  The phase structure of dense quark matter in the two color case has been
investigated with nonzero baryon $\mu_B$, isospin $\mu_I$ and chiral isospin
$\mu_{I5}$ chemical potentials. %in the framework of Nambu--Jona-Lasinio model
with quark-antiquark and quark-quark interaction channels. It has been shown in
the mean-field approximation that there exist three dualities, one of them
between phases with spontaneous chiral symmetry breaking and condensation of
charged pions, found in the three color case. The other two dual symmetries
between the phase with condensation of charged pions and the phase with diquark
condensation and between chiral symmetry breaking and diquark condensation
phenomena. It has been demonstrated that due to the duality properties the
phase diagram is extremely symmetric and the whole phase diagram in two color
case can be obtained just by dualities from the phase structure of three color
case. This shows that the dualities are rather usefull tool. It is shown that
chiral imbalance generates charged pion condensation phenomenon in conditions
of matter in neutron stars, i. e. electrically neutral and $\beta$-equilibrated
dense quark matter. And that diquark condensation does not prohibit the
generation of the charged PC phase by chiral imbalance at least in the two
color case.
