Predictability of Critical Transitions

Abstract

Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socio-economic changes and climate transitions between ice-ages and warm-ages. From bifurcation theory we can expect certain critical transitions to be preceded by a decreased recovery from external perturbations. The consequences of this critical slowing down have been observed as an increase in variance and autocorrelation prior to the transition. However especially in the presence of noise it is not clear, whether these changes in observation variables are statistically relevant such that they could be used as indicators for critical transitions. In this contribution we investigate the predictability of critical transitions in conceptual models. We study the quadratic integrate-and-fire model and the van der Pol model, under the influence of external noise. We focus especially on the statistical analysis of the success of predictions and the overall predictability of the system. The performance of different indicator variables turns out to be dependent on the specific model under study and the conditions of accessing it. Furthermore, we study the influence of the magnitude of transitions on the predictive performance.

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• Saddle avoidance of noise-induced transitions in multiscale systems
• Analysis and Predictability for Tipping Points with Leading-Order Nonlinear Terms
• Scaling Laws and Warning Signs for Bifurcations of SPDEs