  We study the out-of-equilibrium dynamics of a Bardeen-Cooper-Schrieffer
condensate subject to a periodic drive. We demonstrate that the combined effect
of drive and interactions results in emerging parametric resonances, analogous
to a vertically driving pendulum. In particular, Arnold tongues appear when the
driving frequency matches $2\Delta_0/n$, with $n$ a natural number, and
$\Delta_0$ the equilibrium gap parameter. Inside the Arnold tongues we find a
commensurate time-crystal condensate which retains the $U(1)$ symmetry breaking
of the parent superfluid/superconducting phase and shows an additional
time-translational symmetry breaking. Outside these tongues, the synchronized
collective Higgs mode found in quench protocols is stabilized without the need
of a strong perturbation. Our results are directly relevant to cold-atom and
condensed-matter systems and do not require very long energy relaxation times
to be observed.
