  We consider the Cucker-Smale system with multiplicative noise in a harmonic
potential field and investigate the effect of harmonic potential field. In the
presence of external potential force, the system is expected to emerge into
almost surely velocity flocking and spatial concentration, due to the alignment
mechanism, confining harmonic potential field and multiplicative noise. By
constructing a stochastic Lyapunov functional, we derive a sufficient condition
for the almost surely flocking and concentration behavior for the stochastic
particle model, and verify it numerically. Then, we discuss the flocking and
concentration behavior for the mean field Vlasov-type kinetic model. Moreover,
a rigorous analysis of the uniform mean-field limit estimate for the limit
process from the stochastic model to the kinetic one is provided.
