Abstract/Summary

Tipping events in dynamical systems have been studied across many applications, often by measuring changes in variance or autocorrelation in a one-dimensional time series. In this thesis, existing techniques in tipping point analysis are reviewed and a novel method, the Power Spectrum indicator, is introduced. The use of this novel technique is justified by a study of the scaling behaviour of the AR(1) process which is used to model the critical slowing down phenomenon in dynamical systems exhibiting tipping behaviour. Methods for detecting early warning signals of tipping events in multi-dimensional systems are also reviewed and expanded and these techniques are applied to a variety of dynamical systems. An analytical justification of the use of dimension-reduction by empirical orthogonal functions, in the context of early warning signals, is provided. One-dimensional techniques, including the novel Power Spectrum indicator are also extended to spatially separated time series over a 2D field. The challenge of predicting an approaching tropical cyclone by a tipping-point analysis of the sea-level pressure time series is used as the primary example, and an analytical model of a moving cyclone is also developed in order to test predictions. We show that the one-dimensional power spectrum indicator may be used following dimension-reduction, or over a 2D field. We also show the validity of our moving cyclone model with respect to tipping-point indicators.