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Critical transitions are abrupt transition in time-varying systems. They occur in many different scientific contexts, ranging from climate and ecology to physiology and electricity transmission, and can be driven by different underlying mathematical structures. Here we focus on those driven by underlying bifurcations (so-called B-tipping), which are associated with qualitative changes in the underlying system energy landscape. Building on Kuehn's fast-slow framework (Kuehn, 2011), we relax the assumptions of stationarity and reflecting boundary conditions by employing a distribution moment approach, which allows us to classify the utility of early warning signals (such as the variance) even when the timescales are not well separated, or the reflection boundary assumption is restrictive. This allows a more complete characterization of moment-based early warning signals.
Graham M. Donovan (Sat,) studied this question.