It's a Catastrophe! Testing dynamics between competing cognitive states using mixture and hidden Markov models

Dual or multiple systems approaches are ubiquitous in cognitive science, with examples in memory, perception, categorization, cognitive development, and many other fields. Dynamical systems models with multiple stable states or modes of behavior are also increasingly used in explaining cognitive phenomena. Catastrophe theory provides a formal framework for studying the dynamics of switching between two qualitatively distinct modes of behavior. Here we present a parametric approach to testing specific predictions about the dynamics of such switches that follow from catastrophe theory. These so-called catastrophe flags are bimodality, divergence, and hysteresis. We show how these three flags can be tested using (constrained) mixture and hidden Markov models and provide an example of each using three different data sets.