The evolution of various energy components with dark energy was examined. Recently many non-standard gravity models were suggested to explain the current observational data showing an accelerating phase since the recent past. All suggested models should mimic ΛCDM somehow, especially from the near past to the current epoch. However, most of them do not try to explain or predict what happens if their model were extended to the far past and/or the past. In this paper we want to address this point by analyzing the critical points of the evolution equations and their stability. Standard ΛCDM gives three critical points, radiation dominated, matter dominated, and cosmological constant dominated. Furthermore, the radiation-dominated point corresponds to the past stable point, the matterdominated point to the saddle point, and the cosmological-constant–dominated point to the future stable point. This means that this model predicts that the universe
starts from radiation domination then passes through a matter-dominated era and finally evolves into a cosmological-constant–dominated era, that is, the future de Sitter phase. We applied these creteria to few f(R) gravity models to determine viable parameter ranges
