Dynamics of Delay Equations, Theory and Applications - Abstract

Stumpf, Eugen

On a delay differential equation arising from a car-following model

In this talk we will consider a scalar delay dierential equa- tion which arises from a simple car-following model describing the dynamics of innitely many cars moving on a single lane road. In particular, some of the solutions of the delay equation under consideration form wavefront solu- tions for the trac model. Using this correlation, we will prove the existence and analyze the stability of wavefront solutions with constant-speed. Fur- thermore, we will also address the occurrence of stop-and-go trac. The ob- tained results are in accordance with earlier studies of a similar car-following model on a circular road where the existence of stop-and-go trac can be evidently observed in experiments.