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A transverse Ising spin system, in the presence of time-dependent longitudinal field, is studied by the effective-field theory (EFT). The effective-field equations of motion of the average magnetization are given for the simple cubic lattice (Z = 6) and the honeycomb lattice (Z = 3). The Liapunov exponent lambda is calculated for discussing the stability of the magnetization and it is used to determine the phase boundary. The dynamic phase transition diagrams in h(0)/ZJ -Gamma/ZJ plane and in h(0)/ZJ - T/ZJ plane have been drawn, and there is no dynamical tricritical point on the dynamic phase transition boundary. The effect of the thermal fluctuations upon the dynamic phase boundary has been discussed

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