Eddie Wilson

Car-Following Models as Dynamical Systems and the Mechanisms for Macroscopic Pattern Formation

I will use a general linear analysis of car-following models to identify and explain the `dynamic upscaling' effect, where small
wavelength perturbations to traffic flow magnify into large wavelength structures. (Within very broad bounds, almost all car-following models
can be shown to have this property in the correct way.) I will  then show how this outlook is modified by nonlinear effects and how
stop-and-go waves may still be found when uniform flow is linearly stable. If time permits, I will describe some recent results with
Tony Humphries in which we solve for and classify travelling wave  solutions of car-following models in terms of a single advance/delay
differential equation.