  We solve the Wheeler-DeWitt equation for the minisuperspace of a cosmological
model of Bianchi type I with a minimally coupled massive scalar field $\phi$ as
source by generalizing the calculation of Lukash and Schmidt [1]. Contrarily to
other approaches we allow strong anisotropy. Combining analytical and numerical
methods, we apply an adiabatic approximation for $\phi$, and as new feature we
find a period-doubling bifurcation. This bifurcation takes place near the
cosmological quantum boundary, i.e., the boundary of the quasiclassical region
with oscillating $\psi$-function where the WKB-approximation is good. The
numerical calculations suggest that such a notion of a ``cosmological quantum
boundary'' is well-defined, because sharply beyond that boundary, the
WKB-approximation is no more applicable at all. This result confirms the
adequateness of the introduction of a cosmological quantum boundary in quantum
cosmology.
