CSDC Seminar: Distribution moment methods for characterising critical transitions and early warning signals

Critical transitions are abrupt changes 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 caused by underlying bifurcations (so-called B-tipping), which are associated with qualitative changes in the underlying system energy landscape. Building on the existing fast-slow framework we show how distribution moment approximation methods allows us to relax the usual assumptions of stationarity and reflecting boundary conditions, as well as enabling transitional solutions and application to higher dimensional systems, thus allowing a more complete characterisation of early warning signals.