Affiliation:
1. Department of Computer Science & Engineering, Northwest Normal University, Lanzhou, Gansu, P. R. China
2. College of Electrical Engineering, Lanzhou Institute of Technology, Lanzhou, Gansu 730050, P. R. China
Abstract
Based on the new macroscopic two-velocity difference model, this paper analyzes the linear stability of the new model and studies the nonlinear bifurcation theory. First, the linear stability analysis method is used to study the stability conditions of the shock wave in the model. Then, considering the long wave model in the coarse-grained scale, the reduced perturbation method is used to analyze the characteristics of the traffic flow in the metastable region, and the solitary wave solution of the Korteweg-de Vries (KdV) equation in the metastable region is derived. In addition, by using the bifurcation analysis method, the type, and stability of the equilibrium solution are discussed and the existing conditions of the saddle-node bifurcation are proven. Then, taking the saddle-node bifurcation as the starting point, we draw the density space-time diagram and phase plane diagram of the system. It is proven that the newly proposed model can describe complex traffic phenomena such as stop-and-go and sudden changes in stability, which is of great help to solve traffic congestion.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Gansu Province of China
China Postdoctoral Science Foundation Funded Project
Qizhi Personnel Training Support Project of Lanzhou Institute of Technology
Gansu University Innovation Fund Project
Publisher
World Scientific Pub Co Pte Ltd
Subject
Physics and Astronomy (miscellaneous)
Cited by
3 articles.
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