Premium
Breaking the Symmetry in a Car‐Following Model
Author(s) -
Seidel Tilman,
Werner Bodo
Publication year - 2006
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200610309
Subject(s) - symmetry breaking , symmetry (geometry) , ode , class (philosophy) , spontaneous symmetry breaking , explicit symmetry breaking , theoretical physics , classical mechanics , physics , mathematics , statistical physics , computer science , geometry , mathematical analysis , quantum mechanics , artificial intelligence
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)