Multiple Time-Scale Dynamics: Bifurcations and Mixed-Mode Oscillations

First, we will give an introduction to fast-slow systems. The geometric viewpoint of the theory will be emphasized. Then we discuss the three-dimensional FitzHugh-Nagumo (FHN) equation and its bifurcations. The singular limit bifurcation diagram of the FHN equation will be derived. We shall also look at mixed-mode oscillations (MMOs) in the FHN equation and outline the role of MMOs in chemistry, neuroscience and physics in a more general context.