Territory Covered by $N$ Self-Propelled Brownian Agents in 2 dimensions

We consider the problem of the territory covered by $N$ non-interacting self-propelled Brownian agents where self-propulsion is modeled by a non-linear friction term in the Langevin-like equations of motion for each agent. Our study generalizes, to a continuous time and space description, the well known problem of the territory explored by $N$ Random Walkers [1]. Numerical and analytical approaches are presented to exhibit the effects of self-propulsion on the many independent agents exploring two dimensional homogenous regions. Our results may have a wide range of applications in a variaty of non-equilibrium systems. \\[4pt] [1] L Hernan et al. Territory covered by $N$ diffusing particles. Nature 355, 423-426 (1992).