  The stability of the Bianchi type I anisotropic brane cosmology is analyzed
in this paper. We also study the effect of the brane solution by comparing the
models on the 3-brane and the models in the conventional Einstein's space.
Analysis is presented for two different models: one with a perfect fluid and
the other one with a dilaton field. It is shown that the anisotropic expansion
is smeared out dynamically for both theories in the large time limit
independent of the models with different types of matter. The initial states
are, however, dramatically different. A primordial anisotropic expansion will
grow for the conventional Einstein's theory. On the other hand, it is shown
that the initial state is highly isotropic for the brane universe except for a
very particular case. Moreover, it is also shown that the Bianchi type I
anisotropic cosmology is stable against any anisotropic perturbation for both
theories in the large time limit.
