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arXiv · 2304.07550

Families of periodic delay orbits

Peter Albers·Philipp Aretz·Irene Seifert
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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.

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Peter Albers, Philipp Aretz, Irene Seifert. 2023-04-15. Families of periodic delay orbits. https://doi.org/10.1016/j.jde.2024.07.021

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