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. 2020 Jul 29;476(2239):20200303. doi: 10.1098/rspa.2020.0303

Figure 3.

Figure 3.

Transient glaciations can occur even though the warm state remains uniquely stable. Here, S = 1280 W m−2 and V/W0 = 1. The critical manifold T˙=0 is folded (has a local minimum) near the fixed point; the right-hand side branch is stable and the left-hand side branch is unstable (see figure 2). The upper trajectory (green) is able to reach the stable part of the critical manifold (i.e. before the fold), relaxing quickly back to the fixed point. The lowest trajectory (blue) is unable to intersect the stable part of the manifold and passes beneath the fold, heading towards the cold branch of the critical manifold (see figure 2). A transient, million-year glaciation results. There is a special kind of trajectory that separates these two cases: it is known in dynamical systems theory as a ‘canard’ [24]. (Online version in colour.)