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arXiv · 1607.01080

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

Robert Szczelina·Piotr Zgliczyński
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Abstract

We present an algorithm for the rigorous integration of Delay Differential Equations (DDEs) of the form $x'(t)=f(x(t-\tau),x(t))$. 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.

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Robert Szczelina, Piotr Zgliczyński. 2016-07-05. Algorithm for rigorous integration of Delay Differential Equations and the computer-assisted proof of periodic orbits in the Mackey-Glass equation. https://doi.org/10.1007/s10208-017-9369-5

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