CRM CAMP in Nonlinear Analysis

Preuves mathématiques assistées par ordinateur en analyse non linéaire

13 octobre 2020 de 10 h 00 à 11 h 00 (heure de Montréal/HNE) Réunion Zoom

Rigorous computation of periodic solutions and Floquet multipliers in delay differential equations with time-forced discontinuities

Séminaire par Kevin Church (McGill University, Canada)

I will present some recent work on rigorous computation of periodic solutions for delay differential equations with impulse effects. At fixed moments in time, the state of such a system is reset and solutions become discontinuous. Once a periodic solution of such a system has been computed, its Floquet spectrum can be rigorously computed by discretization of the monodromy operator (period map) and some technical error estimates. As an application, we compute a branch of periodic solutions in the pulse-harvested Hutchinson equation and examine its stability.