Families of periodic delay orbits
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 de...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
24 July 2024
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| In: |
Journal of differential equations
Year: 2024, Volume: 410, Pages: 1-23 |
| ISSN: | 1090-2732 |
| DOI: | 10.1016/j.jde.2024.07.021 |
| Online Access: | Verlag, kostenfrei, Volltext: https://doi.org/10.1016/j.jde.2024.07.021 Verlag, kostenfrei, Volltext: https://www.sciencedirect.com/science/article/pii/S0022039624004431 
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| Author Notes: | Peter Albers, Philipp Aretz, Irene Seifert |
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| 520 | |a 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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