  In this paper, we derive a kinetic description of swarming particle dynamics
in an interacting multi-agent system featuring emerging leaders and followers.
Agents are classically characterized by their position and velocity plus a
continuous parameter quantifying their degree of leadership. The microscopic
processes ruling the change of velocity and degree of leadership are
independent, non-conservative and non-local in the physical space, so as to
account for long-range interactions. Out of the kinetic description, we obtain
then a macroscopic model under a hydrodynamic limit reminiscent of that used to
tackle the hydrodynamics of weakly dissipative granular gases, thus relying in
particular on a regime of small non-conservative and short-range interactions.
Numerical simulations in one- and two-dimensional domains show that the
limiting macroscopic model is consistent with the original particle dynamics
and furthermore can reproduce classical emerging patterns typically observed in
swarms.
