Nonlinear Dynamics: Techniques and Applications in by Richard A. Heath

By Richard A. Heath

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Human habit wouldn't be fascinating to us if it remained a similar from one second to the following. furthermore, we have a tendency to be delicate to adjustments in people's habit, specially whilst such swap affects on our personal, and other's, habit. This booklet describes quite a few suggestions for investigating switch in habit. It employs traditional time sequence equipment, in addition to lately built method utilizing nonlinear dynamics, together with chaos, a time period that's not effortless to outline, nor to verify.

even if nonlinear equipment are getting used extra often in psychology, a entire insurance of equipment, thought and functions, with a specific concentrate on human habit, is required. among those covers, the reader is led via a variety of methods for linear and nonlinear time sequence research, together with a few novel approaches that let sophisticated temporal elements of human cognition to be detected. Analyses of response instances, heart-rate, psychomotor ability, determination making, and EEG are supplemented by way of a modern overview of contemporary dynamical learn in developmental psychology, psychopathology, and human cognitive strategies. A attention of nonlinear dynamics assists our realizing of deep concerns similar to: Why is our non permanent reminiscence ability constrained? Why do persistent problems, and in addition cognitive improvement, development via stage-like transitions? Why do humans make irrational judgements?

This booklet should be of specific curiosity to researchers, practitioners, and complex scholars in a number of components in psychology, fairly in human experimental and physiological psychology. facts analyses are played utilizing the most recent nonlinear dynamics machine applications. A complete WWW source of software program and supplementary details is supplied to help the reader's figuring out of the radical, and almost certainly progressive, tactics defined within the book.

