1. Investigation of a traffic modelling inspired two dimensional map
- Author
-
Mark McCartney, Helen Mooney, and Chris Stretch
- Subjects
Numerical Analysis ,Differential equation ,Applied Mathematics ,Context (language use) ,Lyapunov exponent ,Parameter space ,Traffic flow ,symbols.namesake ,Discrete time and continuous time ,Control theory ,Modeling and Simulation ,Attractor ,symbols ,Applied mathematics ,Free parameter ,Mathematics - Abstract
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.
- Published
- 2010