Breaking the Symmetry in a Car‐Following Model

A wide class of microscopic car-following traffic models deals with a system of ODEs describing N cars driving on a circular highway. The symmetry of the road naturally leads to (quasi-)stationary solutions and to an analysis of their stability. Breaking this symmetry with small perturbations we show the existence of a branch of some special solutions that occur instead of the stationary points. Those solutions can be interpreted in reality, they describe the behavior of the cars on the road as expected. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)