  Quantum effects derived through conformal anomaly lead to an inflationary
model that can be either stable or unstable. The unstable version requires a
large dimensionless coefficient of about $5\times 10^8$ in front of the $R^2$
term that results in the inflationary regime in the $R+R^2$ ("Starobinsky")
model being a generic intermediate attractor. In this case the non-local terms
in the effective action are practically irrelevant, and there is a 'graceful
exit' to a low curvature matter-like dominated stage driven by high-frequency
oscillations of $R$ -- scalarons, which later decay to pairs of all particles
and antiparticles, with the amount of primordial scalar (density) perturbations
required by observations. The stable version is a genuine generic attractor, so
there is no exit from it. We discuss a possible transition from stable to
unstable phases of inflation. It is shown that this transition is automatic if
the sharp cut-off approximation is assumed for quantum corrections in the
period of transition. Furthermore, we describe two different quantum mechanisms
that may provide a required large $\,R^2$-term in the transition period.

High Energy Physics - Theory;Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology