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Subcritical Hopf bifurcations in a car-following model with reaction-time delay

Research output: Working paperWorking paper and Preprints

  • G Orosz
  • G Stepan
Original languageEnglish
StatePublished - 2005


A nonlinear car-following model of highway traffic is considered, which includes the reaction-time delay of drivers. Linear stability analysis shows that the uniform flow equilibrium of the system loses its stability via Hopf bifurcations and thus oscillations can appear. The stability and amplitudes of the oscillations are determined with the help of normal-form calculations of the Hopf bifurcation that also handles the essential translational symmetry of the system. We show that the subcritical case of the Hopf bifurcation occurs robustly, which indicates the possibility of bistability. We also show how these oscillations lead to spatial wave formation as can be observed in real-world traffic flows

Additional information

Additional information: Preprint submitted to Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Sponsorship: This research was supported by the University of Bristol under a Postgraduate Research Scholarship and by the Hungarian National Science Foundation under grant no. OTKA T043368

    Research areas

  • subcritical Hopf bifurcation, reaction-time delay, translational symmetry, bistability, vehicular traffic, stop-and-go waves

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    Submitted manuscript, 408 KB, PDF-document


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