  In this paper the phase structure of dense baryon matter composed of $u$ and
$d$ quarks with two colors has been investigated in the presence of baryon
$\mu_B$, isospin $\mu_I$ and chiral isospin $\mu_{I5}$ chemical potentials in
the framework of Nambu--Jona-Lasinio model. In the chiral limit, it has been
shown that the duality between phases with spontaneous chiral symmetry breaking
and condensation of charged pions, found in the three color case, remains valid
in the two color case. In addition, it has been shown that there are two more
dualities in the phase diagram in two color case, namely (as in the case with
$\mu_{I5}=0$), at $\mu_{I5}\ne 0$ the general $(\mu,\mu_I,\mu_{I5})$-phase
portrait of the model has dual symmetry between the phase with condensation of
charged pions and the phase with diquark condensation. This duality stays exact
even in the physical point, $m_0\ne 0$. And at $m_0=0$ the
$(\mu,\mu_I,\mu_{I5})$-phase portrait becomes even more symmetrical, since dual
symmetry between phases with spontaneous chiral symmetry breaking and diquark
condensation appears. It is shown that due to the dualities the phase diagram
is extremely symmetric and has interlacing structure. One can show that the
phase portrait of two-color NJL model can be obtained just by duality
properties from the results of investigations of three-color NJL model (it was
noticed only after the numerical calculations have been performed). Three-color
case shares only one duality of the two color one, and one can only see a facet
of this enormously symmetric picture in the case of three colors. Using
dualities only, it is possible to show that there are no mixed phases (phases
with two non-zero condensates). This prediction of dualities is of great use,
because for sure it can be shown by the direct calculations but it would be
enormously more complicated and time-consuming numerically.
