Computer-Aided Bifurcation Analysis for a Novel Car-Following Model with Relative Velocity Effect

Abstract

The global behaviour of mathematical models for traffic flow is important in order to understand their characteristics because of the bistable property observed in real traffic. This bi-stability can be discussed in a bifurcation analysis. In fact, bifurcation analysis of optimal velocity models in several studies has revealed the global bifurcation structure of the model, which shows a loss of stability due to the Hopf bifurcation and bistable property. Shamoto et al. proposed a novel car-following model with relative velocity effect (STNN model), which was not introduced into the optimal velocity model, but is important in real traffic scenarios. They discussed the linear stability of homogeneous traffic flow; however, they did not reveal the global bifurcation structure of the STNN model. In this paper, we numerically investigated the global bifurcation structure of the STNN model and observed that the strength of the relative velocity effect drastically changes the bifurcation structure. This result provides a possibility of implementing (semi-)automatic driving systems to alleviate traffic jams.