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

Yuri B. Gaididei, Christian Marschler, Mads Peter Sørensen*, Peter L. Christiansen, Jens Juul Rasmussen

*Corresponding author for this work

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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 stability both analytically and numerically. First, we introduce a modified social force model and compute the boundaries between different regimes analytically by a perturbation analysis of the one-lane and two-lane flow. Afterwards, the results are verified by direct numerical simulations in the parameter plane of pedestrian density and repulsion strength from the walls.

Original languageEnglish
JournalEvolution Equations and Control Theory
Issue number1
Pages (from-to)73-100
Number of pages28
Publication statusPublished - 2019


  • Asymmetry
  • Bifurcations and instability
  • General perturbation schemes
  • Nonlinear lattice dynamics
  • Nonlinear modes
  • Pattern formation in complex systems
  • Pedestrian flow

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