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A Kinetic Model for the formation of Swarms with nonlinear interactions

Martin Parisot 1, * Miroslaw Lachowicz 2
* Corresponding author
1 ANGE - Numerical Analysis, Geophysics and Ecology
LJLL - Laboratoire Jacques-Louis Lions, Inria de Paris
Abstract : 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.
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Martin Parisot, Miroslaw Lachowicz. A Kinetic Model for the formation of Swarms with nonlinear interactions. Kinetic and Related Models , AIMS, 2016, 9 (1), pp.33. ⟨10.3934/krm.2016.9.131⟩. ⟨hal-01152397⟩

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