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

G Orosz; G Stepan

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

G Orosz, G Stepan

Department of Engineering Mathematics

Research output: Working paper

125 Citations (Scopus)

465 Downloads (Pure)

Abstract

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

Original language	English
Publication status	Published - 2005

Bibliographical note

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

Keywords

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

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http://hdl.handle.net/1983/136

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title = "Subcritical Hopf bifurcations in a car-following model with reaction-time delay",

abstract = "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",

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AU - Stepan, G

N1 - 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

PY - 2005

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N2 - 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

AB - 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

KW - subcritical Hopf bifurcation

KW - reaction-time delay

KW - translational symmetry

KW - bistability

KW - vehicular traffic

KW - stop-and-go waves

M3 - Working paper

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

ER -

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

Abstract

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Keywords

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