Bifurcation analysis of a heterogeneous traffic flow model

Abstract

In this work, a heterogeneous traffic flow model coupled with the periodic boundary condition is proposed. Based on the previous models, a heterogeneous system composed of more than one kind of vehicles is considered. By bifurcation analysis, bifurcation patterns of the heterogeneous system are discussed in three situations in detail and illustrated by diagrams of bifurcation patterns. Besides, the stability analysis of the heterogeneous system is performed to test its anti-interference ability. The relationship between the number of vehicles and the stability is obtained. Furthermore, the attractor analysis is applied to investigate the nature of the heterogeneous system near its steady-state neighborhood. Phase diagrams of the process of the heterogeneous system from initial state to equilibrium state are intuitively presented.