ewstools: A Python package for early warning signals ofbifurcations in time series data
Thomas M. Bury
Abstract
Many systems in nature and society have the capacity to undergo critical transitions: sudden and profound changes in dynamics that are hard to reverse.Examples include the outbreak of disease, the collapse of an ecosystem, and the onset of a cardiac arrhythmia.From a mathematical perspective, these transitions may be understood as the crossing of a bifurcation (tipping point) in an appropriate dynamical system model.In 2009, Scheffer and colleagues proposed early warning signals (EWS) for bifurcations based on statistics of noisy fluctuations in time series data (Scheffer et al., 2009).This spurred massive interest in the subject, resulting in a multitude of different EWS for anticipating bifurcations (Clements & Ozgul, 2018).More recently, EWS from deep learning classifiers have outperformed conventional EWS on several model and empirical datasets, whilst also providing information on the type of bifurcation (Bury et al., 2021).Software packages for EWS can facilitate the development and testing of EWS, whilst also providing the scientific community with tools to rapidly apply EWS to their own data.ewstools is an accessible Python package for computing, analysing, and visualising EWS in time series data.The package provides: