A Note on Kernel Methods for Multiscale Systems with Critical Transitions

Drastic sudden large events in dynamical systems have become a key area of interest in a broad range of applications [2, 26]. From the perspective of modelling, a successful framework to capture many critical transitions has been to use systems with multiple time scales in combination with bifurcation theory [23]. The idea is that there are fast variables, which are driven slowly towards a bifurcation point, where the system can undergo a sudden jump for certain types of bifurcations. One aim in this context is to determine, whether there are early-warning signs for critical transitions, which can be computed from time series data before the actual event occurred. Groundbreaking work by Wiesenfeld in the 1980s [32] has already clearly shown that 1 precursors of bifurcations exist, and that they can be extracted from stochastic fluctuations based upon critical slowing down.