  We study the dynamics of a Brownian circle swimmer with a time-dependent
self-propulsion velocity in an external temporally varying harmonic potential.
For several situations, the noise-free swimming paths, the noise-averaged mean
trajectories, and the mean square displacements are calculated analytically or
by computer simulation. Based on our results, we discuss optimal swimming
strategies in order to explore a maximum spatial range around the trap center.
In particular, we find a resonance situation for the maximum escape distance as
a function of the various frequencies in the system. Moreover, the influence of
the Brownian noise is analyzed by comparing noise-free trajectories at zero
temperature with the corresponding noise-averaged trajectories at finite
temperature. The latter reveal various complex self-similar spiral or
rosette-like patterns. Our predictions can be tested in experiments on
artificial and biological microswimmers under dynamical external confinement.
