Early-warning indicators in the dynamic regime
Abstract
Early-warning indicators (increase of autocorrelation and variance) are commonly applied to time series data to try and detect tipping points of real-world systems. The theory behind these indicators originates from approximating the fluctuations around an equilibrium observed in time series data by a linear stationary (Ornstein-Uhlenbeck) process. Then for the approach of a bifurcation-type tipping point the formulas for the autocorrelation and variance of an Ornstein-Uhlenbeck process detect the phenomenon `critical slowing down'. The assumption of stationarity and linearity introduces two sources of error in the early-warning indicators. We investigate the difference between the theoretical and observed values for the early-warning indicators for the saddle-node normal form bifurcation with linear drift.
Keywords
Cite
@article{arxiv.1609.07271,
title = {Early-warning indicators in the dynamic regime},
author = {Paul Ritchie and Jan Sieber},
journal= {arXiv preprint arXiv:1609.07271},
year = {2016}
}