KIT

Abstract

We introduce a new particle-based model for flocking and we show that, as with the Cucker-Smale model, flocking occurs when pairwise long range interactions are sufficiently strong. Next, we derive a Vlasov-type kinetic model for these particle models and we inquire about their time-asymptotic flocking behavior for compactly supported initial data and the connectivity of their underlying graph. Finally, we introduce a hydrodynamic descriptions of flocking based on the kinetic models and show flocking behavior without closure of higher moments.