life tasks. This line of research can go far to clarifying the mechanisms linking age-related changes in neural circuitry to change in cognitive functioning and performance. It is likely also to identify opportunities to intervene either at the neural or behavioral levels so as to maintain performance of life activities in the face of neural decline.
A number of mathematical techniques that can be used to characterize the structure and evolution of behavior over time are maturing to a point at which they may be of great benefit in the study of cognitive aging. Four of these are dynamical systems theory, hidden Markov models, connectionist models, and dynamic factor analysis.
Dynamical systems theory characterizes the properties of different patterns of stable behavior, as well as transitions among such patterns. In this approach, behavior is typically represented as a continuous trajectory in a state space, i.e., a space whose dimensions are the important variables needed to describe and predict behavior. Stable behavior is not modeled as simply a constant, but is viewed as resulting from the interaction of various abstract forces and perturbations to a behavioral system. These forces may push a system toward a point in the state space, toward a particular oscillation or limit cycle, or toward some more elaborate pattern of stable behavior. Some perturbations can be compensated for by the system; others result in a loss of stability, and perhaps achievement of a new stable state. This abstract, holistic style of description has been applied to various types of behavior ranging from physiological subsystems (e.g., heartbeat; breathing; see Glass and Mackey, 1988) to coordinated limb movements (e.g., Kelso, 1995). In the developmental domain, this approach has been used to describe changes in perceptual-motor performance in children. It has shown how particular changes in underlying behavioral dynamics combine with each other and with characteristics of the environment to produce stable behavioral patterns (Thelen and Smith, 1994).
A number of intriguing possibilities exist for applying this mathematical approach to older adults. For example, it might be applied to developmental declines in the ways it has been applied to developmental advances. It could clarify the implications for overall performance of declines in particular behavioral dynamics and identify specific types of remediation or environmental modification that could maintain performance despite such declines. Also, because dynamical systems theory characterizes the stability of behavior in terms of a process rather than simply approximating it as a constant, it allows the examination of varieties of stability that differ both qualitatively and quantitatively. Some patterns may be too stable (i.e., rigid) and inhibit adaptive changes in behavior; other patterns may be insufficiently stable and result in