Chaos in a discrete dynamic model of traffic flow

This paper aims to discuss unstable traffic flow and to identify if chaotic phenomena exist in a traffic flow dynamic system. Two discrete dynamic models are proposed, which are derived from the flow-density-speed fundamental diagram and Del Castillo and Benitez's exponential curve model and maximum sensitivity curve model. Both the models have two parameters, which are the ratio of free flow and spacing average speed and the ratio of the absolute value of kinematic wave speed at jam density and free flow speed. Chaos is found in the two models when the two values increase separately. The Liapunov exponents were used to examine the characters of the chaotic behavior in the two models. These results are illustrated by numerical examples.