Citation

Gasser I, Werner B. Philos. Transact. A Math. Phys. Eng. Sci. 2010; 368(1928): 4543-4562.

Affiliation

Department of Mathematics, University of Hamburg, , Bundesstrasse 55, 20146 Hamburg, Germany.

Copyright

(Copyright © 2010, Royal Society Publishing)

DOI

10.1098/rsta.2010.0118

PMID

20819821

Abstract

We study a microscopic follow-the-leader model on a circle of length L with a bottleneck. Allowing large bottleneck strengths we encounter very interesting traffic dynamics. Different types of waves-travelling and standing waves and combinations of both wave types-are observed. The way to find these phenomena requires a good understanding of the complex dynamics of the underlying (nonlinear) equations. Some of the phenomena, like the ponies-on-a-merry-go-round solutions, are mathematically well known from completely different applications. Mathematically speaking we use Poincaré maps, bifurcation analysis and continuation methods beside numerical simulations.

Language: en