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Saddle-node bifurcation control of macroscopic traffic flow model considering vehicle braking effect

Author

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  • Wen Huan Ai

    (Northwest Normal University)

  • Ming Ming Wang

    (Northwest Normal University)

  • Da Wei Liu

    (Lanzhou Institute of Technology)

Abstract

Traffic congestion is usually caused by many factors. When the traffic system passes through some critical bifurcation points, the stability state of the system will change abruptly, resulting in the loss of traffic stability. The saddle-node bifurcation in the static bifurcation will lead to a series of destructive dynamic behaviors, such as jump and delay of the system amplitude. This catastrophic bifurcation behavior can be eliminated or delayed by bifurcation control, help to solve the problem of traffic congestion. Based on this, in this paper, the saddle-node bifurcation control problem of stochastic traffic flow model considering vehicle braking effect is studied. By adding linear feedback control, the changes of bifurcation points and system stability in the system model are studied. It is shown that the bifurcation points can be shifted backwards and forwards by adjusting the values of the control parameters of the controlled system model so as to prevent or alleviate the traffic congestion. Graphical abstract Saddle node bifurcation control graphical abstracts

Suggested Citation

  • Wen Huan Ai & Ming Ming Wang & Da Wei Liu, 2024. "Saddle-node bifurcation control of macroscopic traffic flow model considering vehicle braking effect," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(5), pages 1-13, May.
    • Handle: RePEc:spr:eurphb:v:97:y:2024:i:5:d:10.1140_epjb_s10051-024-00697-1
    DOI: 10.1140/epjb/s10051-024-00697-1
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    References listed on IDEAS

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    1. Daganzo, Carlos F. & Laval, Jorge A., 2005. "Moving bottlenecks: A numerical method that converges in flows," Transportation Research Part B: Methodological, Elsevier, vol. 39(9), pages 855-863, November.
    2. Schadschneider, Andreas, 2002. "Traffic flow: a statistical physics point of view," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(1), pages 153-187.
    3. 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.
    4. Guan, Xueyi & Cheng, Rongjun & Ge, Hongxia, 2021. "Bifurcation control of optimal velocity model through anticipated effect and response time-delay feedback methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    5. 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.
    6. Kaur, Ramanpreet & Sharma, Sapna, 2018. "Analyses of lattice hydrodynamic model using delayed feedback control with passing," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 446-455.
    7. Ngoduy, D., 2021. "Noise-induced instability of a class of stochastic higher order continuum traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 260-278.
    8. Wen Huan Ai & Ming Ming Wang & Da Wei Liu, 2023. "Analysis of macroscopic traffic flow model considering throttle dynamics," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(6), pages 1-18, June.
    9. Zeng, Chao & Ma, Changxi & Wang, Ke & Cui, Zihao, 2022. "Predicting vacant parking space availability: A DWT-Bi-LSTM model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
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