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Holger Kantz, Thomas Schreiber.
Nonlinear Time Series Analysis.
CUP. 1997

Deterministic chaos offers a striking explanation for irregular behaviour and anomalies in systems which do not seem to be inherently stochastic. The most direct link between chaos theory and the real world is the analysis of time series from real systems in terms of nonlinear dynamics. This book provides experimentalists with methods for processing, enhancing, and analysing measured signals using these methods; and for theorists it also demonstrates the practical applicability of mathematical results.

The framework of deterministic chaos constitutes a new approach to the analysis of irregular time series. Traditionally, nonperiodic signals have been modelled by linear stochastic processes. But even very simple chaotic dynamical systems can exhibit strongly irregular time evolution without random inputs. Chaos theory offers completely new concepts and algorithms for time series analysis which can lead to a thorough understanding of the signals. The book introduces a broad choice of such concepts and methods, including phase space embeddings, nonlinear prediction and noise reduction, Lyapunov exponents, dimensions and entropies, as well as statistical tests for nonlinearity. Related topics such as chaos control, wavelet analysis and pattern dynamics are also discussed. Applications range from high-quality, strictly deterministic laboratory data to short, noisy sequences which typically occur in medicine, biology, geophysics, and the social sciences. All the material is discussed and illustrated using real experimental data.

This book will be of value to any graduate student or researcher who needs to be able to analyse time series data, especially in the fields of physics, chemistry, biology, geophysics, medicine, economics, and the social sciences.

Sergio Albeverio, Volker Jentsch, Holger Kantz.
Extreme Events in Nature and Society.
Springer. 2006

Significant, and usually unwelcome, surprises, such as floods, financial crisis, epileptic seizures, or material rupture, are the topics of Extreme Events in Nature and Society. The book, authored by foremost experts in these fields, reveals unifying and distinguishing features of extreme events, including problems of understanding and modelling their origin, spatial and temporal extension, and potential impact. The chapters converge towards the difficult problem of anticipation: forecasting the event and proposing measures to moderate or prevent it. Extreme Events in Nature and Society will interest not only specialists, but also the general reader eager to learn how the multifaceted field of extreme events can be viewed as a coherent whole.