  We study the perturbation of the scalar field interacting with the Maxwell
field in the background of d-dimensional charged AdS black hole and AdS
soliton. Different from the single classical field perturbation, which always
has the decay mode in the black hole background, we observe the possible
growing mode when the perturbation of the scalar field strongly couples to the
Maxwell field. Our results disclose the signature of how the phase transition
happens when the interaction among classical fields is strong. The sudden
change of the perturbation to growing mode is also observed in the AdS soliton
with electric potential. However in the magnetic charged AdS soliton
background, we observe the consistent perturbation behavior when the
interaction between scalar field and Maxwell field is considered. This implies
that for the magnetic charged AdS soliton configuration, unlike the situation
with electric potential, there is no scalar field condensation which causes the
phase change.
