A Kinetic Model for the formation of Swarms with nonlinear interactions

Martin Parisot (1) , Miroslaw Lachowicz (2)

1 ANGE - Numerical Analysis, Geophysics and Ecology
2 IMSM - Institute of Applied Mathematics [Warsaw]

The present paper deals with the modeling of formation and destruction of swarms using a nonlinear Boltzmann–like equation. We introduce a new model that contains parameters characterizing the attractiveness or repulsiveness of individuals. The model can represent both gregarious and solitarious behaviors. In the latter case we provide a mathematical analysis in the space homogeneous case. Moreover we identify relevant hydrodynamic limits on a formal way. We introduce some preliminary results in the case of gregarious behavior and we indicate open problems for further research. Finally , we provide numerical simulations to illustrate the ability of the model to represent formation or destruction of swarms.

Mots clés: orientation interaction; self-organisation; collective behaviour; swarm; kinetic formulation; hydrodynamic limit

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

Martin Parisot, Miroslaw Lachowicz. A Kinetic Model for the formation of Swarms with nonlinear interactions. Kinetic and Related Models , 2016, 9 (1), pp.33. ⟨10.3934/krm.2016.9.131⟩. ⟨hal-01152397⟩