  We investigate the dynamics of kicked pseudo-spin-1/2 Bose-Einstein
condensates (BECs) with spin-orbit coupling (SOC) in a tightly confined
toroidal trap. The system exhibits different dynamical behaviors depending on
the competition among SOC, kick strength, kick period and interatomic
interaction. For weak kick strength, with the increase of SOC the density
profiles of two components evolve from overlapped symmetric distributions into
staggered antisymmetric distributions, and the evolution of energy experiences
a transition from quasiperiodic motion to modulated quantum beating. For large
kick strength, when the SOC strength increases, the overlapped symmetric
density distributions become staggered irregular patterns, and the energy
evolution undergoes a transition from quasiperiodic motion to dynamical
localization. Furthermore, in the case of weak SOC, the increase of kick period
leads to a transition of the system from quantum beating to Rabi oscillation,
while for the case of strong SOC the system demonstrates complex quasiperiodic
motion.
