| Interesting dynamics (called canards) can arise in
multiple timescale systems in the transition from a stable equilibrium
state to a stable oscillation. Interesting dynamics (called bursting)
can also arise in multiple timescale systems exhibiting rapid jumps
between rest and oscillatory states. I will review each of these cases
separately, an d then, motivated by a model for neuronal dynamics that
help to drive respiration, I will discuss what happens when we bring
these two effects together and consider transitions between regimes
within bursting systems. In addition to reviewing well-known results
for an individual bursting neuron model, I will present recent results
on particularly interesting transitions that arise within coupled
bursting models. |