A Class Of Nonlinear Traffic Flow Model

Currently, the rapid development of the social economy and the relative lag of the transportation infrastructure have been a prominent problem all over the world. The economic expenses and the environment pollutions caused by the traffic congestion become more and more serious. Thus, how to utilize the limited traffic resource adequately and effectively, how to guide the traffic planning, designing, controlling and management with scientific theory, how to alleviate the unbalance traffic supply and demand, all of these become urgent problems. Many traffic flow theories have been developed.The goal of theories study on traffic flow is to establish the traffic flow models that can describe the general properties of the real traffic and to uncover the basic laws of traffic flow. According to the different ways of modelling, the various kinds of models can be classified into microscopic ones and including car-following models and cellular automata models, macroscopic continuum ones and mesoscopic gas-kinetic-based ones. The contents of the paper are as follows.To design video survey method and data proceeding flow, and use this method to obtain traffic basic data. Base on survey effects, this method is found to be costless, while it could obtain abundant, correct and comprehensive data.We present a nonlinear model for traffic flow. The model includes modelling of traffic flow near ramps, where the in/out flux of vehicles are coupled with the mainstream vehicles. The main assumption is that the flux has a finite time response to local density disturbances. The model is composed of two partial differential equations(PDEs) coupled with an ordinary differential equation(ODE). By assuming periodic boundary conditions, the equations are projected to the space of zeroth and the first modal waves via a Galerkin procedure, resulting in a fourth order nonlinear ordinary differential equation. In this truncated model, the onset of synchronized flow is identified as a subcritical Hopf bifurcation with a hysteresis. The local Hopf bifurcation can be analyzed via center manifold analysis. Finally, the transient dynamics to congested flow and global bifurcation diagrams are obtained via numerical computations.