Summary: Subcritical Hopf bifurcations in a car-following
model with reaction-time delay
BY GA´ BOR OROSZ
1,
* AND GA´ BOR STE´ PA´ N
2,
1
Bristol Centre for Applied Nonlinear Mathematics, Department of Engineering
Mathematics, University of Bristol, Queen's Building, University Walk,
Bristol BS8 1TR, UK
2
Department of Applied Mechanics, Budapest University of Technology and
Economics, PO Box 91, Budapest 1521, Hungary
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

Source: Awtar, Shorya - Department of Mechanical Engineering, University of Michigan

Collections: Engineering