We investigate the properties of phase transitions in a weakly coupled ultracold atom-molecule boson system based on the phase space analysis approach. We identify the pure molecular and mixed atom-molecule phases of the system by different values of the time average of molecular population. When applying a periodic modulation on the energy detuning, we find that the atom-molecule mixing dynamics can be well controlled. For both high- and low-frequency modulations, it is shown that the transition points can be shifted effectively by choosing parameters of the periodic modulation appropriately. The analytical expressions for the dependence of the transition parameters on the modulation parameters are also obtained for the two cases. In particular, when the modulation with a frequency near the atom-molecule transition frequency is applied, the resonance between the periodic modulation and atom-molecule Rabi oscillation will emerge, which can affect the atom-molecule mixing dynamics dramatically and lead to the complex chaos phenomenon.
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