Abstract
This paper establishes a general bifurcation structure of a car-following model with multiple time delays. By applying the Hopf theorem, analytical calculation and numerical simulation are carried out for some typical car-following models. Our results allow a discussion of the impact of multiple time delays and other model parameters on Hopf bifurcation in various existing car-following models with delays, from elementary car-following models such as the optimal velocity model, the full velocity difference model and the intelligent driver model, to Cooperative Adaptive Cruise Control car-following models. It is particularly interesting to observe that the multiple time delays cancel out the impact of each other on the traffic instability.
Disclosure statement
No potential conflict of interest was reported by the author(s).