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TDGL and mKdV equations for car-following model considering traffic jerk and velocity difference

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Abstract

By introducing optimal velocity car-following model by Bando et al., we present an improved car-following model which is based on an optimal velocity model considering traffic jerk and full velocity difference. The nature of the model is researched by using linear and nonlinear analysis method. The analytical method and numerical simulation results show that the proposed model can describe the phase transition and critical phenomenon with the thermodynamic theory. In order to describe the traffic flow near the critical point, the time-dependent Ginzburg–Landau (TDGL) equation and the modified Korteweg–de Vries (mKdV) equation are derived. Additionally, the connection between the TDGL and the mKdV equation is also given. Theoretical analysis is demonstrated by numerical simulation.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 11372166), the Scientific Research Fund of Zhejiang Provincial, China (Grant Nos. LY15A020007, LY15E080013), the Natural Science Foundation of Ningbo (Grant Nos. 2014A610028, 2014A610022) and the K. C. Wong Magna Fund in Ningbo University, China.

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Authors and Affiliations

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

    Han Song, Hongxia Ge, Fuzhou Chen & Rongjun Cheng

  2. National Traffic Management Engineering and Technology Research, Centre Ningbo University Sub-Centre, Ningbo, 315211, China

    Han Song, Hongxia Ge, Fuzhou Chen & Rongjun Cheng

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

    Han Song, Hongxia Ge, Fuzhou Chen & Rongjun Cheng

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  1. Han Song
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  2. Hongxia Ge
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  3. Fuzhou Chen
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Correspondence to Rongjun Cheng.

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Song, H., Ge, H., Chen, F. et al. TDGL and mKdV equations for car-following model considering traffic jerk and velocity difference. Nonlinear Dyn 87, 1809–1817 (2017). https://doi.org/10.1007/s11071-016-3154-x

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  • DOI: https://doi.org/10.1007/s11071-016-3154-x

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