  The influences of quantum effects on the structure of the phase-space of
generalized Gauss-Bonnet theory, introduced by the Lagrangian F(R,G), have been
studied. G is the Gauss-Bonnet invariant, and the quantum effects are described
via the account of conformal anomaly. It has been shown that the quantum
effects change many aspects of the attractors of F(R,G) gravity models in the
R-H plane, including the location of the attractors, the number of them and
their stability properties. These variations are not, in general, from the type
of small perturbations, but instead, it can induce the great, so not ignorable,
variations which have root in the "singular perturbation" nature of this
effect. In other words, one can not ignore the quantum corrections and must be
always considered. The influences of the perfect barotropic fluids on this
problem have been studied, and it has been shown that this kind of matters do
not alter the quantum effects. It has been shown that the classical
contribution of the coupled-quintessence model, which is responsible for
inducing the quantum effects, is of this type, that is a perfect barotropic
fluid, and therefore can not change our results.
