Complexity/Dynamical Systems Annotated Bibliography in Progress

15 December 2000 Version

With thanks to Joe McGrath and to the members of the Fall 2000 Complexity seminar at the University of Oregon, who contributed some of the titles and commentary. To add to the list, e-mail Holly Arrow at

Abraham, F. D., Abraham, R. H., & Shaw, C. S. (1990). A visual introduction to dynamical systems theory for psychology. Santa Cruz, CA: Aerial Press.

First part presents basic concepts of mathematical dynamics with pictures of phase portraits, buckling columns, etc. Second part gives examples of concepts applied to psychological phenomena -- family conflict, approach-avoidance, and neurological systems.

Arrow, Holly, & Crosson, Scott B. (2000, under revision) Musical chairs: Membership choice and change in self-organized groups.

Looks at group size as an evolving global variable in repeated sessions of self-organized group formation in which groups earn money that they divide amongst their membership. Analysis of transition probabilities over time indicates that the inclusion of extra, unnecessary group members is a broad, stable attractor when those left out earn no money, but this attractor disappears when people left out are given a small "welfare" payment. Illustrates a low-tech application of dynamic systems approaches to short time series.

Arrow, H., McGrath, J. E.,& Berdahl, J. L. (2000). Small groups as complex systems: Formation, coordination, development, and adaptation. Newbury Park, CA: Sage.

High concept, low tech theory piece integrating the ideas of dynamical systems and complexity theory into the study of small groups. Includes a discussion of methodological and philosophy of science issues but does not provide step-by-step how-to instructions.

Boisot, M., & Child, J. (1999). Organizations as adaptive systems in complex environments: The case of China. Organization Science, 10 (3), 237-252.

Conceptual article proposing a three dimensional model for understanding environmental complexity by looking at information. Two dimensions (codification and abstraction) measure cognitive complexity; the third (diffusion of information) measures relational complexity. B&C propose that organizations cope with environmental complexity by either absorbing or reducing it, and apply these ideas to Western firms operating in China, which has high low cognitive complexity, high relational complexity within societal units, and low relational complexity between societal units. Complexity ideas are fully integrated into organizational theory.

Briggs, J. & Peat, F. D. (1989). Turbulent mirror: An illustrated guide to chaos theory and the science of wholeness. New York: Harper & Row.

Very readable introduction to chaos theory, catastrophe theory, complexity, fractals, etc. Basic theme is how order leads to chaos and vice versa. Relates chaos to quantum theory and theoretical biology.

Bruderer, E. & Singh, J. V. (1996). Organizational evolution, learning, and selection: A genetic-algorithm-based model. Academy of Management Journal, 39 (5), 1322-1349.

Integrates three processes of organizational change in a single model: (1) organizational learning, analogous to change and adaptation within the lifetime of an organism (2) organizational variation as new organizational forms are created and (3) selection of organizations by the marketplace, with unfit forms going out of business. Simulation data from the genetic algorithm indicates that in a fixed fitness landscape with a single fitness "spike," organizational learning is effective in finding new and effective forms. In a hill-like landscape, inert organizational forms created by variation and selection are more effective.

Cambel, A. B. (1993). Applied Chaos Theory: A paradigm for Complexity. San Diego, CA: Academic Press.

Casti, J. L. (1994). Complexification: Explaining a paradoxical world through the science of surprise. New York: Harper Collins.

In each chapter Casti tackles a basic intuition we have (e.g., small changes should have small effects) and then elaborates the mathematics underlying phenomena that violate this intuition (e.g., catastrophe theory).

Cohen, Jack, & Stewart, Ian (1994). The collapse of chaos. New York & London: Penguin Books.

The first half reviews the findings of the accepted scientific data base, providing a quick review of chemistry, physics, biology, neuroscience, computer science, and social science through the lens of a reductionist approach. The second half returns to these topics taking a complex systems approach to quantum theory, evolution, chemical reactions, artificial life, consciousness and perception. Includes an annotated "further reading" list.

Crutchfield, J. P., Farmer, J. D., Packard, N. H., & Shaw, R. S. (1986) Chaos. Scientific American, 255 (December), 46-57.

These four physicists comprised the Dynamical Systems Collective at Santa Cruz, who encountered chaotic dynamics in the operation of an analog computer and in the time sequence of dripping faucets.

Eidelson, R. J. (1997). Complex adaptive systems in the behavioral and social sciences. Review of General Psychology, 1, 42-7.

Good introduction to the characteristics of complex systems such as multiple hierarchical levels, self-organization, positive feedback, bifurcations, cusp catastrophes, hysteresis, and coevolution, illustrated throughout with examples of how these ideas are being applied in psychology, sociology, economics, and political science.

Gilbert, Nigel, & Troitzsch, Klaus G. (1999). Simulation for the social scientist. Buckingham, England, & Philadelphia, PA: Open University Press.

Detailed review of different simulation techniques, including discussion of examples from social sciences, sample programs, list of useful web sites.

Gleick, J. (1987). Chaos: Making a new science. New York: Viking Penguin.

Organized as a series of stories about American contributors to chaos, with lots of human interest bibliographical details. Underlying theme is that chaos theory represents a Kuhnian "paradigm shift."

Gottman, J. M., Guralnick, M. J., Wilson, B., Swanson, C. C., & Murray, J. D. (1997). What should be the focus of emotion regulation in children? A nonlinear dynamic mathematical model of children's peer interaction in groups. Development and Psychopathology, 9, 421-452.

Presents a mathematical model of mutual influence between an individual and a group, with the group represented by whoever the focal individual is interacting with at a given point. The model is then tested using data from children's play groups, some of which included children with developmental delays or language disorders. Results are presented as step functions. Graphs and explanations often hard to follow, but paper presents an intriguing strategy for studying ordinal data on mutual influence, decomposed into influence of child on the group & group on the child.

Gregson, R.A.M., Pressing, J. L. (2000). Dynamic modeling. In J. T. Ccioppo, L. G. Tassinary, & G. G. Berntson (Eds.), Handbook of Psychophysiology, 2nd ed. (pp. 924-948). New York: Cambridge University Press.

A dense, thorough overview of how to model and analyze physiological data, including transition matrices, a variety of dimensionality measures, the use of embedding procedures, Lyapunov coefficients, and measures of entropy. G& P provide and explain equations, illustrate the techniques using EEG data, and address issues about measurement quality and the necessary number of data points to conduct various analyses. Includes a useful glossary of technical terms.

Kauffman , Stuart A. (1993). The Origins of Order: Self-organization and Selection in Evolution. Univ. of Pennsylvania and the Santa Fe Institute: Oxford University Press

A large dense book on self-organization, selection, and adaptation in developmental and evolutionary biology. Includes detailed exposition of rugged fitness landscapes, random graphs, hypercycles, and Kauffman's ideas about "order for free." Pretty tough sledding.

Kellert, S. H. (1993). In the wake of chaos. Chicago: The University of Chicago Press.

Excellent discussion of the implications of chaos theory for the philosophy of science. Also discusses the neglect of nonlinear phenomena from a sociopolitical point of view, drawing upon the insights of feminist scholars such as Keller, Harding, and Longino.

Kelso, J. A. S. (1995). Dynamic patterns: The self-organization of brain and behavior. Cambridge, MA: MIT Press.

Lange, R. (1999). A cusp catastrophe approach to the prediction of temporal patterns in the kill dates of individual serial murderers. Nonlinear Dynamics, Psychology, and Life Sciences, 3 (2), 143-159.

Demonstrates that a cusp catastrophe model fits the time series data of 11 murderers much better than linear models. The authors use Guastello's equations for the cusp model, and are able to classify the time series into three dynamic patterns, showing an attractor, a repellor, or a "pulse" pattern. Lots of visuals, many points of methodology not well explained. Shows that catastrophe approach can be employed even with quite short time series for limited number of subjects.

Lewin, Roger.(1992). Complexity: Life at the Edge of Chaos. New York: Macmillan

Good broad introduction to complexity by a science writer based on conversations with dozens of British and American scientists including James Lovelock, Brian Goodwin, John Maynard Smith, Steven Jay Gould, Edward O. Wilson, Chris Langton.

Lewis, M. D. (2000). The promise of dynamic systems approaches for an integrated account of human development. Child Development, 71 (1), 35-43.

Presents developmental psychology as a fragmented field that might be united by focusing on self-organization as an general principle that can be applied to understanding change and novelty. Describes core concepts in dynamical systems thinking, such as far from equilibrium systems, abrupt phase transitions, and increasing complexity over time.

Lewis, Marc D., Lamey, Alex V., & Douglas, Lori. (1999). A new dynamic systems method for the analysis of early socioemotional development. Developmental Science 2 (4), 457-475.

Illustrates the construction of state space grids for ordinal data, the identification of fixed point attractors, and the measurement of basin strength and relaxation time for these attractors, using data on gaze angle and distress of infants during multiple sessions at 2 months and 6 months old. The method is used to look both at similarities within age groups and individual differences among the infants.

Marken, R. S. (1990). Purposeful Behavior: The Control Theory Approach. American Behavioral Scientist, 34, No. 1 [Special Issue].

Contains 15 articles dealing with aspects of control theory. The authors include Powers, Runkel, and others.

Newtson, Darren (1994). The perception and coupling of behavior waves. In R. R. Vallacher & A. Nowak (Eds.), Dynamical systems in social psychology (pp. 139-167). New York: Academic Press.

Looks at the perception of human action using change in joint angles, decomposing the resulting data stream using spectral analysis. Also reports work on the dynamic coupling of gestures and vocal intensity in interacting dyads. Some of the concepts and graphics are rather hard to follow, but the chapter is full of provocative ideas.

Nowak, Szamrej, & Latané (1990). From private attitude to public opinion: A dynamic theory of social impact. Psychological Review, 97, 362-376.

Computer simulation of attitude change based on dynamic social impact theory, using a cellular automata model.

Prigogine I. C. & Stengers, I. (1984). Order out of chaos: Man's new dialogue with nature. NY: Bantam Books.

Prigogine won the Nobel Prize in chemistry in 1977. Stengers is a philosopher, chemist, and historian of science. This beautifully written book contrasts the science of the 17th through 19th century, with its emphasis on stability, order, uniformity, and equilibrium, with the emerging 20th century view of the world that emphasizes fluctuation, turbulence, instability, and far from equilibrium systems.

Rosen, R. (1979) Sixth Annual Ludwig von Bertalanffy Memorial Lecture. Behavioral Science, 24 (4), 238-249.

Excellent article on general systems theory as it applies to biological systems, discusses some contrasts between that theory and earlier Newtonian ones.

Schwartz, J. (1999). Oh my Darwin! Lingua Franca (November), 14-21.

Journalistic piece discussing the intellectual conflicts between Steven Pinker and Steven Jay Gould, with additional discussion of the ideas of Bill Hamilton, Richard Dawkins, Richard Lewontin and E.O. Wilson, framed as a conflict between sociobiology/evolutionary psychology and punctuated equilibrium theory. The description of who is in what camp and who dislikes whom is clearer than the explanation of what, exactly, are the intellectual points of disagreement.

Sawada, D. & Caley, M. T. (1985) Dissipative structures: New metaphors for becoming in education. Educational Researcher 14 (3), 13-19.

They use Prigogine's ideas about dissipative structures -- self-organizing systems far from equilibrium -- as the central idea for how we should think about educational systems.

Vallacher, R. R., & Nowak, A. (1994). The chaos in social psychology. In R. R. Vallacher & A. Nowak (Eds.), Dynamical systems in social psychology (pp. 1-16). New York: Academic Press.

I like this article because it articulates my own dissatisfaction with the state of social psychology. Diagnoses the key problems of social psychology as fragmentation, conceptual incoherence, proliferation of multiple mini-theories to explain every conceivable phenomena, ill-defined topics, and the lack of integrating metatheories that allow us to make some sense out of this mess. Optimistic interpretations of this state of affairs are considered and rejected, and a dynamical systems perspective is prescribed as an integrating meta-theory that will also turn the attention of social psychologists to a more serious treatment of time and complexity. Waldrop, M. M. (1992). Complexity: The emerging science at the edge of order and chaos.

Waldrop, M. M. (1992). Complexity: The emerging science at the edge of order and chaos. New York: Simon & Schuster.

Presents contributions to complexity theory, the new umbrella term for the intersection of chaos theory, neural nets, AI, developments in evolutionary biology, and so on. Main focus is on researchers connected to the Santa Fe Institute.