Many commonly occurring natural systems are modelled with mathematical expressions and exhibit a certain stability. The inherent stability of these equations allows them to serve as the basis for engineering predictions. More complex models, such as those for modelling traffic flow, lack stability and thus require considerable care when used as a basis for predictions. In 1960, Gazis, Herman, and Rothery introduced their generalised car-follow equation for modelling traffic flow. Experience has shown that this equation may not be continuous for the entire range of input parameters. The discontinuous behaviour and nonlinearity of the equation suggest chaotic solutions for certain ranges of input parameters. Understanding the chaotic tendencies of this equation allows engineers to improve the reliability of models and predictions based on those models. This paper describes chaotic behaviour and briefly discusses the methodology of the algorithm used to detect its presence in the car-follow equation. Also discussed are two systems modelled with the equation and their associated chaotic properties.
Samenvatting