  A model of CuO$_2$ planes of cuprate perovskites, containing $d_{x^2-y^2}$
copper orbitals and symmetric combinations of oxygen $p_\sigma$ orbitals, is
investigated using the strong coupling diagram technique. This approach allows
one to take into account the interactions of carriers with spin and charge
fluctuations of all ranges. Derived equations for Green's function are
self-consistently solved for the set of parameters corresponding to hole- and
electron-doped cuprates. It is shown that the mentioned interactions lead to
the appearance of spin polarons -- bound states of carriers with spin
excitations, which show themselves as sharp peaks of the density of states and
spectral functions at the Fermi level. Hole and electron doping are strongly
asymmetric. This, in particular, manifests itself in the antiferromagnetic
response for the electron-doped case and in an incommensurate magnetic ordering
for hole doping. In the latter case, the incommensurability parameter grows
with doping. The double occupancy shows that the electron-doped system retains
strong correlations up to the concentration 0.23, while for hole doping the
correlations decay rapidly. These results are in agreement with experimental
observations in cuprates.
