Families of periodic delay orbits

2023/04/15 by Peter Albers, Albers, Peter, Philipp Aretz +3
Computer Science · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2304.07550

openalex publication_date 2023/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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