Chaos Theory and Transportation Systems: Instructive Example

Chaos theory is used to analyze highly complex systems and thus may be useful for transportation applications. A series of analyses with which to find and exploit chaos is outlined, including time delays and embedding dimensions, Fourier power series, the correlation dimension, the largest Lyapunov exponent, and predictions. As an example, traffic flow data are analyzed and found to be chaotic, although it is shown that this could be the result of high-frequency noise. When used with a low-pass filter, predictions based on chaos theory are shown to have greater predictive power than a nonlinear least-squares method.