Investigation of a traffic modelling inspired two dimensional map

Commencing with a class of differential equation based car following models for traffic flow a simplified discrete time model on a closed loop is found. A two dimensional map, containing two free parameters, and corresponding to the behaviour of two vehicles on the loop is investigated. Bounds on the prisoner set of the map are determined, and a number of strange attractors are presented. The variation of largest Lyapunov exponent over a range of parameter space is considered. The resulting behaviour of the map is considered within a traffic flow context.