Dynamical Systems Analysis

The Oxford Dictionary defines behavior as, “The way in which one acts or conducts oneself, especially toward others”  From this perspective, behavior involves directed action.  A psychologist studying human behavior is likely to not only be interested in the actions themselves, but also in the means and methods by which the actions are directed.   

In classical physics, action involves movement: change in position with respect to time.  In a more general sense, action can be defined as, “The fact or process of doing something, typically to achieve an aim.” Distilling this together with the definition of behavior, we may conclude that behavior is a goal-directed process.  All three of these words are heavily layered with meaning.  Suppose that a goal implies some ideal state and directed implies an ability to perceive the difference between the current state and the ideal state as well as an intention towards the ideal.  Finally, let us use the word process to imply that behavior unfolds over time.  This view of the study of behavior thus involves goals, perception, intention, and the process by which perception and intention directs the organism in relation to goals. While these statements may seem self-evident, they lead directly to why psychologists should be interested in dynamical systems analysis.  

The study of dynamical systems is the study of action.  Its origins are in the study of movement over time for which the tools of differential calculus were developed. Early physicists wished to understand the processes by which observed actions were directed. Not satisfied with simply recording that an apple tends to fall toward the ground, these “natural philosophers” wished to understand the process by which the apple seeks the goal of being closer to the Earth.  Similarly, the study of psychology is not simply the recording of behavior. We wish to build models that will help us identify and understand goals while learning about the nature of the processes by which perception and intention direct action with respect to those goals. In order to do so, we must measure human directed action in relation to the environment, and so we are faced with the same category of question asked by the early physicists: How does change in one variable relate to change in another variable?

A system becomes a dynamical system when the current state of the variables comprising the system is at least in part dependent on previous states of the system.  It is this dependence over time that defines the intrinsic dynamics of the system. If behavior involves directed action, and since both action and direction imply time-dependence, it is reasonable to conclude that a part of behavior involves time-dependence.  Thus, if a behaving organism is measured over time, a naturally connected set of variables exhibiting time-dependence will be the result: a dynamical system. According to this line of reasoning, whenever one measures behavior the resulting data comprises a dynamical system.  

Dynamical systems analysis includes tools for analyzing equilibria, the set of states toward (or away from) which a system tends.  We could consider equilibria as the goals for a dynamical system.  Dynamical systems models account for the process by which the system changes over time in relation to its equilibria.  To say this in psychological terms, dynamical systems models attempt to account for the process by which perception and intention direct the organism in relation to goals. 

Ongoing methodological work by members of the Human Dynamics Laboratory involves developing new methods for the analysis of data from a dynamical systems perspective.  A number of methods for fitting differential equations models to data have been developed.  But many other methods have been proposed and are under development for understanding complex data resulting from measuring human dynamics.