基于复杂网络的空中交通流分形特征分析

为准确把握空中交通流量变化规律，掌握空中交通系统内在特性，需要对空中交通流时间序列进行基于复杂网络的分形特征分析。收集空中交通流量数据，利用可视图方法构建复杂网络模型，分析网络拓扑结构，验证了该网络度分布服从幂律分布，拟合直线斜率为-2.086,证明了网络是无标度网络，具有单分形特征。验证了覆盖整个网络所有节点所需要的最少盒子数目与盒子直径成幂律关系，拟合直线斜率为-0.212 1,相关系数为-0.872 2,再次证明了网络具有单分形特征。通过验证网络广义分形维数关于参数的图像为非线性，拟合直线斜率分别为-1.942、-1.936、-1.78,相关系数均在0.8以上，拟合效果较好，证明了网络具有多重分形特性。通过计算重整化前后网络的幂指数相似，证明了网络具有自相似性。结果表明，应用复杂网络的理论分析空中交通流时间序列是可行有效的，为进一步深入应用研究奠定了基础。

Fractal Characteristics Analysis of Air Traffic Flow Based on Complex Network

In order to accurately grasp the changing law of air traffic flow and the inherent characteristics of the air traffic system, it is necessary to analyze the time series of air traffic flow based on fractal characteristics of complex networks. The air traffic flow data was collected, a complex network model was constructed using the visual graph method, and the network topology was analyzed. It was verified that the degree distribution of the network obeyed a power-law distribution, and the slope of the fitted straight line was -2.086, which proved that the network is a scale-free network with a single Fractal features. It is verified that the minimum number of boxes required to cover all nodes in the entire network has a power-law relationship with the diameter of the box. The slope of the fitted line is -0.2121, and the correlation coefficient is -0.8722, which again proves that the network has monofractal characteristics. By verifying that the image of the network generalized fractal dimension with respect to the parameters is nonlinear, the slopes of the fitting lines are -1.942, -1.936, and -1.78, respectively, and the correlation coefficients are all above 0.8. The fitting effect is good, which proves that the network has multifractal characteristics. . By calculating the similarity of the power exponents of the network before and after renormalization, it is proved that the network has self-similarity. The results show that it is feasible and effective to apply the theory of complex network to analyze the time series of air traffic flow, which lays a foundation for further in-depth application research.