We assess the proximity of a system to a bifurcation point using a degenerate fingerprinting method that estimates the declining decay rate of fluctuations in a time series as an indicator of approaching a critical state. The method is modified by employing Detrended Fluctuation Analysis (DFA) which improves the estimation of short-term decay, especially in climate records which generally possess power-law correlations. When the modified method is applied to GENIE-1 model output that simulates collapse of the Atlantic thermohaline circulation, the bifurcation point is correctly anticipated. In Greenland ice core paleotemperature data, for which the conventional degenerate fingerprinting is not applicable due to the short length of the series, the modified method detects the transition from glacial to interglacial conditions. The technique could in principle be used to anticipate future bifurcations in the climate system, but this will require high-resolution time series of the relevant data.
Reference
A modified method for detecting incipient bifurcations in a dynamical system
V. N. Livina, T. M. Lenton
GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L03712, doi:10.1029/2006GL028672, 2007
There is DFA code in Julia, but the repo doesn't look super trustworthy: https://github.com/johncwok/DetrendedFluctuationAnalysis.jl (hasn't been updated in 4 years). I know the author, and I can ask if the repo is LGTM still. I've used used DFA extensively in the past in the context of music timeseries analysis, I'm sure this one will be easy to tackle.
Indicator summary
Reference
A modified method for detecting incipient bifurcations in a dynamical system V. N. Livina, T. M. Lenton
GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L03712, doi:10.1029/2006GL028672, 2007
https://doi.org/10.1029/2006GL028672
Implementation plan
There is DFA code in Julia, but the repo doesn't look super trustworthy: https://github.com/johncwok/DetrendedFluctuationAnalysis.jl (hasn't been updated in 4 years). I know the author, and I can ask if the repo is LGTM still. I've used used DFA extensively in the past in the context of music timeseries analysis, I'm sure this one will be easy to tackle.