Timing and nature of the GOE

The GOE corresponds to a transition between Equilibrium E₁ and Equilibrium E₂.

One possibility is that the GOE is gradual. Initially, E₁ is stable, while E₂ is unstable. When E₁ loses dynamical stability, a stable interior fixed point, given by Eqs. (⁸), (⁹), (¹⁰), and (¹¹), appears near E₁ in phase space. As parameter values become more favorable to cyanobacteria, the interior fixed point moves toward E₂ in phase space, and oxygenation is progressive. When E₂ gains dynamical stability, the GOE is complete.

Another possibility is that the GOE is sudden. In this case, E₂ gains dynamical stability first. An unstable interior fixed point, given by Eqs. (⁸), (⁹), (¹⁰), and (¹¹), appears near E₂ in phase space, and the interior fixed point moves toward E₁ in phase space. When E₁ loses dynamical stability, sudden oxygenation results, and the GOE is complete.