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

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.

postprint version

References in corpus (2)

• DelayAndPeriodicity
• Characteristic matrices for linear periodic delay differential equations

Cited by in corpus (8)

• Spatio-temporal phenomena in complex systems with time delays
• Chaos in time delay systems, an educational review
• Delay-induced patterns in a two-dimensional lattice of coupled oscillators
• Stochastic switching in delay-coupled oscillators
• Embedding the dynamics of a single delay system into a feed-forward ring
• Emergence and combinatorial accumulation of jittering regimes in spiking oscillators with delayed feedback
• Delay master stability of inertial oscillator networks
• Delayed feedback control of self-mobile cavity solitons in a wide-aperture laser with a saturable absorber