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Nonlinear Dynamics

, Volume 83, Issue 4, pp 2019–2033 | Cite as

A novel lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian’s memory effect

  • Jie Zhou
  • Zhong-Ke Shi
  • Zhi-Song Liu
Original Paper
  • 214 Downloads

Abstract

Due to the bad environmental conditions such as bad weather, smoky condition, insufficient light, it is difficult for a pedestrian to capture the precise position of others in these situations. Thus, memory effect could be influential and the pedestrian may walk with his/her memory. Considering the effect of pedestrian’s memory, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed in this paper. The stability condition is obtained by the use of linear stability analysis. It is shown that the memory effect term can significantly reduce the stability region on the phase diagram. 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 regions, respectively. The theoretical results show that jams may be aggravated by considering the effect of pedestrian’s memory. Numerical simulations are carried out in order to verify the theoretical results.

Keywords

Pedestrian flow Nonlinear analysis Memory effect  MKdV equation 

Notes

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 Natural Science Foundation (Grant Nos. LY12A01009; LQ12A01007), and Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. Y201328023).

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.School of Mathematics, Physics and Information ScienceZhejiang Ocean UniversityZhoushanChina
  2. 2.Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang ProvinceZhejiang Ocean UniversityZhoushanChina
  3. 3.College of AutomationNorthwestern Polytechnical UniversityXi’anChina

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