Instability of pedestrian flow and phase structure in a two-dimensional optimal velocity model

A two-dimensional optimal velocity model was proposed for the study of pedestrian and granular flow. We investigate the stability of homogeneous flow in the linear approximation and show the phase diagram of the model. We also investigate the property of the model by numerical simulation in the cases of unidirectional and counter flow. From these results, we present a unified understanding of the behavior of pedestrians and other related systems.