In this presentation, I will focus on the modelling of systems with numerous agents. We'll begin with a concise presentation of various phenomena within particle systems, such as particle interactions in plasma physics and the dynamics of a bird flock, and how they are modeled. We shall give a few examples of the emergence of complex behaviors from this kind of modelling. Finally, we shall see how one can go from a microscopic description of every agent, based on Newton's equations, to a description of the statistical distribution of agents in the limit of a large number of particles. This approximation leads indeed to huge computational savings for numerical simulations.
