Figure 2
(a) Phase portrait of Anderies’ model (Eq. 5, α = 0.1). We choose initial terrestrial (ct) and marine (cm) carbon stocks, the colour scale then indicates the minimum of ct over the whole time evolution commencing from a point. An example trajectory with a long excursion to the desert state (ct < m) is plotted in blue and ends at the attractor which is circled in yellow, the stream plot indicates the vector field of the right-hand-side (cf. Eq. 5). The dashed black line indicates the value of the safety margin m = 0.1. (b) Bifurcations in the carbon cycle model. Basin stability (SB, blue) and finite-time survivability (S(t = 500), green) estimates for different values of the terrestrial human carbon off-take α. For the survivability estimation we assumed a safety margin m = 0.1. The shading around the curves indicates one standard error, the background colour indicates the different dynamical regimes. In the inset, we give survivability curves for five selected values of α, i.e. α ∈ {0.1, 0.2, 0.3, 0.4, 0.5} from top to bottom as indicated.
