The behaviors of trajectories of nonlinear dynamical systems are notoriously hard to characterize and predict. Rather than characterizing dynamical behavior at the level of trajectories, we consider following the evolution of sets. There are often collections of sets that behave in a very predictable way, in spite of the fact that individual trajectories are entirely unpredictable. Such special...

Oscillating population data often exhibit cycle irregularities such as episodes of damped oscillation and abrupt changes of cycle phase. The prediction of such irregularities is of interest in applications ranging from food production to wildlife management. We use concepts from dynamical systems theory to present a model-based method for quantifying the risk of impending cycle irregularity.

Connectionist and dynamic systems approaches to development are similar in that they are both emergentist theories that take a very different perspective from more traditional symbolic systems. Moreover, they are both based on similar mathematical principles. Nevertheless, connectionism and dynamic systems differ in the approach they take to the study of development. We argue that differences b...

It is now widely accepted that qualitative and quantitative research traditions, rather than being seen as opposed or in competition with each other (Hammersley & Atkinson, 1995; Furlong, 2004) should be used, where appropriate, in some kind of combination (Bryman & Cramer, 1999; Moore et. al. 2003). How this combining is to be understood ontologically, and therefore epistemologically, however,...