  In this paper, we present a rigorous analysis of symmetry and underlying
physics of the nonlinear two-mode system driven by a harmonic mixing field, by
means of multiple scale asymptotic analysis method. The effective description
in the framework of the second-order perturbative theory provides an accurate
picture for understanding the Floquet eigenspectrum and dynamical features of
the nonlinear two-mode system, showing full agreement with the prediction of
symmetry considerations. We find that two types of symmetries play significant
role in the dynamical features of this model, the mechanism behind which can be
interpreted in terms of the effective description. The results are of relevance
for the phase control of the atomic localization in Bose-Einstein condensates
or switch of the optical signals in nonlinear mediums.
