Applied Mathematics and Mechanics (English Edition) ›› 2012, Vol. 33 ›› Issue (12): 1505-1512.doi: https://doi.org/10.1007/s10483-012-1640-x

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Phase-plane analysis of conserved higher-order traffic flow model

Chun-xiu WU1,2, Tao SONG1,2, Peng ZHANG1,2, S. C. WONG3   

  1. 1. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China;
    2. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, P. R. China;
    3. Department of Civil Engineering, The University of Hong Kong, Pokfulam Road, Hong Kong, P. R. China
  • Received:2012-01-05 Revised:2012-04-30 Online:2012-12-10 Published:2012-12-10
  • Supported by:

    Project supported by the National Natural Science Foundation of China (No. 11072141), the Shanghai Program for Innovative Research Team in Universities, the Graduate Innovation Foundation of Shanghai University (No. SHUCX101078), and the University Research Committee, HKU SPACE Research Fund and Faculty of Engineering Top-up Grant of the University of Hong Kong (No. 201007176059)

Abstract: The phase-plane analysis is used to study the traveling wave solution of a recently proposed higher-order traffic flow model under the Lagrange coordinate system. The analysis identifies the types and stabilities of the equilibrium solutions, and the overall distribution structure of the nearby solutions is drawn in the phase plane for the further analysis and comparison. The analytical and numerical results are in agreement, and may help to explain the simulated phenomena, such as the stop-and-go wave and oscillation near a bottleneck. The findings demonstrate the model ability to describe the complexity of congested traffic.

Key words: axisymmetrically loaded, stepped pressure vessel, radial vibration, free vibration, forced response, traffic flow, Lagrange coordinates, phase-plane analysis, traffic congestion pattern

2010 MSC Number: 

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