  We investigate the perturbations of charged scalar field in $5$-dimensional
Gauss-Bonnet AdS black hole backgrounds. From the perturbation behaviors we
obtain the objective picture on how the high curvature influence the spacetime
perturbation and the condensation of the scalar hair. The high curvature
effects can also be read from the linear response function such as the
susceptibility and the correlation length, when the system approaches the
critical point. We find that the Gauss-Bonnet term does not affect the critical
exponents of the system and they still take the mean-field values.
