  We analyse the relation between the activity cycle length and the Rossby
number and collected a sample of 44 main sequence stars with well-known
activity cycle periods and rotation periods. We find a linear behaviour in the
double-logarithmic relation between the Rossby number and cycle period. The
bifurcation into a long and a short period branch is clearly real but it
depends, empirically, on the colour index B-V, indicating a physical dependence
on effective temperature and position on the main sequence. Furthermore, there
is also a correlation between cycle length and convective turnover time with
the relative depth of the convection zone. Based on this, we derive empirical
relations between cycle period and Rossby number, and for the short period
cycle branch relations, we estimate a scatter of the relative deviation between
14% and 28% on the long-period cycle branch. With these relations, we obtain a
good match with the 10.3 yr period for the well known 11-year solar Schwabe
cycle and a long-period branch value of 104 yr for the Gleissberg cycle of the
Sun. Finally, we suggest that the cycles on the short-period branch appear to
be generated in the deeper layers of the convective zone, while long-period
branch cycles seem to be related to fewer deep layers in that zone. We show
that for a broader B-V range, the Rossby number is a more suitable parameter
for universal relation with cycle-rotation than just the rotation period alone.
As proof, we demonstrate that our empirical stellar relations are consistent
with the 11-year solar Schwabe cycle, in contrast to earlier studies using just
the rotation period in their relations. Previous studies have tried to explain
the cycle position of the Sun in the cycle-rotation presentation via other
kinds of dynamo, however, in our study, no evidence is found that would suggest
another type of dynamo for the Sun and other stars.
