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

In nature, self-organized systems such as flocks of birds, schools of fish and herds of sheep have to deal with the presence of external agents such as predators or leaders that modify their internal dynamics. Such situations involve a large number of individuals with their own social behavior interacting with a small number of other individuals acting as external point-source forces. Starting from a microscopic description, we derive a kinetic model using the mean-field limit and introduce a macroscopic model via a suitable hydrodynamic approximation.