Mathematics of Planet Earth

The term “tipping point” describes the moment when a system suddenly changes state, with no obvious trigger other than a slowly changing environment. Tipping points are difficult to predict and difficult to reverse. Examples range from capsizing boats to fishery collapse; they include financial market crashes, the poverty trap, melting polar ice caps, shifts in ecosystems, and mood changes. A mathematical framework for understanding how tipping points can arise as bifurcations has long been in place. Pressing sustainability questions are now placing the study of tipping points in the context of policy decision support, and driving efforts to explore the interaction between tipping and stochasticity in noisy systems. Can we extract, from measurements, indicators of resilience to tipping and early warning signals for proximity to a tipping point? We will introduce the bifurcation framework and discuss these questions in the context of applications to climate and biology.