Nonlinear Dynamics

, Volume 91, Issue 3, pp 2007–2017 | Cite as

KdV-Burgers equation in the modified continuum model considering the “backward looking” effect

  • Zhaoze Liu
  • Jufeng Wang
  • Hongxia Ge
  • Rongjun Cheng
Original Paper
First Online:
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Accepted:
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Abstract

Considering the backward looking effect, a modified continuum model is put forward. The stability criterion of this continuum model is deduced by performing linear stability analysis. The theoretical result demonstrates that the traffic flow is stabilized considering backward looking effect. The KdV-Burgers equation is obtained through perturbed nonlinear analysis, which could show the propagating process of density wave. Numerical simulation is carried out to explores how backward looking affected each car’s velocity, density and energy consumption. Numerical results demonstrate that backward looking effect has significant impact on traffic dynamic characteristic. In addition, the energy consumptions of this modified continuum model are also studied. Numerical simulation results indicate that the effect of backward looking will suppress the traffic jam and decrease cars’ energy consumptions during the whole evolution of small perturbation.

Keywords

Traffic flow Continuum traffic model Backward looking effect Nonlinear analysis Energy consumption 
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Notes

Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant Nos. 11702153, 71571107, 61773290), the Natural Science Foundation of Zhejiang Province, China (Grant No. LY18A010003) and the K.C. Wong Magna Fund in Ningbo University, China. Funding was provided by National Natural Science Foundation of China (Grant No. 11372166), the Scientific Research Fund of Zhejiang Provincial, China (Grant Nos. LY15A020007, LY15E080013).

Compliance with ethical standards

Conflict of Interests

The authors declare that there is no conflict of interests regarding the publication of this article.

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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2017

Authors and Affiliations

  • Zhaoze Liu
    • 1
    • 2
    • 3
    • 4
  • Jufeng Wang
    • 5
  • Hongxia Ge
    • 1
    • 2
    • 3
    • 4
  • Rongjun Cheng
    • 1
    • 2
    • 3
    • 4
  1. 1.Faculty of Maritime and TransportationNingbo UniversityNingboChina
  2. 2.Jiangsu Province Collaborative Innovation Center for Modern Urban Traffic TechnologiesNanjingChina
  3. 3.Engineering and Technology Research Centre Ningbo University Sub-centreNingboChina
  4. 4.Center for Collaborative Innovation on Port Trading Cooperation and DevelopmentNingbo UniversityNingboChina
  5. 5.College of Information TechnologyNingbo Dahongying UniversityNingboChina

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