Synchronization of stochastic motions in swarms of active Brownian particles with global coupling

We consider here the dynamics and stochastic theory of swarms of self-propelled particles. Driving is modelled by the Schienbein-Gruler expression for negative friction. Global coupling is introduced by linear forces attracting to the center of mass and to the mean velocity of the swarm. Solutions for the stationary distribution of swarms are given which represent: (i) synchronized translation of the swarm with small fluctuations around its center of mass and, (ii) synchronized rotations around the center of mass which is at rest or slowly moving.