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

7 December 2022
Start time 
10:30 am
PovoZero - Via Sommarive 14, Povo (Trento)
Seminar Room -1
Department of Mathematics
Target audience: 
University community
Contact person: 
Prof. Andrea Pugliese
Contact details: 
Staff Dipartimento di Matematica
Mattia Sensi (INRIA - Antibes)


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.