Dynamical Cognitive Science makes available to the cognitive science community the analytical tools and techniques of dynamical systems science, adding the variables of change and time to the study of human cognition. The unifying theme is that human behavior is an "unfolding in time" whose study should be augmented by the application of time-sensitive tools from disciplines such as physics, mathematics, and economics, where change over time is of central importance. The book provides a fast-paced, comprehensive introduction to the application of dynamical systems science to the cognitive sciences. Topics include linear and nonlinear time series analysis, chaos theory, complexity theory, relaxation oscillators, and metatheoretical issues of modeling and theory building. Tools and techniques are discussed in the context of their application to basic cognitive science problems, including perception, memory, psychophysics, judgment and decision making, and consciousness. The final chapter summarizes the contemporary study of consciousness and suggests how dynamical approaches to cognitive science can help to advance our understanding of this central concept.
Chapter 1 Magic, Ritual, and Dynamics
1.1 Magic and Ritual
1.2 Dynamics
Chapter 2 Sequence
2.1 The Serial Universe
2.2 The Problem of Serial Order in Behavior
2.3 Markovian Analysis of Behavior
Chapter 3 Rhythms of Behavior
3.1 The Dance of Life
3.2 Music and Rhythm
3.3 Rhythms in the Brain
Chapter 4 Time
4.1 Space-Time
4.2 The Arrow of Time
4.3 Measuring Time
Chapter 5 Cognitive Processes and Time
5.1 Temporal Unfolding of Cognitive Behavior
5.2 Timing of Cognitive Behavior
5.3 Memory
Chapter 6 Systems and General Systems Theory
6.1 Systems
6.2 General Systems Theory
6.3 Dynamical Systems Theory
Chapter 7 Science and Theory
7.1 The Mandala of Science
7.2 Formal Theories
7.3 Principle of Complementarity
Chapter 8 Dynamical Versus Statistical Models
8.1 Theories, Models, and Data
8.2 Statistical Models
8.3 Dynamical Models
8.4 Why We Need Both Statistical and Dynamical Models
Chapter 9 Dynamical and Structural Models
9.1 Structural Models
9.2 Graph Theory
9.3 Interplay between Dynamical and Structural Models
Chapter 10 Deterministic Versus Stochastic
10.1 Deterministic Models vs. Dynamical Models
10.2 Stochastic Models
10.3 Do We Need Both?
Chapter 11 Linear Time Series Analysis
11.1 Time Series and Noise
11.2 ARIMA (p,d,q)
11.3 ARIMA Model of Time Estimation
11.4 Mixed Regression-ARIMA Model of Psychophysical Judgment
Chapter 12 Probability Theory and Stochastic
12.1 Dynamical Cognitive Science Models and Mathematics
12.2 Stochastic Processes: A Random Walk to Ruin
12.3 Critical Points in Stochastic Models
12.4 Ergodicity and the Markov Property
Chapter 13 Stochastic Models in Physics
13.1 The Master Equation
13.2 Quantum Physics
13.3 Complementarity Redux
Chapter 14 Noise
14.1 What Is Noise?
14.2 Probabilistic Description of Noise
14.3 Spectral Properties of Noise
Chapter 15 Colored Noise
15.1 The Ubiquity of Colored Noise
15.2 The Vicissitudes of the Exponent alpha
15.3 Colored Noise in Living Systems
Chapter 16 1/f Noise in Human Cognition
16.1 Music and Time Perception
16.2 Reaction Time
Chapter 17 1/f Noise in the Brain
17.1 Neural Activity
17.2 Magnetoencephalogram Recordings
17.3 Electroencephalogram and Event-Related Potential Recordings
Chapter 18 Models of 1/f Noise
18.1 The Simplest Case
18.2 Multiplicative Noise
18.3 Self-Organized Criticality
18.4 Center-Surround Neural Network
Chapter 19 Statistical Theory of 1/f Noise
19.1 What Must Be Explained
19.2 Queuing in a Wire
19.3 ARIMA (1,0,0)
19.4 Multifractals and Wild Self-Affinity
Chapter 20 Stochastic Resonance
20.1 What is Stochastic Resonance?
20.2 Stochastic Resonance in a Threshold Detector
Chapter 21 Stochastic Resonance and Perception
21.1 Detection of Weak Signals by Animals
21.2 Stochastic Resonance in Human Perception
Chapter 22 Stochastic Resonance in the Brain
22.1 Stochastic Resonance in Neurons
22.2 Neural Networks
Chapter 23 Chaos
23.1 Chaos Is Not What You Think It Is
23.2 What Chaos Really Is
23.3 Phase Space Drawings and Strange Attractors
Chapter 24 Chaos and Randomness
24.1 A Random Walk through the Logistic Difference Equation
24.2 Dimensionality of an Attractor
24.3 Chaos and Noise
Chapter 25 Nonlinear Time Series Analysis
25.1 State Space Reconstruction
25.2 Out-of-Sample Forecasting
25.3 Surrogate Data
Chapter 26 Chaos in Human Behavior?
26.1 Could Unexplained Variance Be Chaos?
26.2 Nonlinear Forecasting Analysis of Time Estimation
26.3 Nonlinear Analysis of Mental Illness
26.4 Memory and the Logistic Difference Equation
Chapter 27 Chaos in the Brain?
27.1 The Smell of Chaos
27.2 Dimensionality of the Electroencephalogram
27.3 Chaotic Event-Related Potentials?
Chapter 28 Perception of Sequence
28.1 The Gambler's Fallacy
28.2 Estimation of Short-Run Probabilities
28.3 Evolution of Contingency Perception
Chapter 29 Can People Behave Randomly?
29.1 No!
29.2 Sometimes
29.3 Sequential Dependencies and Extrasensory Perception
Chapter 30 Can People Behave Chaotically?
30.1 Yes!
30.2 Not Really
30.3 Heuristics and Chaos
Chapter 31 Relaxation Oscillators: A Foundation
31.1 A Brief Taxonomy of Oscillators for Dynamical Modeling
31.2 The van der Pol Relaxation Oscillator
31.3 Noisy Oscillators in the Brain
Chapter 32 Evolution and Ecology of Cognition
32.1 Evolution of Cognition
32.2 Ecology of Cognition
Chapter 33 Dynamical Cognitive Neuroscience
33.1 Brain Imaging
33.2 Brain Dynamics
33.3 Hybrid Models
Chapter 34 Dynamical Computation
34.1 Numerical Methods
34.2 Neural Network Models
34.3 Exotic Computers
Chapter 35 Dynamical Consciousness
35.1 Consciousness
35.2 Unity of Science
Lawrence M. Ward is Professor of Psychology at the University of British Columbia.
