The charge-density excitations in bilayer graphene at the filling-factor  <<1 at small momenta are considered in the frame of the Hartree-Fock  approximation. The presence of small asymmetry of graphene layers is included. The dependence of the magnetoplasmon energy on the bilayer ground state is shown. The energy splitting proportional to square root of H for the symmetric case with half-filled zero-energy levels is found both for bilayer and monolayer graphene.
Recent experimental progress has allowed the fabrication and study of monolayer and bilayer graphene.  The electronic band structure of these objects is gapless and has a chirality. The monolayer has Dirac-type spectrum with linear dispersion and chirality exhibiting Berry phase \pi. In magnetic field there is zero-energy Landay level, fourfold degenerate due to two spins and two valleys. The bilayer graphene is the unique object which combines the parabolic dispersion law of quasiparticles with their chirality exhibiting Berry phase  2\pi. In magnetic field there is a double-degenerate zero-energy Landay level incorporating two different orbital states with the same energy. Taking into account spin and valley degeneracies, the zero-energy Landau level is eightfold degenerate. For the bilayer with small asymmetry there are  four weakly split  two-fold levels, close to zero. This one-electron structure was confirmed in experiments on integer quantized Hall effect and Shubnikov-de Haas oscillations.These properties are understood in terms of non-interacting electrons. The electron-electron interaction is an important problem in the study of cyclotron resonance in monolayer, bilayer and multilayer graphene .
The charge-density excitations  at small momenta are considered in the frame of the Hartree-Fock approximation. The case of filling-factor <<1  is considered. This filling-factor means the absence of free carriers due to doping. The presence of small asymmetry of graphene layers is included. Without magnetic field, the asymmetry gives rise to the gap in the spectrum; in the presence of the field, the asymmetry splits the eightfold degenerate zero-energy Landau level into two fourfold levels. The energy of the magnetoplasmon excitations is considered and the strong  dependence of the energy on the form of the bilayer ground state is shown.  In asymmetric bilayer taking into account spin we have four transitions with equal energies. Energy splitting due to asymmetry is absent, only additional shift takes place. In the case of symmetric ground state with half-filled 0 and 1 for each valley and spin there are two combined transitions splitted in energy.  This splitting for combined electron-hole transitions from half-filled level is not specific to bilayer graphene. For monolayer graphene with filling-factor $\nu=0$ the value of splitting is practically the same as for bilayer graphene. If this splitting would be observed it would be the evidence of Coulomb interaction in  graphene.