  We report an interesting phenomenon of noise-induced vortex reversal in a
two-dimensional system of self-propelled particles (SPP) with soft-core
interactions. With the aid of forward flux sampling, we analyze the
configurations along the reversal pathway and thus identify the mechanism of
vortex reversal. We find that statistically the reversal exhibits a
hierarchical process: those particles at the periphery first change their
motion directions, and then more inner layers of particles reverse later on.
Furthermore, we calculate the dependence of the average reversal rate on noise
intensity $D$ and the number $N$ of SPP. We find that the rate decreases
exponentially with the reciprocal of $D$. Interestingly, the rate varies
nonmonotonically with $N$ and a minimal rate exists for an intermediate value
of $N$.
