Geometric methods for slow-fast dynamical systems: theory and applications

This mini-course provides an opportunity to gain experience with the dynamical systems approach to singularly perturbed ODEs so-called slow-fast systems. Multiple timescales are ubiquitous in models of real-world phenomena. For instance, many important biological processes evolve on different time scales and therefore consist of slow and fast components, think of neural and cardiac rhythms.

Differential equations involving variables evolving on widely different time scales yield rich and notoriously hard mathematical questions. The mini-course will present geometric techniques to study singularly perturbed ODEs, i.e., the main concepts from so-called geometric singular perturbation theory (part I) and geometric desingularizion based on the blow-up method (part II). Non-trivial applications arising in cell biology, biochemistry, and neuroscience will be discussed (part III).

Take-home message

• Biologist dissect frogs, we will dissect singular perturbation problems
• Lots of things to discover - even in fairly simple problems!

Date and time info
Monday 10.15 - 11.45

Keywords
slow-fast dynamics, geometric singular perturbation theory, blow-up method, relaxation oscillations, canards, biological oscillatory phenomena, mathematical modelling

Prerequisites
basic ODE's

Audience
MSc students, PhD students

Language
English