IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v95y2022i12d10.1140_epjb_s10051-022-00469-9.html
   My bibliography  Save this article

Two-parameter bifurcation and energy consumption analysis of the macro traffic flow model

Author

Listed:
  • Lixia Duan

    (North China University of Technology)

  • Shuangshuang Fan

    (North China University of Technology)

  • Danyang Liu

    (Beijing Institude of Technology)

  • Zhonghe He

    (North China University of Technology)

Abstract

Bifurcation of traffic flow involves complex dynamic characteristics of the system. In order to understand the complex traffic phenomenon, this work designed a macro traffic model considering the driver’s memory which plays an important role in the traffic flow. Based on this model, we investigate the effects of the driver’s memory and wave velocity on the stability of the traffic flow. By means of one and two parameter bifurcation analysis, we explore how these parameters affect the bifurcation structure of the system, and further investigate the dynamic mechanisms of traffic flow. We explain various traffic phenomena related to the different types of equilibrium points and limit cycles by phase plane analysis. We also study how the initial density and bifurcation structure affect the energy consumption in the system. The results show that the driver’s memory and wave velocity play an important role in the stability of the traffic flow. By considering the change of bifurcation structure, we can better understand the source of traffic congestion, and further predict and control the possible traffic congestion. Graphic abstract

Suggested Citation

  • 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.
    • Handle: RePEc:spr:eurphb:v:95:y:2022:i:12:d:10.1140_epjb_s10051-022-00469-9
    DOI: 10.1140/epjb/s10051-022-00469-9
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1140/epjb/s10051-022-00469-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1140/epjb/s10051-022-00469-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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).
    2. 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.
    3. Zhu, Wen-Xing & Zhang, H.M., 2018. "Analysis of mixed traffic flow with human-driving and autonomous cars based on car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 274-285.
    4. Wei Pan & Xiaolu Chen & Xiaojun Duan, 2022. "Energy dissipation and particulate emission at traffic bottleneck based on NaSch model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(7), pages 1-13, July.
    5. Sun, Yuqing & Ge, Hongxia & Cheng, Rongjun, 2019. "An extended car-following model considering driver’s memory and average speed of preceding vehicles with control strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 752-761.
    6. Nagatani, Takashi, 1999. "TDGL and MKdV equations for jamming transition in the lattice models of traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 581-592.
    7. Cao, Bao-gui, 2015. "A new car-following model considering driver’s sensory memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 427(C), pages 218-225.
    8. Tang, Tie-Qiao & Huang, Hai-Jun & Shang, Hua-Yan, 2017. "An extended macro traffic flow model accounting for the driver’s bounded rationality and numerical tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 322-333.
    9. Huang, Keke & Liu, Yishun & Zhang, Yichi & Yang, Chunhua & Wang, Zhen, 2018. "Understanding cooperative behavior of agents with heterogeneous perceptions in dynamic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 234-240.
    10. Tang, T.Q. & He, J. & Wu, Y.H. & Caccetta, L., 2014. "Propagating properties of traffic flow on a ring road without ramp," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 164-172.
    11. Zhang, H. M., 2003. "Driver memory, traffic viscosity and a viscous vehicular traffic flow model," Transportation Research Part B: Methodological, Elsevier, vol. 37(1), pages 27-41, January.
    12. 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).
    13. D. Helbing & M. Moussaid, 2009. "Analytical calculation of critical perturbation amplitudes and critical densities by non-linear stability analysis of a simple traffic flow model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(4), pages 571-581, June.
    14. Herrmann, Matthias & Kerner, Boris S, 1998. "Local cluster effect in different traffic flow models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 255(1), pages 163-188.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cheng, Rongjun & Ge, Hongxia & Sun, Fengxin & Wang, Jufeng, 2018. "An extended macro model accounting for acceleration changes with memory and numerical tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 270-283.
    2. Qingtao, Zhai & Hongxia, Ge & Rongjun, Cheng, 2018. "An extended continuum model considering optimal velocity change with memory and numerical tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 774-785.
    3. 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).
    4. 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).
    5. Kaur, Daljeet & Sharma, Sapna & Gupta, Arvind Kumar, 2022. "Analyses of lattice hydrodynamic area occupancy model for heterogeneous disorder traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    6. Wang, Zihao & Ge, Hongxia & Cheng, Rongjun, 2020. "An extended macro model accounting for the driver’s timid and aggressive attributions and bounded rationality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Rongjun, Cheng & Hongxia, Ge & Jufeng, Wang, 2018. "The nonlinear analysis for a new continuum model considering anticipation and traffic jerk effect," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 493-505.
    8. Zhaoze, Liu & Rongjun, Cheng & Hongxia, Ge, 2019. "Research on preceding vehicle’s taillight effect and energy consumption in an extended macro traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 304-314.
    9. Yifan Pan & Yongjiang Wang & Baobin Miao & Rongjun Cheng, 2022. "Stabilization Strategy of a Novel Car-Following Model with Time Delay and Memory Effect of the Driver," Sustainability, MDPI, vol. 14(12), pages 1-20, June.
    10. Kun Zhang & Yu Xue & Hao-Jie Luo & Qiang Zhang & Yuan Tang & Bing-Ling Cen, 2023. "Cyber-attacks on the optimal velocity and its variation by bifurcation analyses," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(12), pages 1-19, December.
    11. Liu, Zhaoze & Ge, Hongxia & Cheng, Rongjun, 2018. "KdV–Burgers equation in the modified continuum model considering the effect of friction and radius on a curved road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1218-1227.
    12. Zhai, Cong & Wu, Weitiao, 2022. "A continuum model considering the uncertain velocity of preceding vehicles on gradient highways," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    13. Peng, Guanghan & Jia, Teti & Kuang, Hua & Tan, Huili, 2022. "Energy consumption in a new lattice hydrodynamic model based on the delayed effect of collaborative information transmission under V2X environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    14. Cen, Bing-ling & Xue, Yu & Zhang, Yi-cai & Wang, Xue & He, Hong-di, 2020. "A feedback control method with consideration of the next-nearest-neighbor interactions in a lattice hydrodynamic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 559(C).
    15. Chang, Yinyin & He, Zhiting & Cheng, Rongjun, 2019. "An extended lattice hydrodynamic model considering the driver’s sensory memory and delayed-feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 522-532.
    16. 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.
    17. Changtao-Jiang, & Rongjun-Cheng, & Hongxia-Ge,, 2019. "Mean-field flow difference model with consideration of on-ramp and off-ramp," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 465-476.
    18. Jiang, Changtao & Cheng, Rongjun & Ge, Hongxia, 2018. "Effects of speed deviation and density difference in traffic lattice hydrodynamic model with interruption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 900-908.
    19. Yongjiang-Wang, & Han-Song, & Rongjun-Cheng,, 2019. "TDGL and mKdV equations for an extended car-following model with the consideration of driver’s memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 440-449.
    20. Chen, Can & Cheng, Rongjun & Ge, Hongxia, 2019. "An extended car-following model considering driver’s sensory memory and the backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 278-289.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:eurphb:v:95:y:2022:i:12:d:10.1140_epjb_s10051-022-00469-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.