[PDF] Algorithm for Rigorous Integration of Delay Differential Equations and the Computer-Assisted Proof of Periodic Orbits in the Mackey–Glass Equation | Semantic Scholar

Algorithm for Rigorous Integration of Delay Differential Equations and the Computer-Assisted Proof of Periodic Orbits in the Mackey–Glass Equation

@article{Szczelina2018AlgorithmFR,
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 P. Zgliczynski},
journal={Foundations of Computational Mathematics},
year={2018},
volume={18},
pages={1299-1332}
}

We present an algorithm for the rigorous integration of delay differential equations (DDEs) of the form $$x'(t)=f(x(t-\tau ),x(t))$$x′(t)=f(x(t-τ),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.