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Bifurcation analysis of a class of ‘car following’ traffic models. (English) Zbl 1068.34038
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.

##### MSC:
 34C23 Bifurcation (ODE) 34C60 Qualitative investigation and simulation of models (ODE) 34C25 Periodic solutions of ODE
##### Keywords:
traffic model; nonlinear system of ODEs; Hopf bifurcation