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Forecasting a class of bifurcations: theory and experiment.

Abstract

Forecasting bifurcations before they occur is a significant challenge and an important need in several fields. Existing approaches detect bifurcations before they occur by exploiting the critical slowing down phenomenon. However, the perturbations used in those approaches are limited to being very small and this represents a significant drawback. Large levels of perturbation have not been used mainly because of a lack of an adequate formulation that is robust to experimental noise. This paper provides such a formulation, and discusses how this approach to forecasting bifurcations is more accurate, especially when the dynamics are far from the bifurcation. Both numerical and experimental results are presented to demonstrate the technique and highlight its advantages over other prediction methods.

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