Phase-plane analysis to an “anisotropic” higher-order traffic flow model

Abstract

The qualitative theory of differential equations is applied to investigate the traveling wave solution to an “anisotropic” higher-order viscous traffic flow model under the Lagrange coordinate system. The types and stabilities of the equilibrium points are discussed in the phase plane. Through the numerical simulation, the overall distribution structures of trajectories are drawn to analyze the relation between the phase diagram and the selected conservative solution variables, and the influences of the parameters on the system are studied. The limit-circle, limit circle-spiral point, saddle-spiral point and saddle-nodal point solutions are obtained. These steady-state solutions provide good explanation for the phenomena of the oscillatory and homogeneous congestions in real-world traffic.