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Bifurcation Analysis of the Macroscopic Traffic Flow Model Based on Driver’s Anticipation and Traffic Jerk Effect

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Abstract

Based on realistic traffic conditions, the macroscopic traffic flow model that considers the driver’s anticipation and traffic jerk effect is improved, and the bifurcation theory is used to describe and predict nonlinear traffic phenomena on the road from the perspective of global stability. Firstly, the linear stability conditions and the Korteweg–de Vries–Burgers equation are derived using linear and nonlinear methods to characterize the evolution of traffic flow. The type and stability of the equilibrium solution are discussed using the bifurcation analysis method, and the conditions of existence of the Hopf bifurcation and saddle-node bifurcation are proved. Numerical simulations show that the model can describe the complex nonlinear dynamic phenomena observed on the road. The bifurcation analysis will be helpful for improving our understanding of stop-and-go and sudden changes in stability in real traffic flow.

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ACKNOWLEDGMENTS

The authors would like to thank the anonymous referees and the editor for their valuable opinions.

Funding

This work is partially supported by the National Natural Science Foundation of China under the Grants nos. 72361031 and 12275223 and the Qizhi Personnel Training Support Project of Lanzhou Institute of Technology (project no. 2018QZ-11) and the University Youth Doctoral Support Project of Gansu Province of China under the Grant no. 2023QB-049.

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  1. College of Computer Science and Engineering, Northwest Normal University, Lanzhou, Gansu, China

    W. H. Ai, L. Xu & T. Zhang

  2. College of Electrical Engineering, Lanzhou Institute of Technology, Lanzhou, Gansu, China

    D. W. Liu

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  1. W. H. Ai
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Correspondence to W. H. Ai.

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Ai, W.H., Xu, L., Zhang, T. et al. Bifurcation Analysis of the Macroscopic Traffic Flow Model Based on Driver’s Anticipation and Traffic Jerk Effect. Fluid Dyn 58, 1395–1419 (2023). https://doi.org/10.1134/S0015462823601249

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