The main magnetic activity of the Sun can be visualised by Maunder butterfly diagrams which represent the spatio-temporal distribution of sunspots. Besides sunspots there are other tracers of magnetic activity, like filaments and active regions, which are observable over a wider latitudinal range of the Sun. Both these phenomena allow one to consider a complete picture of solar magnetic activity, which should be explained in the framework of one relatively simple model.

A kinematic αѡ-dynamo model of the magnetic field’s generation in a thin convection shell with nonuniform helicity for large dynamo numbers is considered in the framework of Parker’s migratory dynamo. The obtained asymptotic solution of equations governing the magnetic field has a form of a modulated travelling dynamo wave. This wave propagates over the most latitudes of the solar hemisphere equatorwards, and the amplitude of the magnetic field first increases and then decreases with the propagation. Over the subpolar latitudes the dynamo wave reverses, there the dynamo wave propagates polewards and decays with latitude. Butterfly diagrams are plotted and analyzed.

There is an attractive opportunity to develop a more quantitatively precise model taking into account helioseismological data on differential rotation and fitting the solar observational data on the magnetic field and turbulence, analyzing the helicity and the phase shift between toroidal and poloidal components of the field.