  A new cosmological model based on the de Sitter gravity is investigated by
dynamical analysis and numerical discussions. Via some transformations, the
evolution equations of this model can form an autonomous system with 8 physical
critical points. Among these critical points there exist one positive attractor
and one negative attractor. The positive attractor describes the asymptotic
behavior of late-time universe, which indicates that the universe will enter
the exponential expansion phase, finally. Some numerical calculations are also
carried out, which convince us of this conclusion derived from the dynamical
analysis.
