A two-species hydrodynamic model of particles interacting through self-alignment

Laurent Navoret (1, 2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 CALVI - Scientific computation and visualization

In this paper, we present a two-species Vicsek model, that describes alignment interactions of self-propelled particles which can either move or not. The model consists in two populations with distinct Vicsek dynamics that interact only via the passage of the particles from one population to the other. The derivation of a macroscopic description of this model is performed using the methodology used for the Vicsek model: we find out a regime where alignment in the whole population occurs. We obtain a new macroscopic model for the densities of each populations and the common mean direction of the particles. The treatment of the non-conservativity of the interactions requires a detail study of the linearised interaction operator.

Mots clés: Individual based model; sheep behaviour; Vicsek model; asymptotic anal- ysis; orientation interaction; hydrodynamic limit; collision invariants

Domaines: Physique mathématique [math-ph]; Equations aux dérivées partielles [math.AP]

Laurent Navoret. A two-species hydrodynamic model of particles interacting through self-alignment. Mathematical Models and Methods in Applied Sciences, 2012, ⟨10.1142/S0218202513500036⟩. ⟨hal-00924803⟩