Modeling self-organized systems interacting with few individuals: From microscopic to macroscopic dynamics

Giacomo Albi, 
Lorenzo Pareschi
(31/10/2012 Applied Mathematics Letters, 26 (2013), 397-401. arXiv:1210.1172)

In nature self-organized systems as flock of birds, school of fishes or herd of sheeps have to deal with the presence of external agents such as predators or leaders which modify their internal dynamic. Such situations take into account a large number of individuals with their own social behavior which interact with a few number of other individuals acting as external point source forces.
Starting from the microscopic description we derive the kinetic model through a mean-field limit and finally we introduce a macroscopic model through a suitable hydrodynamic approximation.

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