Christian Kühn, Technische Universität München

A Tour through Multiple Time Scale Systems

In this talk, I am going to start with an introduction to the theory and applications of multiple time scale dynamical systems. These systems appear in a wide variety of contexts in the natural sciences and engineering whenever coupled processes on different scales occur. The mathematical analysis for deterministic fast-slow ordinary differential equations is, by now, quite well-developed and I shall introduce the main concepts of slow manifold, asymptotics, geometric desingularization, and exchange lemma. In the second part of the talk, I am going to explain several recent extensions to stochastic fast-slow systems such as stochastic bifurcations for SODEs and patterns for SPDEs. I am going to conclude with a brief outlook on current frontiers in the area.