Dynamical phenomena induced by bottleneck

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.