
Jonathan Rubin 
University of Pittsburgh, Department of Mathematics 
3:00 pm in MSB 318 (Math Colloquium)


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 wellknown results for an individual bursting neuron model, I will present recent results on particularly interesting transitions that arise within coupled bursting models. 