  Long-term variations of solar activity, including the Grand minima, are
believed to result from temporal variations of dynamo parameters. The simplest
approximation of dynamo waves is applied to show that cyclic variations of the
parameters can lead to an exponential growth or decay of magnetic oscillations
depending on the variations frequency. There is no parametric resonance in a
dynamo, however: the selective sensitivity to distinct frequencies,
characteristic of resonant phenomena, is absent. A qualitative explanation for
this finding is suggested. Nonlinear analysis of dynamo-waves reveals the
hysteresis phenomenon found earlier in more advanced models. However, the
simplified model allows a computation of a sufficiently large number of
dynamo-cycles for constructing the distribution function of their amplitudes to
reproduce qualitatively two modes of solar activity inferred recently from
cosmogenic isotope content in natural archives.
