Detecting and distinguishing bifurcations from noisy time series data

Thomas Bury

Numerous systems in the natural sciences have the capacity to undergo an abrupt change in their dynamical behaviour as a threshold is crossed. Prominent examples include the collapse of fisheries, algal blooms and paleoclimatic transitions. Mathematical models reveal such transitions as the result of crossing a bifurcation and help to elucidate the underlying mechanisms. However, the number of unknowns is often large, making it difficult to infer where the bifurcation occurs in the real system.
In this talk, we will look at methods for detecting bifurcations using data-driven approaches. These methods exploit generic dynamical phenomena that occur prior to bifurcations, such as critical slowing down, in order to infer their approach. We will show how the power spectrum of noisy time series data provides information on the type of bifurcation and validate this approach with empirical predator-prey experiment that undergoes a Hopf bifurcation. Finally, we will explore deep learning methods for detection of bifurcations and make comparison to the more traditional statistical methods in their ability to detect bifurcations.