Although its roots can be traced to the 19th century, progress in the study of nonlinear dynamical systems has taken off in the last 30 years. While pertinent source material exists, it is strewn about the literature in mathematics, physics, biology, economics, and psychology at varying levels of accessibility. A compendium research methods reflecting the expertise of major contributors to NDS psychology, Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data examines the techniques proven to be the most useful in the behavioral sciences.
The editors have brought together constructive work on new practical examples of methods and application built on nonlinear dynamics. They cover dynamics such as attractors, bifurcations, chaos, fractals, catastrophes, self-organization, and related issues in time series analysis, stationarity, modeling and hypothesis testing, probability, and experimental design. The analytic techniques discussed include several variants of the fractal dimension, several types of entropy, phase-space and state-space diagrams, recurrence analysis, spatial fractal analysis, oscillation functions, polynomial and Marquardt nonlinear regression, Markov chains, and symbolic dynamics.
The book outlines the analytic requirements faced by social scientists and how they differ from those of mathematicians and natural scientists. It includes chapters centered on theory and procedural explanations for running the analyses with pertinent examples and others that illustrate applications where a particular form of analysis is seen in the context of a research problem. This combination of approaches conveys theoretical and practical knowledge that helps you develop skill and expertise in framing hypotheses dynamically and building viable analytic models to test them.
Table of Contents
Introduction to Nonlinear Dynamical Systems Analysis, R.A.M. Gregson and S.J. Guastello
Principles of Time Series Analysis, R.A.M. Gregson
Frequency Distributions and Error Functions, S.J. Guastello
Phase Space Analysis and Unfolding, M. Shelhamer
Nonlinear Dynamical Analysis of Noisy Time Series, A. Heathcote and D. Elliott
The Effects of the Irregular Sample and Missing Data in Time Series Analysis, D.M. Kreindler and C.J. Lumsden
A Dynamical Analysis via the Extended-Return-Map, J.-S. Li, J. Krauth, and J.P. Huston
Adjusting Behavioral Methods When Applying Nonlinear Dynamical Measures to Stimulus Rates, B.B. Frey
Entropy, S.J. Guastello
Analysis of Recurrence: Overview and Application to Eye-Movement Behavior, D.J. Aks
Discontinuities and Catastrophes with Polynomial Regression, S.J. Guastello
Nonlinear Regression and Structural Equations, S.J. Guastello
Catastrophe Models with Nonlinear Regression, S.J. Guastello
Catastrophe Model for the Prospect-Utility Theory Question, T.A. Oliva and S.R. McDade
Measuring the Scaling Properties of Temporal and Spatial Patterns: From the Human Eye to the Foraging Albatross, M.S. Fairbanks and R.P. Taylor
Oscillators with Differential Equations, J. Butner and T.N. Story
Markov Chains for Identifying Nonlinear Dynamics, S.J. Merrill
Markov Chain Example: Transitions between Two Pictorial Attractors, R.A.M. Gregson
Identifying Ill-Behaved Nonlinear Processes without Metrics: Use of Symbolic Dynamics, R.A.M. Gregson
Information Hidden in Signals and Macromolecules I: Symbolic Time-Series Analysis, M.A. Jiménez-Montaño, R. Feistel, and O. Diez-Martínez
Orbital Decomposition: Identification of Dynamical Patterns in Categorical Data, S.J. Guastello
Orbital Decomposition for Multiple Time-Series Comparisons, D. Pincus, D.L. Ortega, and A.M. Metten
The Danger of Wishing for Chaos, P.E. McSharry
Methodological Issues in the Application of Monofractal Analyses in Psychological and Behavioral Research, D. Delignières, K. Torre, and L. Lemoine
Frontiers of Nonlinear Methods, R.A.M. Gregson
Stephen Gaustello is a professor of Psychology at Marquette University, in Milwaukee Wisconsin.
"By considering systems as nonlinear and by considering the ways in which this nonlinearity can be described, the book offers new ways for Ergonomists to reflect on the central focus of its endeavour, i.e. the ‘system’. As Ergonomics evolves into its twenty-first-century manifestation, it needs to develop and refine its concept of how systems operate. This book provides the foundation for that development and should be required reading for anyone who uses the word ‘system’ in their discussion of Ergonomics."
—Chris Baber, School of Electronic, Electrical and Systems, Engineering University of Birmingham, in Ergonomics, 2014