Predicting catastrophic shifts (1506.03344v1)

Abstract: Catastrophic transitions, where a system shifts abruptly between alternate steady states, are a generic feature of many nonlinear systems. Recently these regime shift were suggested as the mechanism underlies many ecological catastrophes, such as desertification and coral reef collapses, which are considered as a prominent threat to sustainability and to the well-being of millions. Still, the methods proposed so far for the prediction of an imminent transition are quite ineffective, and some empirical and theoretical studies suggest that actual transitions may occur smoothly, without an abrupt shift. Here we present a new diagnostic tool, based on monitoring the dynamics of clusters through time. Our technique discriminates between systems with local positive feedback, where the transition is abrupt, and systems with negative density dependence, where the transition is smooth. Analyzing the spatial dynamics of these two generic scenarios, we show that changes in the critical cluster size provide a reliable early warning indicator for both transitions. Our method may allow for the prediction, and thus hopefully the prevention of such transitions, avoiding their destructive outcomes.