  Contrary to microbial taxis, where a tactic response to external stimuli is
controlled by complex chemical pathways acting like sensor-actuator loops,
taxis of artificial microswimmers is a purely stochastic effect associated with
a non-uniform activation of the particles' self-propulsion. We study the tactic
response of such swimmers in a spatio-temporally modulated activating medium by
means of both numerical and analytical techniques. In the opposite limits of
very fast and very slow rotational particle dynamics, we obtain analytic
approximations that closely reproduce the numerical description. A swimmer
drifts on average either parallel or anti-parallel to the propagation direction
of the activating pulses, depending on their speed and width. The drift in line
with the pulses is solely determined by the finite persistence length of the
active Brownian motion performed by the swimmer, whereas the drift in the
opposite direction results from the combination of ballistic and diffusive
properties of the swimmer's dynamics.
