Abstract

We discuss the dynamics of systems driven by the “social engagement” of its agents with their local neighbors through local gradients. Prototype examples include models for opinion dynamics in human networks, flocking, swarming and bacterial self-organization in biological organisms, or rendezvous in mobile systems.

Two natural questions arise in this context: what is the large time behavior of such systems when the time T tends to infinity, and what is the effective dynamics of such large systems when the number of agents N tends to infinity. The underlying issue is how different rules of engagement influence the formation of clusters, and in particular, the tendency to form “consensus of opinions”. We analyze the flocking dynamics of agent-based models, present novel numerical methods which confirm the large time formation of Dirac masses at the kinetic level, and end up with critical threshold phenomena at the level of social hydrodynamics.