  The dynamic magnetic behaviors of the spin-1 Blume-Capel Ising bilayer system
(BCIS) are studied in an oscillating external magnetic field on a two-layer
square lattice by utilizing the mean field theory based on Glauber-type
stochastic dynamics (DMFT). The dynamic equations describing the
time-dependencies of the average magnetizations are obtained with the Master
equation. The dynamic phases in this system are found by solving these dynamic
equations. The temperature dependence of the dynamic order parameters is
examined to characterize the nature (continuous or discontinuous) of the phase
transitions and to obtain the dynamic phase transition points (DPT). The
dynamic phase diagrams are shown for ferromagnetic / ferromagnetic,
antiferromagnetic / antiferromagnetic, antiferromagnetic / antiferromagnetic
interactions in the plane of the reduced temperature versus magnetic field
amplitude and they display dynamic tricritical and reentrant behavior as well
as the dynamic triple point.
