  We study, via extensive numerical simulations, the force-velocity curve of an
active particle advected by a steady laminar flow, in the nonlinear response
regime. Our model for an active particle relies on a colored noise term that
mimics its persistent motion over a time scale $\tau_A$. We find that the
active particle dynamics shows non-trivial effects, such as negative
differential and absolute mobility (NDM and ANM, respectively). We explore the
space of the model parameters and compare the observed behaviors with those
obtained for a passive particle ($\tau_A=0$) advected by the same laminar flow.
Our results show that the phenomena of NDM and ANM are quite robust with
respect to the details of the considered noise: in particular for finite
$\tau_A$ a more complex force-velocity relation can be observed.
