宏观交通流模型的余维2分岔分析

The traffic flow characteristics are an important factor in mixed traffic flow modeling. The bifurcation in the traffic flow model is one of the issues related to the complex traffic phenomena. The bifurcation phenomenon of traffic flow models involves complex dynamic characteristics and is rarely studied. Therefore, an optimal velocity model is proposed to study the effects of driver's memory on driving behavior. Based on the optimal velocity continuous traffic flow model with memory, we analyze and predict complex traffic phenomena by using nonlinear dynamics. The conditions for the existence of LP bifurcation are derived. We numerically obtain codim-1 Hopf (H) bifurcation, LP bifurcation and homoclinic (HC) bifurcation, and codim-2 generalized Hopf (GH) bifurcation, cusp (CP) bifurcation and Bogdanov-Takens (BT) bifurcation. According to the characteristics of two-parameter bifurcation regions, the influence of memory parameters on the one-parameter bifurcation structures is studied, and the influence of different bifurcation structures on traffic flow is analyzed. The phase plane is used to describe the variational characteristics of the trajectories near the equilibrium point. Selecting the Hopf bifurcation and saddle-node bifurcation as the starting point of density evolution, we describe the uniform flow, stable and unstable crowded flow and stop-and-go phenomena. Further, these outcomes can improve the understanding of go-and-stop waves and local clusters observed on highways. The results show that the driver's memory plays an important role in the stability of the traffic flow. Dynamic behavior can well explain the complex phenomenon of congested traffic. The source of traffic congestion can be better understood by considering the impact of codim-2 bifurcation. The results in this paper can provide some theoretical methods for the suppress traffic congestion.