Classification and detection of critical transitions
Daniele Proverbio, PhD supervisor: Jorge Goncalves
[Expected start: September 2018]
The goal of this subproject is to provide a classification of CTs and associated early warning signals for diverse applications. The success of detecting early warning signals has varied so far with the particular field. In some cases the coefficient of variance or correlation of the time-signals of a particular species has been used (Scheffer 2010; Gorban 2010; Chen 2012). In others, particular distributions, such as the power law have been applied to predict financial crises (Sorentte 2004; Forró 2015). However, most cases have not taken into account the actual dynamics that generated the data: different forms of dynamical behaviours can lead to very different ways a CT occurs (Lovecchio 2012; Gu 2015; Kuehn 2014; Morales 2015; Murray 2002).
Biological, physiological and other systems, such as financial systems, are dynamic in nature (Murray 2002; Tsuchiya 2015; D’Souza 2015; Gorban 2010; Föllmer 2011; Enders 2008). They evolve according to complex stochastic dynamics (Murray 2001; Gu 2015; Föllmer 2011). Understanding these dynamics can lead to better forms of capturing CTs. For example, CTs can occur as bistable systems switch from one stable (desired) equilibrium to the other (undesired) (Morales 2015; D’Souza 2015; Murray 2002). In this case, the system contains both states and the switch can be triggered by external effects (Morales 2015; Aguirre 2015), such as stress or alcohol. Or a system may have a single state (Kuehn 2014), and this may change due to changes in a single parameter (Murray 2002). For example, mutations in DNA can lead to cancer (Tsuchiya 2015). In this case, changes in a single parameter can cause bifurcations (D’Souza 2015) and transform the system into multiple equilibria, oscillations or even chaos (Khalil 1996; Sastry 2013; Strogatz 2014).
The key to anticipating CTs lies in understanding what kind of system we have (Tsuchiya 2015; Morales 2015; Gorban 2010). Hence, the first step is to build a classification tool. This will initially be done using simplified models to gain a deep understanding of CTs. For each class of CT, we will investigate which combination of signals optimally amplifies the detection of CTs. Then it will become possible to classify real-world applications and pinpoint the signals that need to be measured for detecting CTs. We will then proceed to find the optimal combination of available signals to detect CTs. This should also explain the reason why some metrics in the literature can or cannot be used for CTs for different studied applications.