Self-organizing Dynamical Systems

Abstract

Human behavior, broadly conceived, unfolds in time. Human behavior is emergent: behavioral patterns arise from the way individual parts or processes are coordinated together. The patterns that emerge are more than, and different from, a mere superposition of the component parts. Nonlinearity rules: small changes can sometimes produce large effects and large changes no effect at all. Context matters. Interactions, nonlinearity, emergence and context, though omnipresent in the social and behavioral sciences, have proven remarkably resistant to understanding. New light may be shed on these problems by merging the theoretical concepts and methods of self-organization (the formation of pattern and pattern change in complex systems embedded in their environment) and the mathematical tools of (nonlinear) dynamical systems (equations of motion that specify the rules by which behavioral patterns—on any chosen level of description—stabilize and change. Self-organizing dynamics promises both a language for, and a strategy toward, understanding human behavior, both individual and group. A key problem is to identify the essential dynamical variables characterizing patterns so that the pattern dynamics, the rules governing behavior, may be found and their predictions pursued. Here, after a brief history, the main concepts and methods of self-organizing dynamical systems are introduced followed by a few elementary examples to illustrate the power and potential of the approach.