Being able to forecast approaching transitions or tipping points in complex systems is of great importance and very difficult. Since no well-established consensus concerning the most viable approach exists, this project will look at some of the discussions in the literature.
The suggestion that increase in fluctuations and slowing down [384] can be used as early warning signs has attracted significant interest, but the approach is not always successful.
(a) List the various early warning signals suggested in [243, 347, 384]. Comment on the difference between internally and externally triggered transitions and the role of stochasticity.
(b) In [73], Ornstein–Uhlenbeck theory is combined with the bifurcation approach of [384] and applied to model systems and empirical data. Give a summary of the discussion.
(c) Read [175] and explain the weaknesses the authors discuss in using increased fluctuations as precursors in finance. Relate your explanation to Fig. 13.3.

(d) It has been suggested that the forecasting approach presented in [384] can be improved by use of ‘deep learning’. Outline the discussion in [74].
(e) Summarise the findings in [389], which study autocorrelations as early warning in psychopathology.
(f) Briefly explain the idea behind ‘critical speeding up’ as presented in [445]. Discuss how applicable this approach is in your opinion.

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400 120 | Sn(t) 80 300 40 200 0 100 0 3.43 3.53 |Sn(t) Q(t) Q(1) 3.73 3.83 Transition 3.63 Millions of time steps