ABSTRACT
Nonlinear dynamics is a capsule term referring to a variety of fields of research, including nonequilibrium thermodynamics (Nicolis & Prigogine, 1977), catastrophe theory (Thorn, 1975), synergism (Haken, 1983), soliton theory (Toda, 1989), artificial neural network modeling (Grossberg, 1982), and chaos theory (e.g., Ott, 1993). These fields of research have provided us with profound new insights in the self-organizing capabilities and emergent pattern formation of temporal and spatiotemporal processes. Many concepts and techniques of nonlinear dynamics have found their way to the social sciences and have led to novel ways of conceptualizing the temporal organization of behavior. Among the many innovative applications of nonlinear dynamics in psychology we can discern a number of dedicated attempts to construct explicit causal models of time- or age-dependent processes. Examples are the predator-prey model of human cerebral development of Thatcher (chapter 5, this volume), the neural network model relating cortical and cognitive development proposed by Been (chapter 8, this volume), the catastrophe model of stagewise cognitive development of Van der Maas and Molenaar (1992; Van der Maas, chapter 7, this volume), the nonlinear growth models of Van Geert (1991; chapter 6, this volume), and the model of phase transitions in human hand movements of Haken, Kelso, and Bunz (1985). In each of these applications a nonlinear dynamical model has been specified that can explain the self-organizing tendencies of a particular psychological or developmental process. In this chapter the focus is on the way in which these models can be fitted to real data. More specifically, a flexible statistical technique is described with which the nonlinear dynamical models concerned can be applied under a broad range of conditions.
