Near tipping points, a system becomes very sensitive to changes in parameters and boundary conditions and unexpected qualitative changes in its behavior may occur. Many examples of transition behavior exists in the geosciences, such as the transition from zonal to blocked atmosperic flows, the collapse of the Atlantic Meridional Overturning circulation and the extinction of ecosystems in the semi-arid climates.

In this course, we will first provide the necessary background from dynamical systems to understand the occurrence of these tipping points. Next, we discuss the computation of such points in general and then focus on a few prominent examples from the geosciences where the concepts are applied.