Hopf calculations in delayed car-following models

Gábor Stépán, Gábor Orosz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)


A nonlinear car-following model that includes the reaction-time delay of drivers is considered. When investigating the linear stability of the uniform flow solution, boundaries of Hopf bifurcations are determined in the parameter space. Crossing these boundaries, oscillations may appear corresponding to travelling wave solutions. Hopf normal form calculations prove robustly subcritical behavior which leads to bistability between the stable uniform traffic flow and the stop-and-go waves travelling against the flow of vehicles. Analogies with wheel shimmy dynamics and machine tool vibrations are presented.

Original languageEnglish
Title of host publication6th IFAC Workshop on Time Delay Systems, TDS 2006
PublisherIFAC Secretariat
Number of pages6
EditionPART 1
ISBN (Print)9783902661111
Publication statusPublished - 2006

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
NumberPART 1
ISSN (Print)1474-6670


  • Bistability
  • Reaction-time delay
  • Subcritical Hopf bifurcation
  • Translational symmetry
  • Vehicular traffic

ASJC Scopus subject areas

  • Control and Systems Engineering

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  • Cite this

    Stépán, G., & Orosz, G. (2006). Hopf calculations in delayed car-following models. In 6th IFAC Workshop on Time Delay Systems, TDS 2006 (PART 1 ed., pp. 193-198). (IFAC Proceedings Volumes (IFAC-PapersOnline); Vol. 6, No. PART 1). IFAC Secretariat. https://doi.org/10.3182/20060710-3-it-4901.00032