particular, the Randall–Sundrum model [@RS], are inspired directly by the popular string theory (specifically, by the Horava–Witten model [@HW]) and represent an interesting alternative for compactification of extra spatial dimensions. Secondly, there remains a possibility of solving the mass-hierarchy problem in the context of large extra dimensions (see [@ADD; @RS]). And thirdly, it has been shown that models with non-compact extra dimensions and branes can be consistent with the current gravity experiments.

Braneworld models also turned out to be consistent with modern cosmology, at the same time exhibiting new specific features. First of all, this concerns the braneworld models of “dark energy,” or of the currently observed acceleration of the universe (see [@SS] in this respect), but this is also true with respect to the early stages of cosmological evolution such as inflation (see, e.g., [@Maartens]).

A broad class of cosmological solutions in braneworld theory was systematically analyzed by Campos and Sopuerta [@CS] using convenient phase space variables similar to those introduced in [@GE]. These authors gave a complete description of stationary points in an appropriately chosen phase space of the cosmological setup and investigated their stability with respect to homogeneous and isotropic perturbations. The authors worked in the frames 