A significant controversy regarding the climate history of the Earth and its relationship to the development of complex life forms concerns the rise of oxygen in the early Earth's atmosphere. Geological records show that this rise occurred about 2.4 Gyr ago, when the atmospheric oxygen increased from less than 10^–5 present atmospheric level (PAL) to more than 0.01 PAL and possibly above 0.1 PAL. However, there is a debate whether this rise happened relatively smoothly or with well-pronounced ups and downs (the Yoyo model). In our study, we explore a simplified atmospheric chemical system consisting of oxygen, methane, and carbon that is driven by the sudden decline of the net input of reductants to the surface as previously considered by Goldblatt et al. Based on the transition stability analysis for the system equations, constituting a set of non-autonomous and non-linear differential equations, as well as the inspection of the Lyapunov exponents, it is found that the equations do not exhibit chaotic behavior. In addition, the rise of oxygen occurs relative smoothly, possibly with minor bumps (within a factor of 1.2), but without major jumps. This result clearly argues against the Yoyo model in agreement with recent geological findings.