Chapter to appear in Data Analytic Techniques for Dynamical Systems,

Abstract

What is a dynamical system? In simple terms, it is a means to describe the temporal unfolding of a system. It is concerned with two fundamental concepts, change and time. For example, a psychological process, such as memory or cognitive development, unfolds by progressing through a series of discrete states that occurs over time. Every dynamical model has time as a variable, although it is often represented implicitly (Ward, 2002). In more formal terms, a simple dynamical model is a differential equation, such as the following simple linear one dx/dt=at. A somewhat more complex model involves feedback, dx/dt=ax-bx 2, which provides a mechanism by which the system can self organize. (In this latter example,-bx 2 is a negative term and will decrease the rate of change of x at an accelerating rate as x gets larger.) Mathematics is the language of dynamical systems, which is both a strength and a weakness for the psychological sciences. Although the study of dynamical systems has had a long and venerable history in the physical sciences (Abraham, Abraham, & Shaw, 1992), it has yet to have a major impact in the psychological sciences. This seems somewhat paradoxical given tha