Self-organization in pedestrian dynamics: a stochastic port-Hamiltonian approach

Abstract

Understanding pedestrian crowds as complex systems reveals how simple individual interactions yield rich collective behaviors. In this study, we adopt an energy-based modeling framework – port-Hamiltonian (pH) systems – to analyze a minimalist variant of the social-force model with stochastic elements. This perspective interprets the dynamics as an extended Hamiltonian system that incorporates energy dissipation, control inputs, and outputs. Within this formulation, the Hamiltonian, the supplied power and the direction-alignment variable emerge as meaningful macroscopic orderparameters that characterize long-term behavior of the system. This enables us to identify self-organized strip formation by distinguishing ordered from disordered states, and to highlight the interplay between dissipation and diffusion. Moreover, for specific parameter settings, we observe noise-induced ordering. These preliminary findings open promising avenues for deeper theoretical investigation.