Model of intermittency of grand minima and maxima in solar dynamo

Model αΩ-dynamo with casual fluctuations of parameter α reproduces all the basic characteristics of solar grand minima and maxima. Taking into account the dependence of the turbulent diffusivity on a magnetic field shows a hysteresis phenomenon. In a certain range of dynamo numbers, two types of solutions - decaying oscillations of weak fields and magnetic cycles of strong fields of constant amplitude - coexist settling in dependence on the initial conditions. Fluctuations of the α-parameter provoke transitions between these two regimes and the computations show intermittency of magnetic cycles of relatively large amplitudes and epochs of weak magnetic fields. This behavior may serve as a model of grand minima and maxima of solar activity.