Modeling flocking behaviour: dynamics and kinetic limit for self-propelled particle systems with mean field like interactions

We discuss the problem of modeling the emergence of coordinated movements of a network made of a large number of self-propelled particles (agents) in terms of microscopic decisions of each individual member. The emergence of phase space patterns persistent in time described by a large connected cluster of coherently moving particles is called flocking or swarming. We introduce the basic models exhibiting such a behaviour and review the major results about proving its stability for finite size systems as well as, in the kinetic limit, we show that the particle density satisfies Vlasov type equations under suitable conditions on the interaction.