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Publishers 10 Industrial Avenue Mahwah, NJ 07430 Cover design by Kathryn Houghtaling Lacey Nonlinear dynamics : Techniques and applications in psychology. Heath, Richard A. p. cm. Includes bibliographical references and index.  paper) Books published by Lawrence Erlbaum Associates are printed on acid-free paper, and their bindings are chosen for strength and durability. Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 For my mother, Esther and In memory of my father, Robert Charles Table of Contents Preface i 1 Dynamic Psychology: An Introduction to Time Series Analysis 1 Temporal Sequences of Behavioral Events 3 The Time Series Approach 5 Time-Series Analysis of the Anxiety Treatment Data 8 Higher Order Autoregression Models 14 The Effect of Averaging Autocorrelated Data across Subjects 15 Time-Series Analysis with Long Data Sequences 18 Time-Series Analysis Procedures using MINITAB 26 Summary 27 2 The Analysis of Nonstationary Time Series 29 An Adaptive Kalman Filter Model for Estimating Timeseries Parameters 30 Detecting a Change in Autoregression Parameters using Adaptive Kalman Filtering 37 An Application of the Change Detection Procedure 40 Application of Adaptive Kalman Filtering to the IKT Data 42 Summary 47 3 Linear and Nonlinear Systems in Psychological Research 48 The Linear Polynomial Model 49 Nonlinear System Identification: A Generalization of the Polynomial Model 51 A Simplified Nonlinear System Identification Technique Based on Cross-correlation 63 Nonlinear System Identification for Pulse Input and Output Sequences 65 A Smeared Nonlinear System Identification Analysis of a Two-channel Tracking Task 66 Nonlinear Systems Analysis of Differenced Input and Output Sequences 76 Psychological Applications of Nonlinear System Identification 79 Theoretical Interpretation of Linear and Nonlinear Transfer Functions 88 Summary 89 4 Nonlinear System Identification Using a Gradient-Descent Function Minimization Method 91 A Tensor Calculus Representation of the Nonlinear System Identification Equations 95 Fitting the Nonlinear Model to Multiple Times Series Data by Minimizing the Squared Error 101 An Evaluation of the Error Minimization Nonlinear System Identification Procedure Using Simulated Data 103 Prediction of Handwriting Dynamics 104 Analysis of the Two Channel Tracking Data Using the Gradient-Descent Minimization Algorithm 117 Some Artificial Examples of Second-Order Nonlinear Systems 126 Nonlinear System Identification Analysis of Noisy Coupled Logistic Data 128 Evaluating the Appropriate Number of Parameters in Nonlinear System Identification 131 Summary 133 5 Graphical Representation of Nonlinear Dynamics 134 Phase Diagrams 134 Phase Diagrams for the Coupled Logistic Model 139 The Effect of Changes in Initial Values of a Time Series on Its Qualitative Dynamics 141 Recurrence Plots and their Application in the Analysis of Qualitative Dynamics 145 Recurrence Plots for Empirical Data Sets 148 Recurrence Plots for IKT Data 152 Recurrence Plots for Handwriting Velocity Data 153 Recurrence Plots for Heart Interbeat Interval Data 155 Recurrence Plots for EEG Data 156 Recurrence Plots for Sequential RT Data 157 Poincaré Plots 162 Visualization of Data Obtained from Nonlinear Dynamical Systems 163 Summary 164 6 Quantitative Indices of Nonlinear Dynamics 165 Evidence for Low Dimensional Attractors 166 Computing the Correlation Dimension for Data Sets 171 Dimensionality Estimates for the Coupled Logistic System 174 Psychological Applications of the Correlation Dimension Measure 176 Lyapunov Exponents for a Time Series 180 Applications of Lyapunov Exponents in Psychology 190 Comparing the Dynamics of Two or More Time Series 192 Entropy 192 General Comments on Computing Nonlinear Indices 196 Pointwise Dimension Measures 197 Nonlinearity Tests Using Multivariate Time Series 198 The BDS Test for Nonlinearity 201 Alternative Techniques for Detecting Nonlinear Determinism in a Time Series 203 Summary 205 7 Noise Reduction Methods and Hypothesis Testing for Nonlinear Systems 207 The SVD Algorithm 207 Prediction Methods for Quantifying Nonlinear Dynamics 211 Surrogate Data Sets: Testing Statistical Hypotheses for Nonlinear Dynamics 216 Comparison of the Effects of Noise on Nonlinear Indices 220 Analysis of Example Data Sets from Psychology 222 Summary 233 8 Control of Chaos and Its Psychological Applications 234 Control of Chaos Using Unstable Orbits 235 Applying Control of Chaos to Experimental Data 238 A Nonlinear Neural Network Model of Human Cognition 241 A Modular Neural Network Model 248 Control of the Modular Neural Network 252 Nonlinear Dynamics of the Modular Neural Network 253 Application of Control of Chaos Ideas in Behavioral Science 258 Summary 259 9 Complexity Theory and Psychology 261 A Complex Information Processing System 262 Information Processing in a Randomly Connected Boolean Neural Network 264 Evidence for Complex Behavior in Random Boolean Neural Networks 267 Cognitive Phenomena and Complexity Theory 270 Optimal Information Processing and Complexity at the 'Edge-of-Chaos' 276 Edge-of-Chaos Behavior in an Associative Memory Model 277 Complexity Theory and the Future of Cognitive Modeling 287 Summary 288 10 Applications of Nonlinear Techniques in Psychology 290 Psychomotor Skill 290 Behavioral Time Series 292 Decision Making 294 Developmental Processes 297 Perceptual and Cognitive Processes 301 Applications to Physiological Recordings of Psychological Significance 302 Applications in the Social Sciences 311 Human Prediction of Event Sequences 312 Applications in Medical Psychology 319 Summary 324 Epilog 326 Glossary 329 References 335 Appendix 358 Author Index 362 Subject Index 370 Page i Preface Since the 1980s there has been considerable excitement about nonlinear systems and their signature behavior, chaos, in both scientific and lay circles.

Anderson & Darling, 1952) is used, which assumes, under the null hypothesis, that the distribution is normal. 421. 309. 05, the null hypothesis is not rejected and so the conclusion is that the residuals are normally distributed. 5.  The nonsignificant Anderson-Darling test indicates that the residuals are normally distributed. From the table accompanying Fig.

I suspect that like many other social science fads, this too will pass until we have enough well-confirmed dynamic theory to make it useful" (p. 80). As is shown later, the principles of nonlinear dynamics are becoming more widespread in psychology. Productive applications have occurred in areas as diverse as psychophysics, psychomotor skill, developmental psychology, social organization, and psychotherapy. Perhaps the most important contribution of nonlinear dynamics as a methodological tool is its potential for unifying the diverse fields that constitute contemporary psychology.

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