Bifurcation structure of a car-following model with nonlinear dependence on the relative velocity

Understanding the stability of solutions of mathematical models of traffic flow is important for alleviating jams as these are considered stable inhomogeneous solutions of traffic models. Traffic jams can be alleviated by destabilizing these solutions. Solution stability can be studied with the aid of bifurcation analysis, which has been used to describe the global bifurcation structure of a car-following model that exhibits bistable behavior and loss of stability due to Hopf bifurcations. However, previous studies on bifurcation analysis for traffic models have not considered the relative velocity effect, which is important in real-world traffic scenarios. This study analytically derives linear stability conditions and numerically investigates the global bifurcation structure of a car-following model with nonlinear dependence on the relative velocity (the STNN model), which exhibits multistable states. Moreover, the relative velocity drastically changes the bifurcation structure. This supports implementation of (semi-)automatic driving systems as a means to alleviate traffic jams.