Georgia Institute of Technology College of Sciences

Two of the aims in using mathematics in real world applications are: (1) understanding the mechanisms responsible for different effects and phenomena, and (2) predicting the future state of the system under study. Dynamical systems provides a perspective and a lens for addressing these two questions. The system under study is formulated as an evolving set of state variables and the set of trajectories with different initializations are viewed geometrically.

I will use this lens to look at a pressing problem in climate science: how a climate subsystem might abruptly “tip” from its current state into a completely different state. This is a problem that requires dynamical systems to understand, and I will show how we can decode different ways in which the tipping might happen.

Dynamical systems models tend to be simplified; extraneous forces are ignored to produce models which attempt to capture the key mechanisms. The inclusion of data from observations is a way to connect these models with reality and I will discuss the area of data assimilation that achieves a balance between data and physical models in a systematic way.