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Bifurcation analysis of traffic flow through an improved car-following model considering the time-delayed velocity difference

Author

Listed:
  • Zhang, Yicai
  • Xue, Yu
  • Zhang, Peng
  • Fan, Deli
  • di He, Hong

Abstract

In this paper a new car-following model with consideration of time-delayed velocity difference is proposed to investigate the effect of time-delayed velocity on traffic flow via bifurcation analysis. Based on this model, the linear stability analysis is carried out and the corresponding stability condition is obtained. Then the Hopf bifurcation analysis is performed in term of theoretical analysis and numerical simulation. The result shows that there exist Hopf bifurcation critical points and the position of the critical points is found to be located on the boundary of the instability region. Finally, the influence of the delay time and sensitivity of velocity difference on Hopf bifurcation is discussed, respectively.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:514:y:2019:i:c:p:133-140
    DOI: 10.1016/j.physa.2018.09.012
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    References listed on IDEAS

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    Cited by:

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    3. Meng, Jingwei & Jin, Yanfei & Xu, Meng, 2023. "Stochastic dynamics of a discrete-time car-following model and its time-delayed feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
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    6. Jafaripournimchahi, Ammar & Cai, Yingfeng & Wang, Hai & Sun, Lu & Yang, Biao, 2022. "Stability analysis of delayed-feedback control effect in the continuum traffic flow of autonomous vehicles without V2I communication," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 605(C).
    7. 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.
    8. Ammar Jafaripournimchahi & Yingfeng Cai & Hai Wang & Lu Sun, 2022. "Environmental Analyses of Delayed-Feedback Control Effects in Continuum-Traffic Flow of Autonomous Vehicles," Sustainability, MDPI, vol. 14(18), pages 1-18, September.
    9. Ma, Guangyi & Li, Keping, 2024. "Analysis and simulation of vehicle following behavior with consideration of multiple time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).

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