Phase plane analysis of traffic flow based on driver’s expected response model

Abstract

At present, researchers have proposed many traffic flow models and research methods of traffic phenomena, but few of them are analyzed from the perspective of system stability. Therefore, this paper proposes a phase plane analysis method from the perspective of traffic flow stability. This method can describe the nonlinear traffic flow phenomenon on the road from the perspective of system global stability. The nonlinear system of the model is obtained by traveling wave substitution and Taylor expansion, and the equilibrium point of the model is solved by specifying the model parameters. According to the qualitative theory of differential equation, the model is further analyzed to judge the type and stability of equilibrium point. Finally, the simulation diagram is used for numerical verification.

Keywords

• traveling wave solutions
• nonlinear traffic flow phenomena
• traveling wave substitution
• phase plane analysis