  We study dynamical properties of confined, self-propelled Brownian particles
in an inhomogeneous activity profile. Using Brownian dynamics simulations, we
calculate the probability to reach a fixed target and the mean first passage
time to the target of an active particle. We show that both these quantities
are strongly influenced by the inhomogeneous activity. When the activity is
distributed such that high-activity zone is located between the target and the
starting location, the target finding probability is increased and the passage
time is decreased in comparison to a uniformly active system. Moreover, for a
continuously distributed profile, the activity gradient results in a drift of
active particle up the gradient bearing resemblance to chemotaxis. Integrating
out the orientational degrees of freedom, we derive an approximate
Fokker-Planck equation and show that the theoretical predictions are in very
good agreement with the Brownian dynamics simulations.
