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Cyclic magnetic activity in the Sun and other similar stars is interrupted by episodes of reduced activity such as the Maunder Minimum. This pattern is reproduced in mean field (αθ) dynamo models, where growth of the field is limited by the nonlinear action of the Lorentz force on differential rotation. The observed aperiodicity can be ascribed to deterministic rather than stochastic processes, and chaotic modulation is demonstrated for a low-order system, for two-dimensional dynamo waves and for a simple global model. Amplitude modulation that leads to grand minima is distinct from modulation associated with changes in the symmetry of the field. [ABSTRACT FROM AUTHOR]