  The magnetic activity of the Sun becomes stronger and weaker over roughly an
11 year cycle, modulating the radiation and charged particle environment
experienced by the Earth as "space weather". Decades of observations from the
Mount Wilson Observatory have revealed that other stars also show regular
activity cycles in their Ca II H+K line emission, and identified two different
relationships between the length of the cycle and the rotation rate of the
star. Recent observations at higher cadence have allowed the discovery of
shorter cycles with periods between 1-3 yr. Some of these shorter cycles
coexist with longer cycle periods, suggesting that two underlying dynamos can
operate simultaneously. We combine these new observations with previous data,
and we show that the longer and shorter cycle periods agree remarkably well
with those expected from an earlier analysis based on the mean activity level
and the rotation period. The relative turbulent length scales associated with
the two branches of cyclic behavior suggest that a near-surface dynamo may be
the dominant mechanism that drives cycles in more active stars, whereas a
dynamo operating in deeper layers may dominate in less active stars. However,
several examples of equally prominent long and short cycles have been found at
all levels of activity of stars younger than 2.3 Gyr. Deviations from the
expected cycle periods show no dependence on the depth of the convection zone
or on the metallicity. For some stars that exhibit longer cycles, we compute
the periods of shorter cycles that might be detected with future high-cadence
observations.
