Predictability of Complex Dynamical Systems

This is a book book for researchers and practitioners interested in modeling, prediction and forecasting of natural systems based on nonlinear dynamics. It is a practical guide to data analysis and to the development of algorithms, especially for complex systems. Topics such as the characterization of nonlinear correlations in data as dynamical systems, reconstruction of dynamical models from data, nonlinear noise reduction and the limits of predicatability are discussed. The chapters are written by leading experts and consider practical problems such as signal and time series analysis, biomedical data analysis, financial analysis, stochastic modeling, human evolution, and political modeling. The book includes new methods for nonlinear filtering of complex signals, new algorithms for signal classification, and the concept of the "Global Brain".

1 Introduction.- 2 Time Series Analysis: The Search for Determinism.- Method to Discriminate Against Determinism in Time Series Data.- Observing and Predicting Chaotic Signals: Is 2% Noise Too Much?.- A Discriminant Procedure for the Solution of Inverse Problems for Non-stationary Systems.- Classifying Complex, Deterministic Signals.- 3 Dynamical Modeling and Forecasting Algorithms.- Strategy and Algorithms of Dynamical Forecasting.- Parsimony in Dynamical Modeling.- The Bifurcation Paradox: The Final State Is Predictable If the Transition Is Fast Enough.- 4 Prediction of Biological Systems.- Models and Predictability of Biological Systems.- Limits of Predictability for Biospheric Processes.- 5 Analysis and Forecasting of Financial Data.- The Application of Wave Form Dictionaries to Stock Market Index Data.- 6 Socio-Political and Global Problems.- Messy Futures and Global Brains.