Mathematical Biology Seminar Abstract
Nov 3, 2017
Jonathan Rubin
University of Pittsburgh, Department of Mathematics
3:00 pm in MSB 318 (Math Colloquium)

Dynamic transitions in coupled model bursting neurons

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.