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Title: Tipping point analysis of dynamical Authors:  Valerie Livina - National Physical Laboratory (United Kingdom) [presenting]
Abstract: Tipping point analysis helps anticipate, detect and forecast tipping points in a dynamical system. The methodology combines monitoring memory in a time series with potential analysis that visualizes and extrapolates the system states. Early warning signal indicators are based on autocorrelation, power-law scaling exponent of detrended fluctuation analysis, and recently developed power-spectrum-based indicator. When indicators rise monotonically, this signals an upcoming transition or bifurcation. By combining several indicators, it is possible to distinguish different types of tipping, such as forced transitions and genuine bifurcations. The potential analysis detects a transition or bifurcation in a series at the time when it happens, which is illustrated in a colour plot mapping the potential dynamics of the system. Potential analysis is also used in forecasting time series by extrapolation of Chebyshev approximation coefficients of the kernel distribution, with reconstruction of correlations in the data. The methodology has been extensively tested on artificial data and on observed datasets, and proved to be applicable to trajectories of dynamical systems of arbitrary origin.