From microscopic to macroscopic: the large number dynamics of agents and cells, possibly interacting with a chemical background

Abstract

In this paper we review some recent results dealing with the transition between microscopic and macroscopic scales in different fields, including kinetic theory, cells movement in biology, chemotaxis, flocking phenomena and agent systems. The methodology of the mean-field approach of this study uses the concept of marginals instead of the empirical measure paradigm. Numerical computations showing some theoretically unexpected features are presented at the end of the paper.