Analysis of equilibrium point based on nonlinear traffic flow model

In this paper, the traveling wave solution of Kerner konhauser model is obtained by phase plane analysis method, and a new model suitable for stability analysis is obtained by variable transformation. The new model can describe and predict the nonlinear traffic phenomenon on Expressway from the perspective of system global stability. In this paper, the nonlinear system and linear system are obtained respectively by traveling wave substitution and Taylor expansion at the equilibrium point. According to the qualitative theory of differential equations, the equilibrium point type and stability of the linear system are determined. Finally, the simulation results show the consistency between the numerical results and the theoretical analysis.