Open AccessA kinetic model for the formation of swarms with nonlinear interactions
Author(s) -
Martin Parisot,
Mirosław Lachowicz
Publication year - 2015
Publication title -
kinetic and related models
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.987
H-Index - 28
eISSN - 1937-5093
pISSN - 1937-5077
DOI - 10.3934/krm.2016.9.131
Subject(s) - nonlinear system , computer science , homogeneous , statistical physics , space (punctuation) , kinetic energy , attractiveness , mathematics , physics , classical mechanics , quantum mechanics , operating system , psychology , psychoanalysis
International audienceThe 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