  Stemming from the Heisenberg equations of motion, we study the time-evolution
stability of the order parameters for the cold atoms on optical lattices. The
requirement of this stability of the order parameters endows the phase diagram
with a fruitful structure in the superfluid phase. For the one-component
Bose-Hubbard model, we see that this stability of order parameter leads to a
physically receivable phase diagram. For two-component bosons, we show that the
molecules are preformed in the atomic superfluid and then condenses into a
molecular superfluid phase at a critical repulsive inter-species interaction,
which resembles the pre-pairing mechanism in high $T_c$ superconductor of Cu-O
cuprates.
