# Applied Mathematics Colloquium – Naoki Masuda, University at Buffalo

## October 16 @ 4:00 pm - 5:00 pm

**Title:** Early warning signals for dynamics on networks

**Speaker:** Naoki Masuda, Department of Mathematics and Institute for Artificial Intelligence and Data Science, State University of New York at Buffalo

**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 (EWSs) that anticipate tipping events before they occur have been developed. In fact, complex dynamical systems of our interest often form a heterogeneous network, and how to construct EWSs in this situation is not straightforward. Therefore, we first present heuristic methods to select sentinel nodes in a given network to construct good EWSs. 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 EWS affects its performance. The method performs well in particular when different nodes receive different amounts of dynamical noise and stress.