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 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.

Recommended citation: Albers, P., Aretz, P., and Seifert, I. (2024). "Families of periodic delay orbits." Journal of Differential Equations, 410, 228-250. https://doi.org/10.1016/j.jde.2024.07.021
Download Paper | Download Bibtex