要旨: |
I will present a survey of the main results about first and second order models of swarming where repulsion and attraction are modeled through pairwise potentials. We will mainly focus on the stability of the fascinating patterns that you get by random data particle simulations, flocks and mills, and their qualitative behavior. I will give an overview of the different levels of description of collective behavior models highlighting some of the interesting mathematical open problems in the subject. Calculus of variations, dynamical systems, mean-field limits for PDEs, control theory, kinetic and aggregation-diffusion equations together with their numerical simulations naturally show up as necessary tools to solve some of these questions. |