  We study changes of the galactic cosmic ray (GCR) intensity for the ending
period of the solar cycle 23 and the beginning of the solar cycle 24 using
neutron monitors experimental data. We show that an increase of the GCR
intensity in 2009 is generally related with decrease of the solar wind velocity
U, the strength B of the interplanetary magnetic field (IMF), and the drift in
negative (Aneg) polarity epoch. We present that temporal changes of rigidity
dependence of the GCR intensity variation before reaching maximum level in 2009
and after it, do not noticeably differ from each other. The rigidity spectrum
of the GCR intensity variations calculated based on neutron monitors data (for
rigidities greaten than 10 GV) is hard in the minimum and near minimum epoch.
We do not recognize any non-ordinary changes in the physical mechanism of
modulation of the GCR intensity in the rigidity range of GCR particles to which
neutron monitors respond. We compose 2-D non stationary model of transport
equation to describe variations of the GCR intensity for 1996-2012 including
the Apos (1996-2001) and the Aneg (2002-2012) periods; diffusion coefficient of
cosmic rays for rigidity 10-15 GV is increased by 30 percent in 2009 (Aneg)
comparing with 1996 (Apos). We believe that the proposed model is relatively
realistic and obtained results are satisfactorily compatible with neutron
monitors data.
