Delayed loss of stability in multiple time scale models of natural phenomena

Abstract:

Numerous real-world phenomena exhibit mechanisms evolving on greatly different time scales. In this talk, we focus on delayed loss of stability in two classes of mathematical models, stemming from mathematical epidemiology and neuroscience, specifically synaptic transmission, respectively. We comment on the possible asymptotic, and in one case transient, behaviour of such systems. Moreover, we present a recently submitted result on the generalization of the so-called entry-exit function. This function describes the slow passage of orbits close to the critical manifold of slow-fast systems exhibiting loss of stability. In our preprint, we aim at relaxing the separation of eigenvalues hypothesis, starting from a class of 2-fast/1-slow systems of ODEs.