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The anticipation of bifurcation-induced transitions in dynamical systems hasgained relevance in various fields of the natural, social, and economicsciences. When approaching a co-dimension 1 bifurcation, the feedbacks thatstabilise the initial state weaken and eventually vanish; a process referred toas critical slowing down (CSD). This motivates the use of variance and lag-1autocorrelation as indicators of CSD. Both indicators rely on linearising thesystem's restoring rate. Additionally, the use of variance is limited to time-and state-independent driving noise, strongly constraining the generality ofCSD. Here, we propose a data-driven approach based on deriving a Langevinequation to detect local stability changes and anticipate bifurcation-inducedtransitions in systems with generally time- and state-dependent noise. Ourapproach substantially generalizes the conditions underlying existing earlywarning indicators, which we showcase in different examples. Changes indeterministic dynamics can be clearly discriminated from changes in the drivingnoise. This reduces the risk of false and missed alarms of conventional CSDindicators significantly in settings with time-dependent or multiplicativenoise. In multi-dimensional systems, our method can greatly advance theunderstanding of the coupling between system components and can avoid risks ofmissing CSD due to dimension reduction, which existing approaches suffer from.

Anticipating critical transitions in multi-dimensional systems driven by time- and state-dependent noise