic control network. Figure 7: The relationship between network anti-destructive ability and control capacity of control nodes. (**a**) The total number of nodes is 1000. (**b**) The total number of nodes is 2000. (The curves shown in the circle represent the study of the maximum control capacity of control nodes under ideal conditions. Each curve in the figure represents the average result of 25 rounds of random attacks on 10 model networks). The Impact of the Control Capacity and the Number of Control Nodes on the Anti-Destructive Ability of the Air Traffic Control Network  
In this set of experiments, when the control cost \(\theta\) is determined, with the increase of the initial number of failed nodes \(N_{fail}\), the final number of failed nodes \(N_{lose}\) and the load failure threshold value \(\gamma\) of the system were compared under different conditions when the cascading failure ended and the network reached the final steady state. Taking Figure 9a as an example, it can be analyzed that, with the control cost of the air traffic control network determined, from top to bottom, the control capacities of the control nodes are 50, 250, and 500, respectively. With the increase of the control capacity and the decrease of the number of control nodes, the initial cascading failure rate of the network decreases, and the fewer final failed nodes are caused under the same initial number of failed nodes. The load failure threshold value of the system is higher for the system with stronger control capacity. When the network is close to complete destruction, the cascading failure rate of the system with stronger control capacity decreases to 0 later.