A road traffic model with overtaking: Continuation of periodic patterns using symmetry

Abstract

A microscopic model of the traffic flow of three identical cars is considered. The model can be classified as a Filippov system.

It admits several classes of oscillatory solutions (patterns). We explore the possibility to continue the patterns with respect to parameters.

As a particular example, we continue the pattern called the rotating wave. The idea is to exploit the intrinsic symmetry.

Keywords

• traffic
• microscopic models
• overtaking
• piecewise-smooth dynamical systems