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In this paper we investigate the phase structure of a (1+1) and(3+1)-dimensional quark model with four-quark interaction and in the presenceof baryon ($\mu_B$), isospin ($\mu_I$) and chiral isospin ($\mu_{I5}$) chemicalpotentials. It is shown that the chemical potential $\mu_{I5}$ promotes theappearance of the charged PC phase with nonzero baryon density. Results of bothmodels are qualitatively the same, this fact enhances one's confidence in %thefaith in the obtained predictions. It is established that in the large-$N_c$limit ($N_c$ is the number of colored quarks) there exists a dualitycorrespondence between the chiral symmetry breaking phase and the charged pioncondensation one.

Affinity of NJL$_2$ and NJL$_{4}$ model results on duality and pion condensation in chiral asymmetric dense quark matter