  High-$T_c$ cuprates like $La_{2-x}Sr_{x}CuO_{4}$ and $YBa_{2-x}Cu_{3}O_{6+x}$
are considered as a system of the electron and hole polar pseudo-Jahn-Teller
$CuO_{4}$ centers $[{CuO}_{4}^{7-}]_{JT}$ and $[CuO_{4}^{5-}]_{JT}$,
respectively, or a system of the local bosons moving in a lattice of the hole
centers. Ground manifold of the polar centers includes three terms $^{1}A_{1g}$
(Zhang-Rice singlet), $^{1}E_{u}$, $^{3}E_{u}$ with different spin
multiplicity, orbital degeneracy and parity that provides an unconventional
multi-mode behaviour of the cuprates. The spin subsystem of the copper oxides
within the polar Jahn-Teller $CuO_{4}$ centers model is a two-component spin
liquid and corresponds to a singlet-triplet magnet with possible noncollinear
spin configurations. In the framework of a modified mean field approximation
some kinds of spin ordering are discussed including as a trivial singlet or
triplet states as a pure quantum singlet-triplet mixed state. A local boson
movement is accompanied by a modulation of the spin density on the site
resulting in the so called induced spin fluctuations. Some unconventional
features of the induced spin fluctuations are considered including an
appearance of the induced longitudinal ferrimagnetism with an appropriate
contribution to the spin susceptibility, a possibility to observe and examine
the charge fluctuations with the help of the traditional magnetic methods such
as the magnetic inelastic neutron scattering and the spin lattice relaxation
experiments. The suggested model, in comparison with the nearly
antiferromagnetic Fermi-liquid model, represents new approach to the
description of the spin system of the high-$T_c$ cuprates.
