Tj

8000 7000 6000 5000 Years before present

Figure 3.5 Results of Dakos et al. (2008) for three examples based on predictive models: (a) runaway to glaciated Earth {N= 800), (b) collapse of thermohaline circulation (N= 1000), (c) desertification of North Africa {N= 6002). Notice the notional hysteresis loops sketched on (b) and (c). These pictures have been redrawn as mid-window plots.

Figure 3.6 The ancient greenhouse to icehouse tipping with N = 482 data points. This is one of the best correlations obtained by Dakos et al. (2008) in their work on eight recorded tipping points. Here the sediments containing CaCO3 were laid down 30-40 million years ago. Redrawn from Dakos et al. (2008), as described in the text.

Figure 3.6 The ancient greenhouse to icehouse tipping with N = 482 data points. This is one of the best correlations obtained by Dakos et al. (2008) in their work on eight recorded tipping points. Here the sediments containing CaCO3 were laid down 30-40 million years ago. Redrawn from Dakos et al. (2008), as described in the text.

target, as we are doing here (see Section 3.4.1). This forward extrapolation can be made by any appropriate method. In fact, approaching (close to) an underlying fold bifurcation, ARC(1) will vary linearly along the solution path, but parabolically with the control parameter: this parabolic effect will only be relevant if the upper solution path is already curving appreciably, which is not the case in most of the present examples displayed here.

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