Pattern formation in flows of asymmetrically interacting particles: Peristaltic pedestrian dynamics as a case study

The influence of asymmetry in the coupling between repulsive particles is studied. A prominent example is the social force model for pedestrian dynamics in a long corridor where the asymmetry leads to anisotropy in the repulsion such that pedestrians in front, i.e., in walking direction, have a bigger influence on the pedestrian behavior than those behind. In addition to one- and two-lane free flow situations, a new traveling regime is found that is reminiscent of peristaltic motion. We study the regimes and their respective stabilityboth analytically and numerically. First, we introduce a modified social forcemodel and compute the boundaries between different regimes analytically bya perturbation analysis of the one-lane and two-lane flow. Afterwards, theresults are verified by direct numerical simulations in the parameter plane ofpedestrian density and repulsion strength from the walls.