We study a simple model for the solar dynamo in the framework of the Parker
migratory dynamo, with a nonlinear dynamo saturation mechanism based on
magnetic helicity conservation arguments. We find a parameter range in which
the model demonstrates a cyclic behaviour with properties similar to that of
Parker dynamo with the simplest form of algebraic alpha-quenching. We compare
the nonlinear current helicity evolution in this model with data for the
current helicity evolution obtained during 10 years of observations at the
Huairou Solar Station of China. On one hand, our simulated data demonstrate
behaviour comparable with the observed phenomenology, provided that a suitable
set of governing dynamo parameters is chosen. On the other hand, the
observational data are shown to be rich enough to reject some other sets of
governing parameters. We conclude that, in spite of the very preliminary state
of the observations and the crude nature of the model, the idea of using
observational data to constrain our ideas concerning magnetic field generation
in the framework of the solar dynamo appears promising.Comment: 10 pages, 3 Postscript figures, uses aa.cl