Context. Solar cycles vary in their amplitude and shape. There are several empirical relations between various parameters that link the cycle's shape and amplitude, foremost these of the Waldmeier relations. Aims. The solar cycle is believed to be a result of the solar dynamo action, therefore these relations require an explanation in the framework of this theory, which we aim to present here. Methods. We related the cycle-to-cycle variability of solar activity to fluctuations of solar dynamo drivers and primarily to fluctuations in the parameter responsible for the recovery of the poloidal magnetic field from the toroidal one. To be specific, we developed a model in the framework of the mean-field dynamo based on the differential rotation and ?-effect. Results. We demonstrate that the mean-field dynamo model, which is based on a realistic rotation profile and on nonlinearity that is associated with the magnetic helicity balance, reproduces both qualitatively and quantitatively the Waldmeier relations observed in sunspot data since 1750. 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). Conclusions. 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 the Mount Wilson HK project, which measures the Ca H and K line index for other stars, demonstrate the cycle-to-cycle variability similar to solar cycles.

Ключевые слова: Sunspots, Sun: activity, magnetic fields, Sun: dynamo