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. 
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