Hopf bifurcation structure of a generic car-following model with multiple time delays

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.