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

Dong Ngoduy, Tenglong Li

Research output: Contribution to journalArticleResearchpeer-review

15 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)878-896
Number of pages19
JournalTransportmetrica A: Transport Science
Issue number4
Publication statusPublished - 2021


  • Bifurcation
  • car-following model
  • linear stability
  • multiple delays

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