Multiple Timescale Dynamics & Geometric Singular Perturbation Theory Beyond the Standard Form

Date: Thursday 6th March 2025

Abstract

Many physical and biological systems consist of processes that evolve on disparate timescales, and the observed dynamics in such systems reflect these multi-scale features as well. Mathematical models of such multi-scale dynamical systems are considered singular perturbation problems, and my talk will be concerned with the geometric approach known as Geometric Singular Perturbation Theory (GSPT) but with a twist — focusing on a coordinate-independent setup. I will motivate the need for such a theory "beyond the standard form" by looking into neural/electronic oscillator models that show relaxation-type behaviour with an inherent non-uniform scale splitting. I will then introduce a general mathematical framework for this GSPT beyond the standard form to uncover the underlying multi-scale dynamical features.