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

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

Jan Sieber
, Matthias Wolfrum
, Mark Lichtner
, Serhiy Yanchuk

University of Exeter
Weierstrass Institute for Applied Analysis and Stochastics
Humboldt University of Berlin

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a necessary and suficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for suficiently 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.

Original language	English
Pages (from-to)	3109-3134
Number of pages	26
Journal	Discrete and Continuous Dynamical Systems- Series A
Volume	33
Issue number	7
DOIs	https://doi.org/10.3934/dcds.2013.33.3109
Publication status	Published - Jul 2013
Externally published	Yes

Keywords

Asymptotic continuous spectrum
Floquet multipliers
Large delay
Periodic solutions
Stability
Strongly unstable spectrum

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10.3934/dcds.2013.33.3109

Cite this

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title = "On the stability of periodic orbits in delay equations with large delay",

abstract = "We prove a necessary and suficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for suficiently 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.",

keywords = "Asymptotic continuous spectrum, Floquet multipliers, Large delay, Periodic solutions, Stability, Strongly unstable spectrum",

author = "Jan Sieber and Matthias Wolfrum and Mark Lichtner and Serhiy Yanchuk",

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month = jul,

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T1 - On the stability of periodic orbits in delay equations with large delay

AU - Sieber, Jan

AU - Wolfrum, Matthias

AU - Lichtner, Mark

AU - Yanchuk, Serhiy

PY - 2013/7

Y1 - 2013/7

N2 - We prove a necessary and suficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for suficiently 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.

AB - We prove a necessary and suficient criterion for the exponential stability of periodic solutions of delay differential equations with large delay. We show that for suficiently 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.

KW - Asymptotic continuous spectrum

KW - Floquet multipliers

KW - Large delay

KW - Periodic solutions

KW - Stability

KW - Strongly unstable spectrum

UR - https://www.scopus.com/pages/publications/84872108070

U2 - 10.3934/dcds.2013.33.3109

DO - 10.3934/dcds.2013.33.3109

M3 - Article

AN - SCOPUS:84872108070

SN - 1078-0947

VL - 33

SP - 3109

EP - 3134

JO - Discrete and Continuous Dynamical Systems- Series A

JF - Discrete and Continuous Dynamical Systems- Series A

IS - 7

ER -

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

Abstract

Keywords

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