Applied Mathematics and Mechanics

, Volume 33, Issue 12, pp 1505–1512 | Cite as

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

  • Chun-xiu Wu (吴春秀)
  • Tao Song (宋 涛)
  • Peng Zhang (张 鹏)Email author
  • S. C. Wong


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

traffic flow Lagrange coordinates phase-plane analysis traffic congestion pattern 

Chinese Library Classification


2010 Mathematics Subject Classification



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Copyright information

© Shanghai University and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Chun-xiu Wu (吴春秀)
    • 1
    • 2
  • Tao Song (宋 涛)
    • 1
    • 2
  • Peng Zhang (张 鹏)
    • 1
    • 2
    Email author
  • S. C. Wong
    • 3
  1. 1.Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiP. R. China
  2. 2.Shanghai Key Laboratory of Mechanics in Energy EngineeringShanghai UniversityShanghaiP. R. China
  3. 3.Department of Civil EngineeringThe University of Hong KongHong KongP. R. China

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