A novel lattice hydrodynamic model for bidirectional pedestrian flow considering the pedestrians’ anticipation effect of density difference

Pedestrians’ anticipation effect, which is a conscious or unconscious response to the surrounding environment, plays an important role in pedestrian flow, especially under high-density condition. In order to investigate the pedestrians’ anticipation effect of density difference, an extended lattice hydrodynamic model for bidirectional pedestrian flow is proposed in this paper. The stability condition of the proposed model is deduced using linear stability analysis and the analytical result reveals that the anticipation effect of density difference can significantly enlarge the stability region on the phase diagram. By the use of nonlinear analysis method, the time-dependent Ginzburg Landau (TDGL) equation is derived to describe the evolution of pedestrian flow near the critical point. The modified Korteweg-de Vries (MKdV) equation is also derived to characterize the kink-antikink waves in unstable region. The theoretical results indicate that jams can be effectively mitigated by considering the anticipation effect of density difference. Numerical simulations are conducted to validate the accuracy of the theoretical findings.