Dependence of Early Warning Signals on Time Scale Separation

The  two-dimensional stochastic FitzHugh-Nagumo (sFHN) model is a popular idealization of the dynamics of the temperature of Greenland during the Last Glacial Period as measured in the ice-core record. Specifically, the sFHN model is used to simulate the Dansgaard-Oeschger (D-O) events, which are sharp changes in temperature and the most prominent example of abrupt climate change in the paleoclimate. The theory of early warning signals (EWS) has been applied to D-O events, specifically the critical slowdown corresponding to an increase in variance and autocorrelation of the climate signal right before approaching a bifurcation point where the system changes state. There is a debate in the literature on the state of these in the record of D-O events, with studies demonstrating both the absence and existence of these EWS. A desirable element of the sFHN is that it is a fast-slow system with multiple timescales. For a very large time scale separation, a quasi-steady-state in the slow variable causes the system to act as a bistable potential, where EWS do not precede an abrupt change in state. On the other hand, for a smaller time scale separation, the system displays clear EWS. The subject of this study is the case of intermediate time scale separation and its effects on EWS, along with an exploration of the physical implications of the results.