  On the basis of qualitative theory of differential equations it is shown that
dynamic system based on the system of Einstein - Klein - Gordon equations with
regard to Friedman Universe has a stable center corresponding to zero values of
scalar potential and its derivative at infinity. Thus, the cosmological model
based on single massive classical scalar field in infinite future would give a
flat Universe. The carried out numerical simulation of the dynamic system
corresponding to the system of Einstein - Klein - Gordon equations showed that
at great times of the evolution the invariant cosmological acceleration has a
microscopic oscillating character ($T\sim 2\pi mt$), while macroscopic value of
the cosmological acceleration varies from $+1$ at inflation stage after which
if decreases fast to $-1/2$ (non-relativistic stage), and then slowly tends to
$-1$ (ultrarelativistic stage).
