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

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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.

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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).

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Authors and Affiliations

  1. Faculty of Maritime and Transportation, Ningbo University, Ningbo, 315211, China

    Zhaoze Liu, Hongxia Ge & Rongjun Cheng

  2. Jiangsu Province Collaborative Innovation Center for Modern Urban Traffic Technologies, Nanjing, 210096, China

    Zhaoze Liu, Hongxia Ge & Rongjun Cheng

  3. Engineering and Technology Research Centre Ningbo University Sub-centre, Ningbo, 315211, China

    Zhaoze Liu, Hongxia Ge & Rongjun Cheng

  4. Center for Collaborative Innovation on Port Trading Cooperation and Development, Ningbo University, Ningbo, 315211, China

    Zhaoze Liu, Hongxia Ge & Rongjun Cheng

  5. College of Information Technology, Ningbo Dahongying University, Ningbo, 315175, China

    Jufeng Wang

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  1. Zhaoze Liu
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Correspondence to Rongjun Cheng.

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Liu, Z., Wang, J., Ge, H. et al. KdV-Burgers equation in the modified continuum model considering the “backward looking” effect. Nonlinear Dyn 91, 2007–2017 (2018). https://doi.org/10.1007/s11071-017-3999-7

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  • DOI: https://doi.org/10.1007/s11071-017-3999-7

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