On the stability of periodic orbits in delay equations with large delay

TL;DR

This paper establishes a precise criterion for the exponential stability of periodic solutions in delay differential equations with large delays, revealing that the Floquet spectrum near criticality is characterized by delay-independent curves.

Contribution

It introduces a necessary and sufficient stability criterion and characterizes the Floquet spectrum's asymptotic behavior for large delays.

Findings

Stability criterion for delay equations with large delay

Floquet spectrum near criticality described by delay-independent curves

Asymptotic continuous spectrum characterizes stability in large delay regime

Abstract

We prove a necessary and sufficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for sufficiently large delay the Floquet spectrum near criticality is characterized by a set of curves, which we call asymptotic continuous spectrum, that is independent on the delay.