Some Nonlinear Density Wave Equations On City Traffic Flow

In this paper, we consider some important factors in the transportation, in which we made a numerical simulation for micro car-following model and macroscopic lattice hydrodynamic model. And by using the theory of linear and nonlinear method, we discussed the model's critical phase transition and the evolution of traffic density wave under small perturbation.The thesis is arranged as follows:1. Consider the car-following model of expecting effectSeriously, traffic will be impacted by the drivers behavior on usual. On the basis of the dual speed difference model hold by Ge Hong-Xia et al., and the driver prediction effect is considered herein, and then we propose a new model named AD-TVDM, Finally, TDGL and mKdV equation are derived by reductive perturbation method, and the coexistence curve and metastable curve are figured out through the derivation obtained thermodynamic potential.2. Consider the car-following model of urgent push effectIn daily traffic life, the vast majority of drivers have a certain bad driving habits, such as a sudden stop of the vehicle at the red light, a big acceleration at the green light, and a braking emergency of the back vehicle to prevent the collision. To deal with this situation, we propose the car-following model of urgent push effect, and TDGL and mKdV equation are figured out by nonlinear equations, and the link of two equations is studied further.3. Consider the two-lane hydrodynamic model of predicting effectOn the basis of the two-lane lattice hydrodynamic model of Nagatani and the predicting effect, we propose a new two-lane lattice hydrodynamic model. Nowadays, most of the studies on lane continuity model focus on nonlinear analysis, while study on the two-lane continuous model is not focus on nonlinear analysis, but on the numerical simulation. In this paper, we not only get a neutral stability curve through the analysis of the linear, but also get TDGL equation and mKdV equation through the analysis of the nonlinear, furthermore, the relationship between the two equations is studied.