  Following the paper exploring the Anderson localization of monochromatically
perturbed kicked quantum maps [Phys.Rev. E{\bf 97},012210], the
delocalization-localization transition phenomena in polychromatically perturbed
quantum maps (QM) is investigated focusing particularly on the dependency of
critical phenomena upon the number $M$ of the harmonic perturbations, where
$M+1=d$ corresponds to the spatial dimension of the ordinary disordered
lattice. The standard map and the Anderson map are treated and compared. As the
basis of analysis, we apply the self-consistent theory (SCT) of the
localization, taking a plausible hypothesis on the mean-free-path parameter
which worked successfully in the analyses of the monochromatically perturbed
QMs. We compare in detail the numerical results with the predictions of the
SCT, by largely increasing $M$. The numerically obtained index of critical
subdiffusion $t^\alpha$~($t$:time) agrees well with the prediction of
one-parameter scaling theory $\alpha=2/(M+1)$, but the numerically obtained
critical exponent of localization length significantly deviates from the SCT
prediction. Deviation from the SCT prediction is drastic for the critical
perturbation strength of the transition: if $M$ is fixed the SCT presents
plausible prediction for the parameter dependence of the critical value, but
its value is $1/(M-1)$times smaller than the SCT prediction, which implies
existence of a strong cooperativity of the harmonic perturbations with the main
mode.
