English

Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation

Dynamical Systems 2024-07-26 v2

Abstract

We present an algorithm for the rigorous integration of Delay Differential Equations (DDEs) of the form x(t)=f(x(tτ),x(t))x'(t)=f(x(t-\tau),x(t)). As an application, we give a computer assisted proof of the existence of two attracting periodic orbits (before and after the first period-doubling bifurcation) in the Mackey-Glass equation.

Keywords

Cite

@article{arxiv.1607.01080,
  title  = {Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation},
  author = {Robert Szczelina and Piotr Zgliczyński},
  journal= {arXiv preprint arXiv:1607.01080},
  year   = {2024}
}