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GEOPHYSICAL RESEARCH LETTERS, VOL. 34, L03712, doi:10.1029/2006GL028672, 2007

A modified method for detecting incipient bifurcations in a dynamical system

V. N. Livina

School of Environmental Sciences, University of East Anglia, Norwich, UK


T. M. Lenton

School of Environmental Sciences, University of East Anglia, Norwich, UK


Abstract

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.

Received 6 November 2006; accepted 11 January 2007; published 15 February 2007.

Keywords: bifurcation; time series; DFA-propagator.

Index Terms: 1605 Global Change: Abrupt/rapid climate change (4901, 8408); 1622 Global Change: Earth system modeling (1225); 4425 Nonlinear Geophysics: Critical phenomena; 4901 Paleoceanography: Abrupt/rapid climate change (1605); 3270 Mathematical Geophysics: Time series analysis (1872, 4277, 4475).

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Citation: Livina, V. N., and T. M. Lenton (2007), A modified method for detecting incipient bifurcations in a dynamical system, Geophys. Res. Lett., 34, L03712, doi:10.1029/2006GL028672.