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Research Papers: Modeling

Nonlinear Analysis of Road Traffic Flows in Discrete Dynamical System

[+] Author and Article Information
Meng Xu

School of Traffic and Transportation, Beijing Jiaotong University, 100044 Beijing, P.R.C.xumeng@jtys.bjtu.edu.cn

Ziyou Gao

School of Traffic and Transportation, Beijing Jiaotong University, 100044 Beijing, P.R.C.

J. Comput. Nonlinear Dynam 3(2), 021206 (Feb 04, 2008) (6 pages) doi:10.1115/1.2833905 History: Received May 28, 2007; Revised August 13, 2007; Published February 04, 2008

Abstract

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 spacing 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.

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Figures

Figure 5

The Lyapunov exponents of model 12: (a) about μ1 with μ2=0.138 and p0=0.6; (b) about μ2 with μ1=6.7 and p0=0.6

Figure 6

The Lyapunov exponents of model 13: (a) about μ1 with μ2=0.078 and p0=0.6; (b) about μ2 with μ1=6 and p0=0.6

Figure 4

Sensitive dependence on initial conditions of model 13 for p0=0.600 and p0=0.601: (a) with μ1=15 and μ2=0.078; (b) with μ1=6 and μ2=0.23

Figure 3

Sensitive dependence on initial conditions of model 12 for p0=0.600 and p0=0.601: (a) with μ1=11.53 and μ2=0.138; (b) with μ1=6.7 and μ2=0.271

Figure 2

Bifurcation diagram of model 13: (a) for μ1 with μ2=0.078 and p0=0.6; (b) for μ2 with μ1=6 and p0=0.6

Figure 1

Bifurcation diagram of model 12: (a) for μ1 with μ2=0.138 and p0=0.6; (b) for μ2 with μ1=6.7 and p0=0.6

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