Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1897962 | Physica D: Nonlinear Phenomena | 2008 | 22 Pages |
Abstract
We consider a simple microscopic follow-the-leader model of NN identical cars on a circular road. In the classical setting, a car is not allowed to reach its leader. If it happens at a particular time tEtE, we propose to extend the model beyond this time tEtE: The idea is to define a physically reasonable leader for each car. Mathematically, the resulting model is a kind of Filippov system. The objective is to study a long time behavior of the model. In case N=3N=3, we observed several invariant patterns which apparently exhibit spatial–temporal symmetries. We managed to classify and identify two kinds of rotating waves. The classification exploits symbolic dynamical notions.
Related Topics
Physical Sciences and Engineering
Mathematics
Applied Mathematics
Authors
Lubor Buřič, Vladimír Janovský,