A kinetic model for the formation of swarms with nonlinear interactions

Abstract

The present paper deals with the modeling of formation and destruction of swarms using a nonlinear Boltzmann--likeequation. We introduce a new model that contains parameters characterizing the attractiveness or repulsiveness ofindividuals. 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 relevanthydrodynamic limits on a formal way. We introduce some preliminary results in the case of gregarious behavior andwe indicate open problems for further research.Finally, we provide numerical simulations to illustrate the ability of the model to represent formation or destructionof swarms.