Differential Equations Modeling Crowd Interactions
Raul Borsche, Rinaldo M. Colombo, Mauro Garavello, Anne, Meurer
TL;DR
This paper develops a mathematical framework using nonlocal conservation laws and ODEs to model complex crowd interactions, supported by numerical simulations demonstrating practical applications.
Contribution
It introduces a novel analytic framework for nonlocal conservation laws interacting with ODE systems in multiple dimensions, with numerical validation.
Findings
Numerical simulations illustrate crowd interactions and agent dynamics.
The framework effectively models multi-group pedestrian behaviors.
Potential applications include crowd management and agent-based systems.
Abstract
Nonlocal conservation laws are used to describe various realistic instances of crowd behaviors. First, a basic analytic framework is established through an "ad hoc" well posedness theorem for systems of nonlocal conservation laws in several space dimensions interacting non locally with a system of ODEs. Numerical integrations show possible applications to the interaction of different groups of pedestrians, and also with other "agents".
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