  The generalized Gauss-Bonnet theory, introduced by Lagrangian F(R,G), has
been considered as a general modified gravity for explanation of the dark
energy. G is the Gauss-Bonnet invariant. For this model, we seek the situations
under which the late-time behavior of the theory is the de-Sitter space-time.
This is done by studying the two dimensional phase space of this theory, i.e.
the R-H plane. By obtaining the conditions under which the de-Sitter space-time
is the stable attractor of this theory, several aspects of this problem have
been investigated. It has been shown that there exist at least two classes of
stable attractors : the singularities of the F(R,G), and the cases in which the
model has a critical curve, instead of critical points. This curve is R=12H^2
in R-H plane. Several examples, including their numerical calculations, have
been discussed.
