Abstract:
Rhythmic neural activity underlies many repetitive behaviors such
as walking, chewing, and breathing. Models for the generation of such
activity can be dynamically rich and analyzing such models has led to new
insights about multiple-time-scale dynamics. I will illustrate this point
by discussing dynamics of model respiratory neurons. In particular, I will
introduce the phenomenon of canards in the context of some neural models,
as well as their dynamic implications. I will then present new results
relating to canards, including recently discovered torus canards, in the
study of coupled respiratory neurons. If time permits, I may also discuss
ideas about three-time-scale dynamics that also arise in respiratory neuron
models.