CRM CAMP in Nonlinear Analysis

Computer-Assisted Mathematical Proofs in Nonlinear Analysis

October 13, 2020 from 10:00 to 11:00 (Montreal/EST time) Zoom meeting

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

Seminar presented by 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.