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

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

Keywords

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

URI

https://doi.org/10.34657/2917
https://oa.tib.eu/renate/handle/123456789/2592

Citation

Sieber, J., Wolfrum, M., Lichtner, M., & Yanchuk, S. (2011). On the stability of periodic orbits in delay equations with large delay (Vol. 1586). Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik.

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Mathematik

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