Nonlinear Dynamic Analysis of Air Traffic Flow at Different Temporal Scales: Nonlinear Analysis Approach versus Complex Networks Approach

Insights into the temporal-spatial characteristics of air traffic flow is the prerequisite of air traffic flow modeling, prediction and optimization. The intrinsic dynamics of air traffic flow were analyzed according to radar track data by classical nonlinear analysis and complex network methods. The nonlinear dynamic characteristics of air traffic flow were revealed from multiple perspectives by means of phase space reconstruction, recurrence plot, Lyapunov exponent, correlation dimension and Hurst exponent. The experimental results show that the example traffic flow became the most chaotic and the state persistence was poorest at time scale of 30 min. Besides, this paper explored the application of a complex network to analyze the nonlinearity of air traffic flow, and verified the chaotic and fractal characteristics by analyzing the degree distribution of the converted network. The degree distribution of the network derived from the traffic flow time series was approximately fitted to the exponential function and featured a strength level of chaos that was positively correlated with the size of network degree distribution power exponent. The linear relationship between network degree distribution power exponent and Hurst exponent was revealed, and the nonlinearity of air route traffic flow was systematically characterized. Particularly, the complex network-based analysis method helped examine air traffic flow from a new perspective, enriching the research means. These novel findings will provide theoretical basis for aggregated air traffic flow modeling, decision support system design and tactical flow management.