  Magnetic properties of an Ising bilayer system defined on a honeycomb lattice
with non-magnetic interlayers which interact via an indirect exchange coupling
have been investigated by Monte Carlo simulation technique. Equilibrium
properties of the system exhibit ferrimagnetism with $P$-, $N$- and $Q$- type
behaviors. Compensation phenomenon suddenly disappears with decreasing strength
of indirect ferrimagnetic interlayer exchange coupling. Qualitative properties
are in a good agreement with those obtained by effective field theory. In order
to investigate the stochastic dynamics of kinetic Ising bilayer, we have
introduced two different types of dynamic magnetic fields, namely a square
wave, and a sinusoidally oscillating magnetic field form. For both field types,
compensation point and critical temperature decrease with increasing amplitude
and field period. Dynamic ferromagnetic region in the presence of square wave
magnetic field is narrower than that obtained for sinusoidally oscillating
magnetic field when the amplitude and the field period are the same for each
type of dynamic magnetic fields.
