Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data

Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data



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.



Publication Date



CRC Press, Taylor & Francis Group


Boca Raton, FL


Psychiatry and Psychology


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


Nonlinear Dynamical Systems Analysis for the Behavioral Sciences Using Real Data