Families of periodic delay orbits

• Verfasst von: Albers, Peter [VerfasserIn]
• Verfasst von: Aretz, Philipp [VerfasserIn]
• Verfasst von: Seifert, Irene [VerfasserIn]
• Titel: Families of periodic delay orbits
• Verf.angabe: Peter Albers, Philipp Aretz, Irene Seifert
• E-Jahr: 2024
• Jahr: 24 July 2024
• Umfang: 23 S.
• Illustrationen: Illustrationen
• Fussnoten: Gesehen am 15.11.2024
• Titel Quelle: Enthalten in: Journal of differential equations
• Ort Quelle: Orlando, Fla. : Elsevier, 1965
• Jahr Quelle: 2024
• Band/Heft Quelle: 410(2024), Artikel-ID 228-250, Seite 1-23
• ISSN Quelle: 1090-2732
• DOI: doi:10.1016/j.jde.2024.07.021
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1908765097

Abstract

We construct and analyze families of periodic delay orbits for a class of delay differential equations in two dimensions depending on two real-valued functions. These families are parametrized by the delay parameter. It is possible to represent the dependency of these periodic delay orbits on the delay parameter by a curve in the plane, without loss of information. It turns out that the singularities of these curves necessarily are cusps in the non-degenerate case. After discussing degenerate situations in general, we explain how to glue different families of periodic delay orbits at degeneracies in the delay parameter.