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Two-parameter bifurcation and energy consumption analysis of the macro traffic flow model

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
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Abstract

Bifurcation of traffic flow involves complex dynamic characteristics of the system. In order to understand the complex traffic phenomenon, this work designed a macro traffic model considering the driver’s memory which plays an important role in the traffic flow. Based on this model, we investigate the effects of the driver’s memory and wave velocity on the stability of the traffic flow. By means of one and two parameter bifurcation analysis, we explore how these parameters affect the bifurcation structure of the system, and further investigate the dynamic mechanisms of traffic flow. We explain various traffic phenomena related to the different types of equilibrium points and limit cycles by phase plane analysis. We also study how the initial density and bifurcation structure affect the energy consumption in the system. The results show that the driver’s memory and wave velocity play an important role in the stability of the traffic flow. By considering the change of bifurcation structure, we can better understand the source of traffic congestion, and further predict and control the possible traffic congestion.

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Data availability statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Data availability statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (Grant No. 11872003) and North China University of Technology Research Fund Program for Key Discipline (No. 110052972027/014).

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Authors and Affiliations

  1. School of Science, North China University of Technology, 5 Jinyuanzhuang Road, Bejing, 100144, China

    Lixia Duan

  2. School of Electrical and Control Engineering, North China University of Technology, 5 Jinyuanzhuang Road, Bejing, 100144, China

    Shuangshuang Fan & Zhonghe He

  3. School of Automation, Beijing Institude of Technology, 5 Zhongguancun South Street, Bejing, 100081, China

    Danyang Liu

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  1. Lixia Duan
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Contributions

SF designed the study, carried out the computations, analyzed the results, and wrote the first draft. LD supervised the project, contributed to the mathematical formulation. DL and ZH contributed to analysis of the results.

Corresponding author

Correspondence to Lixia Duan.

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Duan, L., Fan, S., Liu, D. et al. Two-parameter bifurcation and energy consumption analysis of the macro traffic flow model. Eur. Phys. J. B 95, 203 (2022). https://doi.org/10.1140/epjb/s10051-022-00469-9

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