Mean-Field Limit of a Microscopic Individual-Based Model Describing Collective Motions

This paper is mainly concerned with a mean-field limit and long time behavior of stochastic microscopic interacting particles systems. Specifically we prove that a class of ODE modeling collective interactions in animals or pedestrians converges in the mean-field limit to the solution of a non-local kinetic PDE. The mathematical analysis, performed by weak measure solutions arguments, shows the existence of measure-valued solutions, asymptotic stability and chaos propagation that are relevant properties in the description of collective behaviors that emerge in animals and pedestrians motions.