## 4 Simulation Experiment and Analysis
### Experimental Explanation
To reflect the anti-destructive ability of the air traffic control network, the load failure threshold value \(\gamma\) of the system is defined as the minimum initial failure node quantity required for the air traffic control network to reach complete failure:  
\[\gamma=N_{fail}\;when\;N_{lose}=N_{ATM}, \tag{7}\]  
Here, \(N_{fail}\) represents the initial number of failed nodes, \(N_{lose}\) represents the final number of failed nodes, and \(N_{ATM}\) represents the number of nodes in the air traffic control network. The stronger the anti-destructive ability of the network, the smaller the final number of failed nodes \(N_{fail}\) at the steady-state of cascading failure will be, under the same initial number of failed nodes \(N_{lose}\), and the larger the load failure threshold value \(\gamma\) of the system will be. The experimental steps are shown in Algorithm 1. In this paper, the route facility network in the air traffic control network is attacked, and the impact of different attack types and parameters on the resilience of the air traffic control network is observed as the attack intensity and initial number of failed nodes increase. \begin{table}
\begin{tabular}{c c} \hline \hline
**Code Name** & **Meaning** \\ \hline \(N_{c}\) & Number of control coordination network nodes \\ \(N_{cm}\) & Number of control nodes \\ \(N_{ch}\) & Number of coordination nodes \\ \(N_{a}\) & Number of air route facility network nodes \\ \(N_{al}\) & Number of route nodes \\ \(N_{ai}\) & Number of facility nodes \\ \(\theta\) & Air traffic control cost \\ \(\gamma\) & Load failure threshold \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Codes and their meanings in the simulation. The Impact of the Control Capacity of Control Nodes on the Anti-Destructive Ability of the Air Traffic Control Network  
In this set of experiments, when the number of nodes in the network topology of the cascading failure model in the air traffic control network is determined (i.e., \(N_{a}\) and \(N_{cm}\) are 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 control capacities \(n\) when the cascading failure ended and the network reached the final steady state. Taking Figure 7a as an example, it can be analyzed that, from top to bottom, the control capacities of the control nodes are 5, 10, 15, and 500, respectively. With the improvement of the control capacity, 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 values of the system are approximately 7, 30, 40, and 50, respectively, and the load failure threshold value of the system with stronger control capacity is higher. When the network is close to complete destruction, the cascading failure rate of the system with stronger control capacity decreases to 0 later. In summary, as shown in Figure 7a,b, when the number of control nodes is determined, with the increase of the control capacity of the control nodes, the number of control dependency edges provided by the control nodes to the air route facility network nodes increases. The destruction of some dependent edges does not easily cause node failure, and the cascading failure rate of the network decreases, enhancing the anti-destructive ability of the air traffic control network. The results show that, by enhancing the control capacity of each control position 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.