WIAS Preprint No. 1586, (2011)

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


  • Sieber, Jan
  • Wolfrum, Matthias
    ORCID: 0000-0002-4278-2675
  • Lichtner, Mark
  • Yanchuk, Serhiy

2010 Mathematics Subject Classification

  • 34K13 34K20 34K06


  • Periodic solutions, large delay, stability, asymptotic continuous spectrum, strongly unstable spectrum, Floquet multipliers




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.

Appeared in

  • Discrete Contin. Dyn. Syst., 33 (2013) pp. 3109--3134.

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