  The study of stability of gravitational perturbations in higher derivative
gravity has shown that at the linear level the massive unphysical ghost is not
generated from vacuum if the initial seed of metric perturbation has frequency
essentially below the Planck threshold. The mathematical knowledge indicated
that the linear stability is supposed to hold even at the nonperturbative
level, but in such a complicated case it is important to perform a verification
of this statement. We compare the asymptotic stability solutions at the linear
and full nonperturbative levels for the Bianchi-I metric with small
anisotropies, which can be regarded as an extreme, zero frequency limit of a
gravitational wave. As one should expect from the combination of previous
analysis and general mathematical theorems, there is a good correspondence
between linear stability and the nonperturbative asymptotic behavior.
