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In the paper a generalization of the (1+1)-dimensional model by Chodos et al[Phys. Rev. D61, 045011 (2000)] has been performed to the case of(2+1)-dimensional spacetime. The model includes four-fermion interaction bothin the fermion-antifermion (or chiral) and fermion-fermion (or superconducting)channels. We study temperature $T$ and chemical potential $\mu$ induced phasetransitions in the leading order of large-$N$ expansion technique, where $N$ isa number of fermion fields. It is shown that at sufficiently large values of$\mu$ and arbitrary relations between coupling constants, superconducting phaseappears in the system both at T=0 and $T>0$. In particular, at T=0 andsufficiently weak attractive interaction in the chiral channel, the Cooperpairing occurs for arbitrary couplings in the superconducting channel even atinfinitesimal values of $\mu$.

Superconducting phase transitions induced by chemical potential in (2+1)-dimensional four-fermion quantum field theory