Giving particles legs: How balance recovery may drive emergent collective dynamics in ultra-dense crowds
- 1Forschungszentrum Jülich, Jülich, Germany
- 2University of Wuppertal, Wuppertal, Germany
- 3Inria Rennes and Universities of Rennes 1 and Rennes 2, Rennes, France
Abstract
Ultra-dense crowds, in which physical contact between individuals cannot be avoided, pose major safety concerns. Nevertheless, the underlying dynamics driving their collective behaviours remain poorly understood. Existing dense crowd models, mostly two-dimensional and contact-based, overlook biomechanical mechanisms that govern human balance motion. In this study, we introduce a minimal two-level pedestrian model that couples upper body and legs dynamics, allowing us to capture how individuals continuously lose and recover balance under physical contact. This coupling generates emergent collective behaviours, such as self‑organised waves and large‑scale rotational motion, which prior modelling attempts failed to achieve. The model bridges basic individual biomechanical concepts and crowd-scale dynamics, offering a new interpretable framework for understanding collective dynamics in ultra-dense crowds. Author summary: Ultra-dense crowds, with continuous inter-individual contacts have been commonly observed in mass events around the world. In these crowds, bodies are so tightly packed that involuntary movement may cascade into uncontrollable, and sometimes deadly, accidents. Despite the scale of these events, we still do not fully understand what drives the sudden, large-scale collective motions previously observed in this context. Existing models consider human bodies as single disks, and consistently fail to reproduce the rich spontaneous behaviours observed in real ultra-dense crowds. In this work, we propose that a key missing ingredient is the human balance recovery mechanisms. When people are pushed and set off balance, their legs and upper bodies are forced to move semi-independently: the upper body tends to topple due to gravity while the legs rush to maintain the upright position. We built a minimal mathematical model capturing this two-level coupling between legs and upper body. Despite its simplicity, our model spontaneously reproduces both propagating crowd waves and collective rotations, emerging purely from local physical interactions without any need for intentional coordination. Our findings suggest that individual balance control is a plausible engine driving complex collective behaviours observed in dense crowds.
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BibTeX
@article{chatagnon2026giving,
title = {{Giving particles legs: How balance recovery may drive emergent collective dynamics in ultra-dense crowds}},
author = {Thomas Chatagnon and Mohcine Chraibi and Julien Pettré and Armin Seyfried and Antoine Tordeux},
journal = {PLOS Complex Systems},
year = {2026},
month = oct,
doi = {10.1371/journal.pcsy.0000110},
url = {https://journals.plos.org/complexsystems/article?id=10.1371/journal.pcsy.0000110},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Giving particles legs: How balance recovery may drive emergent collective dynamics in ultra-dense crowds
AU - Thomas Chatagnon
AU - Mohcine Chraibi
AU - Julien Pettré
AU - Armin Seyfried
AU - Antoine Tordeux
PY - 2026
DA - 2026/10/06
JO - PLOS Complex Systems
DO - 10.1371/journal.pcsy.0000110
UR - https://journals.plos.org/complexsystems/article?id=10.1371/journal.pcsy.0000110
AB - Ultra-dense crowds, in which physical contact between individuals cannot be avoided, pose major safety concerns. Nevertheless, the underlying dynamics driving their collective behaviours remain poorly understood. Existing dense crowd models, mostly two-dimensional and contact-based, overlook biomechanical mechanisms that govern human balance motion. In this study, we introduce a minimal two-level pedestrian model that couples upper body and legs dynamics, allowing us to capture how individuals continuously lose and recover balance under physical contact. This coupling generates emergent collective behaviours, such as self‑organised waves and large‑scale rotational motion, which prior modelling attempts failed to achieve. The model bridges basic individual biomechanical concepts and crowd-scale dynamics, offering a new interpretable framework for understanding collective dynamics in ultra-dense crowds. Author summary: Ultra-dense crowds, with continuous inter-individual contacts have been commonly observed in mass events around the world. In these crowds, bodies are so tightly packed that involuntary movement may cascade into uncontrollable, and sometimes deadly, accidents. Despite the scale of these events, we still do not fully understand what drives the sudden, large-scale collective motions previously observed in this context. Existing models consider human bodies as single disks, and consistently fail to reproduce the rich spontaneous behaviours observed in real ultra-dense crowds. In this work, we propose that a key missing ingredient is the human balance recovery mechanisms. When people are pushed and set off balance, their legs and upper bodies are forced to move semi-independently: the upper body tends to topple due to gravity while the legs rush to maintain the upright position. We built a minimal mathematical model capturing this two-level coupling between legs and upper body. Despite its simplicity, our model spontaneously reproduces both propagating crowd waves and collective rotations, emerging purely from local physical interactions without any need for intentional coordination. Our findings suggest that individual balance control is a plausible engine driving complex collective behaviours observed in dense crowds.
SN - 2837-8830
ER -