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

Jan Sieber; Matthias Wolfrum; Mark Lichtner; Serhiy Yanchuk

doi:10.3934/dcds.2013.33.3109

Article Contents

2013, Volume 33, Issue 7: 3109-3134. Doi: 10.3934/dcds.2013.33.3109

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

1.
Harrison Building, North Park Road, CEMPS, University of Exeter, Exeter, EX4 4QF
2.
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, 10117 Berlin
3.
Institute of Mathematics, Humboldt University of Berlin, Rudower Chaussee 25, 12489, Berlin

Received: January 31, 2012

Revised: November 30, 2012

Published: June 2013

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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.

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Mathematics Subject Classification: 34K08, 34K13, 34K20, 37G15, 37L10.

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