Mathematical modeling of crowds dynamics: Complexity and kinetic approach

摘要

This paper deals with the kinetic theory framework for the modeling of the complex dynamics of crowds constituted by a large number of individuals (pedestrians) that interact in a non-linear fashion in a domain with and without obstacles. The kinetic frameworks are coupled with the stochastic games theory and Gaussian thermostats in order to model the interactions which occur at microscopic scale. After introducing the mathematical structures for continuous and granular flows, the paper outlines suitable applications and research perspectives.