Nonlinear Analysis of Road Traffic Flows in Discrete Dynamical System

In this paper, we investigate the dynamic behavior of road traffic flows and study if chaotic phenomena exist in a traffic flow dynamic system. Two discrete dynamic models are proposed, which are derived from Del Castillo and Benitez's exponential curve model and maximum sensitivity curve model. Both models have two parameters, which are the ratio of free flow and sensitivity average speed and the ratio of the absolute value of kinematic wave speed at jam density and the free flow speed. Chaos is found in the two models when the two values increase separately. The Lyapunov exponents and fractal dimension were used to examine the characters of the chaos in the two models.