The dynamic phase transitions are studied, within a mean-field approach, in the kinetic Blume-Emery-Grifftihs model under the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics and the set of the dynamic equations of motion is obtained. The behavior of the time-dependence of the order parameters and the behavior of the average order parameters in a period, which is also called the dynamic order parameters, as a function of the reduced temperature are investigated. The nature (continuous and discontinuous) of transition is characterized by studying the average order parameters in a period. The dynamic phase transition points are obtained and the phase diagrams are presented in the reduced magnetic field amplitude and reduced temperature plane. We have found that the behavior of system strongly depends on the interaction parameters and nine main different phase diagram topologies have been obtained. We also calculate the Liapunov exponents to verify the stability of the solutions and the dynamic phase transition points.