  This work is the extension of author`s research, where the modified theory of
induced gravity (MTIG) is proposed. The theory describes two systems (stages):
Einstein (ES) and "restructuring" (RS). We consider equations with quadratic
potential that are symmetric with respect to scale transformations. The
solutions of the equations obtained for the case of spaces defined by the
Friedman-Robertson-Walker metric, as well as for a centrally symmetric space
are investigated. In our model arise effective gravitational and cosmological
"constants", which are defined by the "mean square" of the scalar fields. In
obtained solutions the values of such parameters as "Hubble parameter",
gravitational and cosmological "constants" in the RS stage fluctuate near
monotonically evolving mean values. These parameters are matched with
observational data, described as phenomena of dark energy and dark matter. The
MTIG equations for the case of a centrally symmetric gravitational field, in
addition to the Schwarzschild-de Sitter solutions, contain solutions that lead
to the new physical effects at large distances from the center. The
Schwarzschild-Sitter solution becomes unstable and enters the oscillatory
regime. For distances greater than a certain critical value, the following
effects can appear: deviation from General relativity and Newton's law of
gravitational interaction, antigravity.
