## 3 Simulation Analysis of Interdependent Networks  
In this paper, in the simulated airspace of 300 km \(\times\) 300 km \(\times\) 10 km, 180 aircraft are generated as nodes in MATLAB software according to 20 aircraft per sector, and a total of 9 control sectors with the range of 100 km \(\times\) 100 km \(\times\) 10 km are constructed in accordance with the requirements in the Civil Aviation Administration of China (CAAC)'s \"Reference Study Materials on Fatigue Management for Civil Aviation Controllers\". Considering the actual flight operation, the speed of the aircraft is set: the instantaneous speed is 800 km/h and the heading is 0-360\({}^{\circ}\). To simulate the situation in general airspace, the distribution of aircraft positions is set to follow a uniform distribution. The flight conflict network is modeled for this airspace, and the modeling results are shown in Figure 7.  
The adjacency matrix of the interdependent network is used to describe the adjacency and edge rights of the interdependent network according to the rules for setting the  
Figure 7: Flight conflict network. **(a)** 3D conflict network diagram. **(b)** Plane conflict network diagram. In Figure (a), all three colored circles indicate randomly generated aircraft in the hypothetical airspace. The orange and yellow ones indicate aircraft flying horizontally in the lower and upper boundaries of the airspace. The blue ones indicate aircraft flying in the middle range.  
adjacency and edge rights of the intra-layer and inter-layer networks in the interdependent network.  
Adjacency matrix of the flight conflict network.  
\[A_{G1}=\begin{cases}0&0&0&0&0&\cdots&0\\ \vdots&\vdots&\vdots&\vdots&\vdots&\ddots&\vdots\\ 0&0&0.451&0&0&\cdots&0\\ 0&0&0&0&0&\cdots&0\\ 0&0.807&0&0&0&\cdots&0\\ \vdots&\vdots&\vdots&\vdots&\vdots&\ddots&\vdots\\ 0&0&0&0&0&\cdots&0\end{cases}\]  
The adjacency matrix is a \(180\times 180\) matrix, which represents the edge rights between two aircraft nodes.  
Adjacency matrix of the control network.  
\[A_{G2}=\begin{cases}0&1&0&1&0&0&0&0&0\\ 1&0&1&0&1&0&0&0&0\\ 0&1&0&0&0&1&0&\cdots&0\\ 1&0&0&0&1&0&1&\cdots&0\\ 0&1&0&1&0&1&0&\cdots&1\\ 0&0&0&1&0&0&0&\cdots&0\\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\ddots&\vdots\\ 0&0&0&0&1&0&\cdots&0\end{cases}\]  
The adjacency matrix is a \(9\times 9\) matrix, which represents the continuous edge relationship between the control sectors. If there is a control handover relationship, then \(a_{ij}=1\); conversely, \(a_{ij}=0\).  
Adjacency matrix of the interdependent network.  
\[A_{G}=\{A_{G1}+A_{G2}+A_{E12}\}\] \[=\begin{cases}0&0&0.819&\cdots&0&1.456&\cdots&0\\ 0&0&0&\cdots&0&0&\cdots&0.086\\ 0.819&0&0&\cdots&0&3.431&\cdots&0\\ \vdots&\vdots&\vdots&&&\vdots&&\vdots\\ 0&0&0&\cdots&0&0&\cdots&0\\ 1.456&0&3.431&\cdots&0&0&\cdots&0\\ \vdots&\vdots&\vdots&&&\vdots&\ddots&\vdots\\ 0&0.086&0&\cdots&0&0&\cdots&0\end{cases}\]  
The matrix a is a \(189\times 189\) matrix that represents the weights of the dependent edges of the interdependent network. The \(180\times 180\) matrix at the top left is the weighted adjacency matrix of the aircraft network, the \(9\times 9\) matrix at the bottom right is the adjacency matrix of the control network, and the matrices at the bottom left and top right are transposed matrices of each other, both of which indicate the weights of the connected edges between the layers of the interdependent network.