  In the present paper, we describe the antiferromagnetic and excitonic
correlations in the AA-stacked bilayer graphene. We consider the applied
external electric field potential to the structure which leads to the
electronic charge imbalance between the layers in the system. By using the
generalized two-layer Hubbard Hamiltonian, we consider different particle
filling regimes in the layers. We calculate the important energy scales in the
system and we establish the conditions for the appearance of the
antiferromagnetic order in the system. We consider both large and small Coulomb
interaction limits in the layers and the effect of the electric field potential
on the calculated order parameters. We discuss the coexistence of
antiferromagnetism and excitonic phases and we show that they can coexist only
in the regime away from half-filling. In the case away from the half-filling,
we show the existence of a critical value $U_{\rm C}$ of the Coulomb
interaction potential at which we establish the transition from the
single-valued to the triple valued excitonic states, governed by the strong
electronic reconfiguration, in the system. The zero-temperature limit is
considered in the problem.
