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

ABSTRACT

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.

Keywords:

• Car-following model
• relative velocity effect
• linear stability analysis
• bifurcation analysis

Acknowledgements

This study used computers at the ‘Center for Mathematical Modeling and Applications’ (Ministry of Education , Culture, Sports, Science and Technology (MEXT) Joint Usage/Research Center) and MIMS at Meiji University.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This study was supported by MIMS Joint Research Project for Mathematical Sciences. Authors AT and KI would like to express their appreciation to the Japan Society for the Promotion of Science (JSPS), which provided support through Grants-in-Aid for Young Scientists (B) (Nos. 25790099 and 15K17594).