Cosmological dynamics of spatially flat Einstein-Gauss-Bonnet models in
  various dimensions: Low-dimensional $\Lambda$-term case
  In this paper we perform a systematic study of spatially flat
[(3+D)+1]-dimensional Einstein-Gauss-Bonnet cosmological models with
$\Lambda$-term. We consider models that topologically are the product of two
flat isotropic subspaces with different scale factors. One of these subspaces
is three-dimensional and represents our space and the other is D-dimensional
and represents extra dimensions. We consider no {\it Ansatz} on the scale
factors, which makes our results quite general. With both Einstein-Hilbert and
Gauss-Bonnet contributions in play, the cases with $D=1$ and $D=2$ have
different dynamics due to the different structure of the equations of motion.
We analytically study equations of motion in both cases and describe all
possible regimes. It is demonstrated that $D=1$ case does not have physically
viable regimes while $D=2$ has smooth transition from high-energy Kasner to
anisotropic exponential regime. This transition occurs for two ranges of
$\alpha$ and $\Lambda$: $\alpha > 0$, $\Lambda > 0$ with $\alpha \Lambda
\leqslant 1/2$ and $\alpha < 0$, $\Lambda > 0$ with $\alpha\Lambda < -3/2$. For
the latter case if $\alpha\Lambda = -3/2$, extra dimensional part has $h\to 0$
and so the size of extra dimensions (in the sense of the scale factor) is
reaching constant value. We report substantial differences between $D=1$ and
$D=2$ cases and between these cases and their vacuum counterparts, describe
features of the cases under study and discuss the origin of the differences.
