Parametric Modulation of Dynamo Waves

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.