  Ten-dimensional models, arising from a gravitational action which includes
terms up to the fourth order in curvature tensor, are discussed. The spacetime
consists of one timelike dimension and two maximally symmetric subspaces,
filled with matter in the form of an anisotropic fluid. Numerical integration
of the cosmological field equations indicates that exponential, as well as
power law, solutions are possible. We carry out a dynamical study of the
results in the H_{ext} - H_{int} plane and confirm the existence of
"attractors" in the evolution of the Universe. Those attracting points
correspond to "extended De Sitter" spacetimes, in which the external space
exhibits inflationary expansion, while the internal one contracts.
