Early Warning Signals for Bifurcations Embedded in High Dimensions
arxiv(2024)
摘要
Recent work has highlighted the utility of methods for early warning signal
detection in dynamic systems approaching critical tipping thresholds. Often
these tipping points resemble local bifurcations, whose low dimensional
dynamics can play out on a manifold embedded in a much higher dimensional state
space. In many cases of practical relevance, the form of this embedding is
poorly understood or entirely unknown. This paper explores how measurement of
the critical phenomena that generically precede such bifurcations can be used
to make inferences about the properties of their embeddings, and, conversely,
how prior knowledge about the mechanism of bifurcation can robustify
predictions of an oncoming tipping event. These modes of analysis are first
demonstrated on a simple fluid flow system undergoing a Hopf bifurcation. The
same approach is then applied to data associated with the West African monsoon
shift, with results corroborated by existing models of the same system. This
example highlights the effectiveness of the methodology even when applied to
complex climate data, and demonstrates how a well-resolved spatial structure
associated with the onset of atmospheric instability can be inferred purely
from time series measurements.
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