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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:

    1. Lixia Duan & Shuangshuang Fan & Danyang Liu & Zhonghe He, 2022. "Two-parameter bifurcation and energy consumption analysis of the macro traffic flow model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(12), pages 1-12, December.
    2. Chen, Dong & Sun, Dihua & Zhao, Min & Zhou, Tong & Cheng, Senlin, 2018. "Modeling and analyses for an extended car-following model accounting for drivers’ situation awareness from cyber physical perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 52-68.
    3. Ren, Weilin & Cheng, Rongjun & Ge, Hongxia, 2021. "Bifurcation analysis for a novel heterogeneous continuum model considering electronic throttle angle changes with memory," Applied Mathematics and Computation, Elsevier, vol. 401(C).
    4. Zhang, Yicai & Xue, Yu & Zhang, Peng & Fan, Deli & di He, Hong, 2019. "Bifurcation analysis of traffic flow through an improved car-following model considering the time-delayed velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 133-140.
    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.
    6. Lyu, Hao & Cheng, Rongjun & Ge, Hongxia, 2022. "Bifurcation analysis of an extended macro model considering time delay and anticipation effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    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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