The talk considers the duality correspondence between fermion-antifermion and difermion interaction channels as established in two (2+1)-dimensional Gross-Neveu type models with a fermion number chemical potential $\mu$
and a chiral chemical potential $\mu_5$. The role and influence of this property on the phase structure of the models are investigated. In particular, it is shown that the chemical potential $\mu_5$ promotes the appearance of dynamical chiral symmetry breaking, whereas the chemical potential $\mu$ contributes to the emergence of superconductivity.