Hunting French Ducks in a Noisy Environment

In this talk I am going to present a study on the influence of noise on oscillations in multiple time scale systems. We start with a brief introduction to fast-slow dynamical systems. We introduce the normal form of a folded node singularity in three dimensions with two slow variables and one fast variable. In this context, we encounter canard (="duck") orbits that produce local oscillations. The influence of noise on this singularity will be explored. Our results are expected to form a main building block to understand mixed-mode oscillations that appear in many different applications.