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We show that double mills are more stable than single mills under stochasticperturbations in swarming dynamic models with basic attraction-repulsionmechanisms. In order to analyse accurately this fact, we will present anumerical technique for solving kinetic mean field equations for swarmingdynamics. Numerical solutions of these equations for different sets ofparameters will be presented and compared to microscopic and macroscopicresults. As a consequence, we numerically observe a phase transition diagram interm of the stochastic noise going from single to double mill for smallstochasticity fading gradually to disordered states when the noise strengthgets larger. This bifurcation diagram at the inhomogeneous kinetic level isshown by carefully computing the distribution function in velocity space.

Single to Double Mill Small Noise Transition via Semi-Lagrangian Finite Volume Methods