  We consider Brownian particles with the ability to take up energy from the
environment, to store it in an internal depot, and to convert internal energy
into kinetic energy of motion. Provided a supercritical supply of energy, these
particles are able to move in a ``high velocity'' or active mode, which allows
them to move also against the gradient of an external potential. We investigate
the critical energetic conditions of this self-driven motion for the case of a
linear potential and a ratchet potential. In the latter case, we are able to
find two different critical conversion rates for the internal energy, which
describe the onset of a directed net current into the two different directions.
The results of computer simulations are confirmed by analytical expressions for
the critical parameters and the average velocity of the net current. Further,
we investigate the influence of the asymmetry of the ratchet potential on the
net current and estimate a critical value for the asymmetry in order to obtain
a positive or negative net current.
