Analysis of Dynamic Behavior of Gravity Model Using the Techniques of Road Saturation and Hilbert Curve Dimensionality Reduction

In this study, we investigate the relationship between parameters and the dynamic behavior of traffic flow in road traffic systems, and we propose a segmented cost function to describe the effects of this flow on the dynamic gravity model at different saturation levels. We use single-parameter bifurcation analysis, maximum Lyapunov exponent calculation, and three-parameter bifurcation analysis to reveal the effects of parameter variations on the nonlinear dynamical behaviors of the modified gravity model, and we investigate the evolution laws of the traffic system in depth. In order to solve the problems of low efficiency and poor visualization ability in traditional dynamics analysis techniques, this paper proposes the Hilbert curve dimensionality reduction technique, which can completely retain the original data features. The three-dimensional pseudo-Hilbert curve is used to traverse the three-parameter bifurcation data, realizing the transformation of data from three- to one-dimensional. Then, the two-dimensional pseudo-Hilbert curve is used to traverse the reduced one-dimensional data, and the two-dimensional visualization of the three-parameter bifurcation diagram is successfully realized. The dimensionality reduction technique provides a new way of thinking for parameter analysis in the engineering field. By analyzing the two-dimensional bifurcation plan obtained after this reduction, it is found that the modified gravity model is more stable compared with the original model, and this conclusion is also verified by the wavelet transform results. Finally, a new robustness evaluation index is defined based on the dynamics of the model, and the simulation results reveal the intrinsic correlation between the saturation parameter and road congestion, which provides an important basis for promoting sustainable transportation in the road network.