  The dynamics of a small rigid spherical particle in an unbounded pulsating
vortex is considered, keeping constant the particle Stokes number St and
varying the particle-to-fluid density ratio $\varrho$ and the pulsation
frequency of the vortex $\omega$. We show that the asymptotic dynamics of a
particle of given St and $\varrho$ can be controlled by varying $\omega$,
turning the vortex core either into an attractor or a repellor. The creation of
non-trivial particle limit cycles characterizes the boundaries between
centrifugal and centripetal regions in parameter space. The discovered
phenomenon is termed oscillatory switching centrifugation and its implications
for particle demixing processes, biological protocols, lab-on-a-chip devices
and dynamical system theory are discussed in the end.
