Analysis of equilibrium point based on viscous traffic flow model

Abstract

In this paper, the phase plane analysis method is used, which can describe and predict the nonlinear traffic phenomenon on Expressway from the perspective of system global stability. The nonlinear system of the model is obtained by the traveling wave substitution and Taylor expansion of the model, and the equilibrium point of the model is solved by specifying the model parameters. According to the definite theory of differential equation, the model is further analyzed to judge the type and stability of equilibrium point. Finally, numerical verification is carried out according to the simulation diagram. Through numerical verification, the simulation results of the model are consistent with the conclusions of theoretical analysis. It can more clearly describe the change of density or speed with time or road section.

Keywords

• traveling wave solution
• nonlinear traffic phenomena
• traveling wave substitution