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Discrete Dynamics in Nature and Society
Volume 2014, Article ID 535167, 11 pages
http://dx.doi.org/10.1155/2014/535167
Research Article

Nonlinear Analysis on Traffic Flow Based on Catastrophe and Chaos Theory

School of Transportation, Southeast University, Nanjing 210008, China

Received 22 May 2014; Revised 6 October 2014; Accepted 15 October 2014; Published 27 November 2014

Academic Editor: Seenith Sivasundaram

Copyright © 2014 Jian Gu and Shuyan Chen. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We applied catastrophe and chaos theory to analyze the traffic nonlinear characteristics of expressway condition. Catastrophe theory was generally used to explore the mathematical relationships among the traffic data collected from highway conditions, which could not be appropriate for the urban expressway conditions. Traffic flow data collected from the 3rd ring road expressway in Beijing was used to build flow-density model and speed-density Greenshields model. Then the density was discussed based on the traffic wave speed function with cusp catastrophe theory; in particular, density conditions on median lanes and shoulder lanes were deeply discussed. Meanwhile the chaotic characteristics were analyzed based on the traffic temporal sequence data collected from 29 detectors located at the 3rd ring road expressway, and C-C method was used to reconstruct the phase space and the largest Lyapunov exponents were estimated by Wolf method and the small data sets method. The results indicated that the traffic operation catastrophe density on the median lanes was a bit higher than that on the shoulder lanes; additionally chaotic characteristics obviously existed in the local corridor composed of 29 detectors in the 3rd ring road expressway traffic flow system.