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KdV–Burgers equation in the modified continuum model considering anticipation effect

Author

Listed:
  • Liu, Huaqing
  • Zheng, Pengjun
  • Zhu, Keqiang
  • Ge, Hongxia

Abstract

The new continuum model mentioned in this paper is developed based on optimal velocity car-following model, which takes the drivers’ anticipation effect into account. The critical condition for traffic flow is derived, and nonlinear analysis shows density waves occur in traffic flow because of the small disturbance. Near the neutral stability line, the KdV–Burgers equation is derived and one of the solutions is given. Numerical simulation is carried out to show the local cluster described by the model.

Suggested Citation

  • Liu, Huaqing & Zheng, Pengjun & Zhu, Keqiang & Ge, Hongxia, 2015. "KdV–Burgers equation in the modified continuum model considering anticipation effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 26-31.
    • Handle: RePEc:eee:phsmap:v:438:y:2015:i:c:p:26-31
    DOI: 10.1016/j.physa.2015.05.014
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    References listed on IDEAS

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    Cited by:

    1. Tang, Tie-Qiao & Zhang, Jian & Liu, Kai, 2017. "A speed guidance model accounting for the driver’s bounded rationality at a signalized intersection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 45-52.
    2. 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.
    3. 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).
    4. 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.

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