Early Warning Signals for Dynamics on Networks

Abstract: Complex dynamical systems often show sudden major changes, or tipping points, as the system gradually changes. Examples include mass extinctions in an ecosystem, deforestation, and aggressive progression of a disease in a human body. Exploiting critical slowing down phenomena among other things, various early warning signals that anticipate tipping events before they occur have been developed. Complex dynamical systems for which we want to anticipate sudden regime shifts often form a heterogeneous network. First, we present heuristic methods to select sentinel nodes in a given network to construct informative early warning signals given that the network may be heterogeneous and show multistage transitions. We show that carefully chosen small subsets of nodes can anticipate transitions as well as or even better than using all the nodes. Second, we present a mathematically supported sentinel node selection method based on theory of stochastic differential equations. This method crucially takes into account that uncertainty as well as the magnitude of the early warning signal affects its performance.