Phase Plane Analysis of Traffic Flow Evolution Based on a Macroscopic Traffic Flow Model

  • WenHuan AiEmail author
  • Tao Xing
  • YuHang Su
  • DaWei Liu
  • Huifang Ma
Conference paper
Part of the IFIP Advances in Information and Communication Technology book series (IFIPAICT, volume 581)


In this paper, a new phase plane analysis method is proposed to study the nonlinear phenomena of traffic flow. Most of the papers describe only one or several traffic phenomena and do not analyze all of them from the perspective of system stability. Therefore, this paper studies the phase plane analysis of traffic flow phenomenon from the perspective of traffic system stability, and describes various complicated nonlinear traffic phenomena through phase plane analysis.


Phase plane diagrams Stop-and-go waves Stability analysis Phase plane analysis 



This work is partially supported by the National Natural Science Foundation of China under the Grant No. 61863032 and the China Postdoctoral Science Foundation Funded Project (Project No.: 2018M633653XB) and the “Qizhi” Personnel Training Support Project of Lanzhou Institute of Technology (Grant No. 2018QZ-11) and the National Natural Science Foundation of China under the Grant No. 11965019.

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this paper.


  1. 1.
    Tang, T.Q., Huang, H.J., Shang, H.Y.: A new macro model for traffic flow with the consideration of the driver’s forecast effect. Phys. Lett. A 374, 1668–1672 (2010)CrossRefGoogle Scholar
  2. 2.
    Liu, D.W., Shi, Z.K., Ai, W.H.: Anew car-following model accounting for impact of strong wind. Math. Prob. Eng. 1, 1–12 (2017)Google Scholar
  3. 3.
    Liu, D.W., Shi, Z.K., Ai, W.H.: An improved car-following model from the perspective of driver’s forecast behavior. Int. J. Mod. Phys. C 28(4), 1750046 (2017)CrossRefGoogle Scholar
  4. 4.
    Jiang, R., Wu, Q.S., Zhu, Z.J.: A new continuum model for traffic flow and numerical tests. Transp. Res. Part B: Methodol. 36, 405–419 (2002)CrossRefGoogle Scholar
  5. 5.
    Kerner, B.S., Konhäuser, P.: Structure and parameters of clusters in traffic flow. Phys. Rev. E 50, 54–86 (1994)CrossRefGoogle Scholar
  6. 6.
    Ai, W.H., Shi, Z.K., Liu, D.W.: Bifurcation analysis of a speed gradient continuum traffic flow model. Phys. A 437, 418–429 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Ai, W.H., Shi, Z.K., Liu, D.W.: Bifurcation analysis method of nonlinear traffic phenomena. Int. J. Mod. Phys. C 26, 1550111 (2015)MathSciNetCrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2020

Authors and Affiliations

  • WenHuan Ai
    • 1
    Email author
  • Tao Xing
    • 1
  • YuHang Su
    • 1
  • DaWei Liu
    • 2
  • Huifang Ma
    • 1
  1. 1.College of Computer Science and EngineeringNorthwest Normal UniversityLanzhouChina
  2. 2.College of Electrical EngineeringLanzhou Institute of TechnologyLanzhouChina

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