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TDGL and mKdV equations for car-following model considering driver’s anticipation

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Abstract

Car-following models are proposed to describe the jamming transition in traffic flow on a highway. In this paper, a new car-following model considering the driver’s forecast effect is investigated to describe the traffic jam. The nature of the model is studied using linear and nonlinear analysis method. A thermodynamic theory is formulated to describe the phase transition and critical phenomenon in traffic flow and the time-dependent Ginzburg–Landau (TDGL) equation is derived to describe the traffic flow near the critical point. It is also shown that the modified Korteweg-de Veris (mKdV) equation is derived to describe the traffic jam. The connection between the TDGL and the mKdV equations is given.

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Acknowledgments

Project supported by the National Natural Science Foundation of China (Grant Nos. 11372166, 11372147 and 61074142), the Natural Science Foundation of ZheJiang Province (Grant No.Y13A010029) and K.C.Wong Magna Fund in Ningbo University.

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Authors and Affiliations

  1. Faculty of Science, Ningbo University, Ningbo, 315211, China

    Feng Lv

  2. Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo, 315211, China

    Hui-Bing Zhu

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

    Hong-Xia Ge

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  1. Feng Lv
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  2. Hui-Bing Zhu
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Correspondence to Hong-Xia Ge.

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Lv, F., Zhu, HB. & Ge, HX. TDGL and mKdV equations for car-following model considering driver’s anticipation. Nonlinear Dyn 77, 1245–1250 (2014). https://doi.org/10.1007/s11071-014-1374-5

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  • DOI: https://doi.org/10.1007/s11071-014-1374-5

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