Geometric singular perturbation theory beyond the standard form
Peter Szmolyan (March 23, 2011)
Please install the Flash Plugin
In many biological models multiple time scale dynamics occurs due to the presence of variables and parameters of very different orders of magnitudes. Situations with a clear "global" separation into fast and slow variables governed by singularly perturbed ordinary differential equations in standard form have been investigated in great detail.
For multi-scale problems depending on several parameters it can already be a nontrivial task to identify meaningful scalings. Typically these scalings and the corresponding asymptotic regimes are valid only in certain regions in phase-space or parameter-space. Another issue is how to match these asymptotic regimes to understand the global dynamics. In this talk I will show in the context of examples from enzyme kinetics that geometric methods based on the blow-up method provide a systematic approach to problems of this type.
(Joint work with Ilona Kosiuk, MPI MIS Leipzig)