Volume 22, Issue 1, December 2014, Pages 117 - 143
Mean-Field Limit of a Microscopic Individual-Based Model Describing Collective Motions
Laboratoire de Physique Théorique de la Matière Condensée, CNRS and Sorbonne Universités, UPMC Univ Paris 06, UMR 7600 4, place Jussieu, case courrier 121, 75252 Paris cedex 05, France.firstname.lastname@example.org
Département de Mathématiques, Université de Caen Basse-Normandie, Laboratoire de Mathématiques Nicolas Oresme, LMNO CNRS, UMR 6139, 14032 Caen Cedex, France.email@example.com
Received 10 May 2014, Accepted 6 October 2014, Available Online 6 January 2021.
- 10.1080/14029251.2015.996444How to use a DOI?
- Collective motion; interacting stochastic particle systems; weak solutions; uniqueness
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.
- © 2015 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - Carlo Bianca AU - Christian Dogbe PY - 2021 DA - 2021/01/06 TI - Mean-Field Limit of a Microscopic Individual-Based Model Describing Collective Motions JO - Journal of Nonlinear Mathematical Physics SP - 117 EP - 143 VL - 22 IS - 1 SN - 1776-0852 UR - https://doi.org/10.1080/14029251.2015.996444 DO - 10.1080/14029251.2015.996444 ID - Bianca2021 ER -