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

Abstract: 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.

analysis of PDEsclassical analysis and ODEsdynamical systemsfunctional analysisnumerical analysis

Audience: researchers in the discipline

CRM CAMP (Computer-Assisted Mathematical Proofs) in Nonlinear Analysis

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