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Zbl 1068.34038
Gasser, I.; Sirito, G.; Werner, B.
Bifurcation analysis of a class of `car following' traffic models. (English)
[J] Physica D 197, No. 3-4, 222-241 (2004). ISSN 0167-2789

Authors' abstract: We consider a follow-the-leader traffic model describing the dynamics of $N$ cars on a circular road, where each car driver chooses his acceleration according to a certain law. The model is represented by a nonlinear system of ODEs. This model is known to have a solution with constant velocities and headways which, in a certain parameter regime, is stable. Varying the density of the cars, we prove that the loss of stability is generally due to a Hopf bifurcation. Also we investigate numerically the global bifurcation diagram for periodic solutions and obtain a complete picture of the dynamics of general optimal velocity models. Finally, some analytical results on the stability of solutions in the case of non-equal drivers are given.
[Josef Hainzl (Freiburg)]

MSC 2000:: *34C23 Bifurcation (periodic solutions)
34C60 Applications of qualitative theory of ODE
34C25 Periodic solutions of ODE

Keywords: traffic model; nonlinear system of ODEs; Hopf bifurcation

Cited in: Zbl 1163.34345

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