A novel lattice hydrodynamic model for bidirectional pedestrian flow with the consideration of pedestrian’s memory effect
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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.
KeywordsPedestrian flow Nonlinear analysis Memory effect MKdV equation
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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