  Solar cycles vary in their amplitude and shape. There are several empirical
relations between various parameters linking cycle's shape and amplitude, in
particular the Waldmeier relations. As solar cycle is believed to be a result
of the solar dynamo action, these relations require explanation in the
framework of this theory.Here we aim to present a possible explanation of such
kind. We relate the cycle-to-cycle variability of solar activity to
fluctuations of solar dynamo drivers and primarily to fluctuations in the
parameter responsible for recovery of the poloidal magnetic field from the
toroidal one. To be specific, we develop such a model in the framework of the
mean-field dynamo based on the differential rotation and $\alpha$-effect. We
demonstrate that the mean-field dynamo based on a realistic rotation curve and
nonlinearity associated with the magnetic helicity balance reproduces both
qualitatively and quantitatively the Waldmeier relations observed in sunspot
data since 1750 (SIDC data). The model also reproduces more or less
successfully other relations between the parameters under discussion, in
particular, the link between odd and even cycles (Gnevyshev-Ohl rule). We
conclude that the contemporary solar dynamo theory provides a way to explain
the cycle-to-cycle variability of solar activity as recorded in sunspots. We
discuss the importance of the model for stellar activity cycles which, as known
from the data of HK project, demonstrate the cycle-to-cycle variability similar
to solar cycles.
