investigated by numerical simulation. First，for the free potential case，the results show that

active Brownian particles do not per- form directed motion and the mean squared displacement of

active Brownian particle is a nonlinear function of time. Then in the harmonic potential case，we

find that the free diffusion of particle is restricted and the range of diffusive motion of active

Brownian particle is larger than that of passive Brownian particle during the same time interval.

At last，for asymmetric period potential we calculate the distribution of the displacement of the

active Brownian particle and the averaged velocity of the active Brownian particle change in time

with different potential barriers. The results show whether or not active Brownian particle is

able to transfer the depot energy into directed motion depends on the height of asymmetric

potential barrier.