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A new lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian’s anticipation effect

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Abstract

Considering the effect of pedestrian’s anticipation, an extended lattice hydrodynamic model for bidirectional pedestrian flow with passing is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the anticipation term can significantly enlarge the stability region on the phase diagram, and the passing term may reduce the stability region and aggravate the pedestrian jam. Based on nonlinear analysis method, the Burgers, Korteweg–de Vries and modified Korteweg–de Vries equations are derived to describe the shock waves, soliton waves and kink–antikink waves in the stable, metastable and unstable region, respectively. The theoretical results show that jams may be alleviated efficiently by considering the effect of pedestrian’s anticipation. Numerical simulations are carried out in order to verify the theoretical results.

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Acknowledgments

The authors wish to thank the anonymous referees for their useful comments. This work was partially supported by the National Natural Science Foundation of China (Grant No. 61134004), Zhejiang Province National Science Foundation (Grant No. LY12A010 09) and Zhejiang Province Educational Research Project(Grant No. Y2013 28023).

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Authors and Affiliations

  1. School of Mathematics, Physics and Information Science, Zhejiang Ocean University, Zhoushan, 316000, China

    Jie Zhou

  2. Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province, Zhejiang Ocean University, Zhoushan, 316022, China

    Jie Zhou

  3. College of Automation, Northwestern Polytechnical University, Xi’an, 210097, Shanxi, China

    Jie Zhou & Zhong-Ke Shi

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  1. Jie Zhou
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Correspondence to Jie Zhou.

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Zhou, J., Shi, ZK. A new lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian’s anticipation effect. Nonlinear Dyn 81, 1247–1262 (2015). https://doi.org/10.1007/s11071-015-2065-6

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  • DOI: https://doi.org/10.1007/s11071-015-2065-6

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