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Bifurcation analysis of a speed gradient continuum traffic flow model

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  • Ai, Wen-Huan
  • Shi, Zhong-Ke
  • Liu, Da-Wei

Abstract

A bifurcation analysis approach is presented based on the macroscopic traffic flow model. This method can be used to describe and predict the nonlinear traffic phenomena on the highway from a system global stability perspective. Based on a recently proposed speed gradient continuum traffic flow model, the types and stabilities of the equilibrium solutions are discussed and the existence of Hopf bifurcation and saddle–node bifurcation is proved. Then various bifurcations such as Hopf bifurcation, saddle–node bifurcation, Limit Point bifurcation of cycles, Cusp bifurcation and Bogdanov–Takens bifurcation are found and the traffic flow behaviors at some of them are analyzed. When the Hopf bifurcation is selected as the starting point of density temporal evolution, it may help to explain the stop-and-go traffic phenomena.

Suggested Citation

  • Ai, Wen-Huan & Shi, Zhong-Ke & Liu, Da-Wei, 2015. "Bifurcation analysis of a speed gradient continuum traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 418-429.
    • Handle: RePEc:eee:phsmap:v:437:y:2015:i:c:p:418-429
    DOI: 10.1016/j.physa.2015.06.004
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    References listed on IDEAS

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    Cited by:

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    5. Fan, De-li & Zhang, Yi-cai & Shi, Yin & Xue, Yu & Wei, Fang-ping, 2018. "An extended continuum traffic model with the consideration of the optimal velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 402-413.
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    7. Mondal, Satyajit & Gupta, Ankit, 2021. "Speed distribution for interrupted flow facility under mixed traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 570(C).
    8. Huang, Chengdai, 2018. "Multiple scales scheme for bifurcation in a delayed extended van der Pol oscillator," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 643-652.

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