Detecting tipping points in systems with spatial structure: applications to the asthmatic lung

Tipping points (or critical transitions) are abrupt changes in time-varying systems; typical examples are ice sheet or ecosystem collapse. Early warning signals are potentially valuable leading indicators of these transitions. While the theory of tipping points and early warning signals is reasonably well-developed for temporal systems, in systems with spatial structure it may be more valuable to consider spatially-informed early warning signals which take advantage of the spatial structure. This talk will discuss ongoing efforts to develop the theory of spatio-temporal early warning signals, and the particular application of this theory to changes in the lung in asthma.