ABSTRACT
This chapter outlines how interesting and diagnostically useful properties of dynamic nonlinear systems can be exposed graphically. A single factor score should provide an informative index of nonlinear dynamics for short time series. A phase diagram provides a spatial snapshot of the evolving dynamics of a nonlinear system to assist in the understanding of how parameter changes affect the system's behavior. Persistent oscillatory states characterize a number of physiological systems under certain conditions. Gaze fixing fluctuates periodically while participants view ambiguous figures, such as the Maltese cross. The coupled logistic model is used to reveal the variety of qualitative dynamics that can be obtained from nonlinear models using phase diagrams as a diagnostic tool. A useful ancillary package from the same research group allows the fixed point behavior of known dynamical systems to be visualized. This knowledge provides a benchmark for determining the qualitative characteristics of time series generated by physiological and behavioral processes of relevance to psychology.
